UNIVERSITÀ DEGLI STUDI DI CAGLIARI

Transcription

1 UNIVERSITÀ DEGLI STUDI DI CAGLIARI Scuola di Dottorato in Scienze e Tecnologie Fisiche XX Ciclo- ( 2004/2007 ) CORRELATING STRUCTURE AND MAGNETISM IN LA 0.7 SR 0.3 MNO 3 EPITAXIAL FILMS ON FERROELASTIC LAALO 3 SUBSTRATE Thesis by Carla Sanna Supervisor: Alessandra Geddo Lehmann

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3 CONTENTS INTRODUCTION... 1 CHAPTER AN OVERVIEW OF DOPED MANGANITES Energetics of Mn: Jahn-Teller effect Orbital ordering Charge ordering Magnetic interactions: superexchange and double exchange Ferromagnetic double- exchange Low vs wide bandwidth systems: prototypical phase diagrams Bulk properties of La 1-x Sr x MnO Orthorhombic and rhombohedral distortions of the perovskite structure in La 1-x Sr x MnO 3 phases...29 CHAPTER PROPERTIES OF EPITAXIAL THIN FILMS OF LA1-XSR XMNO Mismatch and relaxation degree in epitaxial films Strain effect on phase equilibria in La1-xSrxMnO3 x = ( 0 1 ) CHAPTER CRYSTALLOGRAPHY OF FERROELASTIC LAALO3: THEORY AND EXPERIMENTAL CONFIRMATION Optical microscopy on LaAlO3 substrates Polarized light microscopy (PLM) As received substrate Substrate after the deposition of LSMO 20 nm film Substrate after deposition of 9 nm film AFM on LAO substrate CHAPTER EXPERIMENTAL RESULTS AND DISCUSSION Results on relaxed films High resolution X-ray diffraction Magnetic properties Comparison with LSMO films on SrTiO Results and discussion on strained LSMO films High resolution x-ray diffraction I

4 4.2.2 HRTEM results Magnetic properties Discussion on strained films ZFC-FC magnetization curves Comparison with strained film of LSMO/STO The time evolution of the magnetization CHAPTER CONCLUSION AND FUTURE DEVELOPMENT APPENDIX A X-RAY DIFFRACTION A.1 Laue formulation of Bragg law A.2 Ewald sphere construction A.3 D8 Discover (BRUKER-AXS) High resolution diffractometer A.3.1 Göbel Mirror A.3.2 V-groove compressor monochromator A.3.3 Eulerian Cradle A.5 Epitaxial film description in reciprocal space and concept of relaxation line A.5.1 Concept of Truncation rod APPENDIX B EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION B.1 Optical Microscopy B.1.1 Optical birefringence B.2 Transmission electron microscopy B.2.1 Basics of Transmission electron microscopy B.2.1 Sample preparation for TEM cross section observation B.3 Magnetic measurements SQUID BIBLIOGRAPHY 136 ACKNOWLEDGMENTS 142 II

5 INDEX OF TABLES AND FIGURES CHAPTER 1 Figure 1.1-left panel: Unit cell of a simple cubic perovskite with A cation in green, the B-site in blue and the oxygen ion in red. Right panel: Perovskite structure peculiarity: corner sharing octahedra... 9 Table 1.1- Examples of Glazer notation for octahedra rotation and relative explanation Figure 1.2-Orthorhombic structure on the left and rhombohedral one on the right. Space group and Glazer system are shown together with the relation between the unit cell (dashed lines) and the ideal cubic phase Figure 1.3- The five 3d-orbitals of a transition metal in octahedral environment. The six ligands are shown as green balls Figure 1.4- Crystal field splitting of 3d orbitals. The orbital filling refers to a 3d 4 ion Figure 1.5- Tetragonal distortion from an ideal (all green atoms) to an elongated octahedron (white atoms along z), the elongation is δz Figure 1.6- Jahn Teller effect with tetragonal distortion. Left panel: elongation along z-axis, right panel: contraction along z-axis. The orbital filling corresponds to the case of high spin 3d 4 species Figure 1.7- C-type orbital ordering in LaMnO3 as a consequence of the cooperative Jahn-Teller effect Figure 1.8- Different antiferromagnetic phases for the simple cubic Mn lattice: A-type constituted by ferromagnetic planes antiferro coupled along c axis; C-type constituted by an antiferromagnetic coupling along x and y axis and a ferromagnetic coupling along z axis and G-type where the interaction are antiferromagnetic along all axes Figure 1.9- Schematic view of the DE mechanism, the hopping probability is proportional to the angle subtended by the direction the core-spin moment Figure 1.10-Phase diagram of the low bandwidth system Pr 1-x Ca x MnO 3 ; paramagnetic insulator (PI) phase and charge ordered insulator (COI) are present at high temperature. Moreover below the line of critical temperatures TN and TC canted, ferromagnetic, canted antiferromagnetic phases can be recognized (CI), (FI), (CAFI) and (AFI) Figure Phase diagram of the intermediate bandwidth compound La1-xCaxMnO3. Depending on the doping level several states: canted antiferromagnet (CAF), charge/orbital ordered phases (OO/CO), ferromagnetic insulator (FI), and antiferromagnetic (AF) III

6 Figure Phase diagram of the wide bandwidth system La1-xSrxMnO3. At low temperature the system experienced insulating antiferromagnetism (AFI), insulating ferromagnetism (FI) and metallic ferromagnetism (FM). At high temperature paramagnetic phases are stabilized, either insulating (PI) or metallic (PM) Figure Phase diagram of La1 -x Sr x MnO 3 as function of Sr concentration and temperature. Antiferromagnetic insulator (AFI) is realized for lower level of Sr doping and low temperature. Ferromagnetic metallic (FM) phase can be obtained increasing the doping level, while at high temperature paramagnetic phase are realize ( PI and PM). The gray line marks the line of structural transitions from orthorhombic (lower doping level) to rhombohedral structures for higher doping level. For x = 0.175, at which a structural and magnetoelectronic transition happens at the same time, the magnetoresistance effect has his maximum extent.. 26 Figure [From Urushibara et al. 1995] Temperature dependence of resistivity for La1-xSrxMnO3 (0 < x < 0.4). The critical temperatures are indicated by an arrow, while open triangles indicates anomalies due to structural transition Figure Lattice parameter at room temperature for La1-xSrxMnO Figure Comparison between the rhombohedral (dashed grey line) and orthorhombic (black line) variants to respect to the perovskite cubic cell (thin grey line). The double cubic unit cell is also represented CHAPTER 2 Figure 2.1- [From Konishi et al. 1999] Left panel: The extended phase diagram of La 1-x Sr x MnO 3 (LSMO) as a function of lattice strain c/a and doping level x. The dashed line represent the results for LSMO bulk, the result s for LSMO on LaAlO 3 and on SrTiO 3 are represented by means black triangles and black circles respectively. Right panel: The corresponding calculated magnetic phase diagram, the magnetic structures corresponding to the (c/a, x) coordinates marked with x are represented ion Figure Figure 2.2 -[from Konishi et al.1999] Electron density distribution for the energy window of 0.6 ev width just below the Fermi level for the magnetic structure to the x in the left panel of Figure 2.1. The up-spin component and low spin component are shown separately. Manganese and oxygen atoms are denoted respectively by black and white spheres IV

7 CHAPTER 3 Figure 3.1-Four ferroelastic rhombohedral domains (in red) each with the [111] rhombohedral axis parallel to the <111> of the original cubic cell...39 Figure 3.2- Hexagonal, rhombohedral and cubic cell on the left; on the right: relation between hexagonal, cubic and rhombohedral unit cells Table 3.1- Lattice properties for the three representations of the LaAlO3 cell Table 3.2: The four domains due to ferroelastic transition with correspondent strain tensor and unique threefold axis of rotation Table 3.3- Possible domain wall for each couple of domains Figure 3.3- Schematization of a typical chevron tiling structure originated by the four different domains in the same region Figure Schematic of what happens during the deposition procedure Figure 3.5-(magnification 10x)-Domain structure on an as-received (001) LaAlO3 substrate at room temperature. PLM image shows strongly birefringent lamellas oriented approximately along [100]pc and [010]pc.Different coloured stripes correspond to different domains Figure 3.6 -(magnification 10x)- As received LaAlO3 substrate under crossed polars in nearly extinction position, the traces of domain wall running along [100] and [010] pseudocubic directions are visible; residual birefringence is evident in highly strained area Figure 3.7- Upper panel: (magnification 10x) Optical micrograph of LaAlO 3 substrate after deposition of a 20 nm thin layer of LSMO. The domains pattern is still present and well recognizable as well as an area where domain with domain walls oriented perpendicular to each other approach. The marked region, at higher magnification (20 x) and after a rotation of 45 under the microscope is shown in the bottom panel. Domain wall running along [010]pc direction is well recognizable and a not flat deposition surface can be noted by this image...46 Figure 3.8-Schematic representation of domain of type I and type II separated by domain wall of (100) type, giving rise to a non flat surface Figure 3.9- (magnification 10x) Substrate with 20 nm LSMO film under crossed polars. Stripes running along [100] and [010] directions with width as small as 5? m are visible Figure (magnification 20x) Substrate with 20 nm LSMO film under crossed polars, the complex microstructure is evident Figure The marked region of Figure 3.9 is shown at higher magnification (32x); the complicated microstructure of the substrate can be observed. Domain walls running along [100], [010] and [110] can be observed, the typical chevron tiling structure is also recognizable V

8 Figure Optical micrograph of LaAlO3 substrate with 20 nm LSMO layer, beside of the wider coloured striper running along [010] direction a smaller microstructure with stripes running along both [100] and [010] direction is visible, and the narrower recognizable domains ( marked by white arrows) have dimension down to 2 μm Figure LaAlO 3 substrate with 9 nm LSMO layer under crossed polars. Upper panel- (magnification 4x) Overview of the sample with two different chevron orientation running parallel to ] [010] direction, the marked region with the so-called chevron boundary is rotated by 45 and shown at 10x magnification in the bottom panel Figure 3.14-(magnification 10 x) Optical micrograph of LaAlO3 substrate with overgrown 9 nm LSMO film Figure AFM on a 10 μm x 10 μm region of LaAlO 3. The presence of two different chevron orientation is evident, with chevron domain wall oriented along [100] and [010] pseudocubic directions Figure AFM on a 5 μm x 5 μm region of LaAlO3. The presence of two different chevron orientations is evident, with chevron domain walls oriented along long [100] and [010] pseudocubic directions CHAPTER 4 Figure 4.1-Schematic representation of the general principle of rocking curve for a twinned crystal containing two domains (A and B). By rotating the crystal, one domain at time can be brought consecutively in diffraction position Figure 4.2- Rocking curve of LaAlO3 substrate of LSMO20r made around the (002)pc reflection. Four domains marked as D are visible Figure 4.3- Reciprocal space map around the (002)pc reflection of the LAO substrate of LSMO20r sample Figure 4.4-Reciprocal space map around the (103) pc reflection of LaAlO3 substrate for LSMO20r. Along the longitudinal direction (represented by a dot-dashed line) there are the intensity nodes due to diffraction from the (32 1 ) and (431) planes of LaAlO3 for both kα1 and kα2 components (marked as D 1 and D 2 respectively), while following the transversal direction from the D 2 node a ferroelastic domain can be observed, marked as D 3. The presence of the diffusion due to LSMO20r film in longitudinal direction (evidenced by means a dashed blue ellipse) indicates that the film is relaxed Figure 4.5- Simulation of the powder pattern of LaAlO3 using cubic description Figure Simulation of the powder pattern of LaAlO3 using rhombohedral description. 62 VI

9 Figure 4.7- Splitting of the (310) cubic reflection (on the left) when the rhombohedral description for LaAlO3 is adopted (on the right). In rhombohedral description the two peaks correspond to (32 1 ) and (431) planes Figure 4.8- Rocking curve of LaAlO3 substrate of LSMO9r. Two ferroelastic domains marked with D are recognizable as two peaks with comparable intensity Figure 4.9-Reciprocal space map around (002)pc reflection of the substrate for LSMO9r Figure [From Liu et al. 2004], ZFC FC magnetization curve at 20 Oe evidencing a non spin glass behaviour of the sample Figure ZFC-FC magnetization curves vs. temperature for LSMO 20r.The magnetic field is applied parallel to the deposition plane, being the magnitude 5 Oe, 1kOe and 10 koe respectively Figure ZFC-FC magnetization vs temperature curves with 5 Oe ( left panel) and 50 koe (right panel) magnetic field applied perpendicular to film plane for LSMO 20r Figure ZFC-FC magnetization curves vs. temperature for LSMO9r. The magnetic field is applied parallel to the film plane, being the magnitude 5 Oe, 1kOe and 10 koe respectively.70 Figure ZFC-FC magnetization vs temperature curves with 500 Oe ( left panel) and 1 koe (right panel) magnetic field applied perpendicular to the film plane for LSMO 9r Figure ZFC-FC magnetization curve on a 20 nm thickness film of LSMO deposited on STO substrate Figure 4.16-left panel: Rocking curve on LSMO 5 film. Four rhombohedral domains marked with D are recognizable; right panel: Reciprocal space map around the (002)pc reflection of the substrate for LSMO5. The same domain structure of the substrate is re-proposed also by the film Figure left panel: Rocking curve on LSMO10 film, two well resolved rhombohedral domains marked with D are recognizable; right panel: Reciprocal space map around the (002) pc reflection of the substrate for the LSMO10 film. For lower L values the same division in domain as that of the substrate can be appreciated also for the film. Also thickness fringes marked with F are visible Figure 4.18-left panel: Rocking curve on LSMO20 film, at least four domains marked with Ds are recognizable; right panel: Reciprocal space map around the (002)pc reflection of the substrate for LSMO 20, four domains of the substrate are visible along L = 2, and as many perfectly aligned in longitudinal direction also for the LSMO20 film. Thickness fringes marked with F are visible VII

10 Figure 4.19-left panel: Rocking curve on LSMO 40 film; right panel: Reciprocal space map around the (002)pc reflection of the substrate for the 20 nm LSMO film, four domains of the substrate are visible along L = 2, and as many perfectly aligned in longitudinal direction also for the LSMO film Figure left panel: Rocking curve on LSMO40a film deposited onto LaAlO 3 (001) substrate, in which different domains are marked by Ds; right panel: Reciprocal space map around the (002) pc reflection of the substrate for the LSMO40a film, with along horizontal direction L = 2 several intensity nodes due to different domains of the substrate, and corresponding domains for the LSMO film perfectly aligned in longitudinal direction Figure left panel: Scheme of the reciprocal space for the two extreme situations: fully relaxed layer and fully strained layer, and relaxation line in the right panel Figure Reciprocal space map on (103)pc asymmetric reflection of the substrate for four thickness film: 40 nm, 20 nm, 10 nm and 5 nm. All films are fully strained as can be deduced from the perfect alignment in H direction of reciprocal lattice nodes of LSMO films and LAO substrate. The black arrows are an eyes guide for better see that alignment. The longitudinal direction where the reciprocal lattice node of the film is supposed to be in case of relaxation is represented with a dashed line Figure 4.23 HRTEM cross section image of 10 nm (001) La 0.7 Sr 0.3 MnO 3 film on (001) LaAlO 3 substrate. The crystallographic [001] orientation is shown; the interface is marked with white dashed arrows (magnification: 1 Mx)...84 Figure Inverse Fast Fourier transform (IFFT) obtained from the image of Figure Differently oriented regions leading to a texture in the film can be recognized. This texture is driven by the structure of the substrate Figure left panel from [Bueble et al 1997]: Schema of mechanism that leads to have roughness at the interface. (a) Cubic prototype at high temperature, (b) twin domain formation after cooling down through ferroelastic transition temperature, (c) cutting an polishing procedure leading to a nearly flat surface, (d) Twin disappearance during deposition procedure and (e) new twin domain formation; Right panel: HRTEM cross section image of 10 nm (001) LSMO film onto (001) LAO (magnification: 1 M x), black arrows are a eyes guide to better evidenced the roof-like interface Figure Rocking curve on SrTiO 3 substrate of LSMO 5nm/ STO sample. A single peak with FWHM of 0.04 is indicative of a high degree of crystallization Figure 4.27-Upper left panel: HRTEM cross section image of LSMO 5 nm film deposited onto STO substrate, the magnification is 1 M x. Bottom right panel: IFFT of the region in the box, the sharp interface is marked with dashed red line VIII

11 Figure ZFC-FC magnetization curve for LSMO40 for different applied field ( 25 Oe, 50 Oe and 1 koe) parallel to film plane Figure ZFC-FC magnetization curve for LSMO 20 for different applied field ( 25 Oe, 50 Oe and 1 koe) parallel to film plane Figure ZFC-FC magnetization curve for LSMO 10 for 25 Oe applied field parallel to film plane Figure ZFC-FC magnetization curve for LSMO 5 for 25 Oe applied field parallel to film plane Figure Thermoremnant (TRM) magnetization decay measurements for LSMO 40 performed at 25 Oe at Tm = 50 K for different waiting time (a) tw = 0, (b) 1200s, (c) 5000 s, (d) s and (e) s Figure ZFC-FC magnetization curve for LSMO film with thickness of 12 nm deposited onto SrTiO3 substrate. The magnetic field of 5Oe is parallel to the deposition plane Figure 4.34-[from Kornyei 2006] Typical evolution of magnetization in a double logarithmic scale. A first decrease (1) due to the dissolution of ferromagnetic cluster disturbed by the random field is followed by non equilibrium reorganization (2) and by an equilibrium relaxation (3) The four insets show the spin configuration system in different regimes APPENDIX A Figure A.1- Schema showing constructive interference of x-rays wave planes according to Bragg s law Figure A.2- Geometry for x-ray diffraction: k and k are the incoming and scattered wave respectively, the position of the detector to respect to the origin O is R while to respect to the scattered atom is r Figure A.3- Relation between the scattering vector and the atomic planes having distance d Figure A.4- Ewald sphere: any reciprocal nodes that falls on it gives rise to Bragg diffraction peaks Figure A.5- D8 Discover (Bruker); high resolution triple axes diffractometer Figure A.6- Göbel mirror which converts the divergent beam coming from the x-ray tube into a quasi-monochromatic and highly parallel (divergence 0.03?) beam of high intensity Figure A.7- V-Groove monochromator: eliminates of kα 2 component and reduces five times the lateral dimension of the beam IX

12 Figure A.8- Accessible reciprocal space region in a diffraction experiment Figure A.9- Different scans in reciprocal space, to perform reciprocal space map iterative ω-scans and ω-2θ scans have to be performed Figure A.10- Reciprocal space map Figure A.11 -Schematic representing the film on the substrate and some crystallographic direction identifying two sections in the reciprocal space Figure A.12-Right panel: Section of the reciprocal space showing nodes of reciprocal lattice of a fully relaxed layer (red) onto a substrate (black) left panel Figure A.13- Right panel: Section of the reciprocal space showing nodes of reciprocal lattice of a fully strained layer (red) onto a substrate (black) (left panel). The perfect alignment of the reciprocal lattice nodes of the layer with that of the substrate in Qx direction for all reflection except of those of (00l)-type is the proof of the pseudomorphic growth Figure A.14 -Relaxation line relative to (103) reflection for a LSMO (001)/LAO (001) Table A.2- Lattice parameter and correspondent H and L value for a LSMO relaxed and fully strained film on LAO substrate APPENDIX B Figure B.1-Basic principle of molecular beam epitaxy showing co-evaporation of atoms or molecules from different sources onto a heated substrate Figure B. 2- Optic indicatrix or index ellipsoid for uniaxial crystal np = nq n r Figure B.3- Schema of a TEM: objective lens and projective lens are shown Figure B.4- Bright field mode and dark field mode; in bright field mode the image is created by means transmitted beam while in dark field mode the final image is created by the diffracted beam Figure B.5- FEI FIB200TEM used from TEM thin lamellae preparation (Queen s University Belfast) Figure B.6- Upper panel: Schematic representation of the first phase of lamella preparation, a first bar is obtained by milling trenches of material from each side; bottom panel: plan view of the bar Figure B.7- The U-cut which is made before starting the fine thinning procedure X

13 FigureB.8- Upper panel: one step in the thinning procedure is shown: the removed area is that in the yellow rectangular. Bottom panel: image of the lamellae after the thinning procedure before the final cut on the lateral edges Figure B.9- Scheme of a SQUID magnetometer Figure B.10- Detection coils in which the magnetic moment of the sample in movement induce an electrical current XI

14 - 1 - INTRODUCTION INTRODUCTION Doped manganese perovskites (DMP) with general formula Re 1-x Ak x MnO 3 ( x between 0 and 1, Re = rare earth or lanthanum, Ak= divalent cations (i. e. Sr Ba Ca etc.) show in their phase diagram as a function of hole doping concentration x an incredible variety of different states and properties. Despite the large research effort currently carried out and the abundant work produced in the last ten years (i.e. since the discovery of colossal magnetoresistance (CMR)) [Tokura et al. 1996, Cheong et al. 1999] that started the rush towards a new technology based on the integration of magnetic and electronic properties) novel aspects and peculiarities of DMP continue to emerge at overwhelming rate, so much that the knowledge of their fundamental mechanisms can hardly keep pace with the flow of experimental findings. The basis for the richness and complexity of DMP is that the magnetic, electronic and crystal structures of any given manganite are intimately related. Thus one may parameterize any given phase in the manganites by the nature of the spin, charge, orbital and structural degrees of freedom. At a microscopic level one can understand the strong interaction between the magnetic, electronic and crystal structures as follows. The electronic sub-lattice of a perovskite manganite consists of a cubic network of cornersharing MnO 6 octahedra in which potential charge carriers arise in certain orbitals if, for example, the interstitial A-site cations comprise a mixture of trivalent and divalent species such that they act as a charge reservoir. This electronic sub-lattice is also the home of the magnetic sub-lattice since the magnetic structure arises primarily from the magnetic nature of the manganese atoms. Therefore the electronic and magnetic sub-lattices are one and the same such that they must interact strongly. The intimate connection with the crystal lattice arises both because Mn is Jahn-Teller (JT) distorted by charge carriers, and also because the radius of the A-site cations is invariably less than ideal. The three main phases which compete to be the stable thermodynamic one in a DMP are a paramagnetic phase (PM) at high temperature, and, at low temperature, an antiferromagnetic insulator (AFMI) with possible orbital ordering (OO) and charge 1

15 - 2 - INTRODUCTION ordering (CO) phenomena, and a ferromagnetic metal (FMM). The transition between the two magnetically ordered phases is first order, with possible phase coexistence for hole concentration near the AFMI/FMM phase boundary. Which phase is realized on hole doping can be controlled via the key energy parameter W, i.e. the effective one electron e g bandwidth, related to the transfer integral of the conducting particles between neighbouring Mn sites. The bandwidth W depends on the average size of A-type cation =(xr Re )+(1-x)R Ak (R indicates ionic radium), which modifies the tendency towards long range lattice distortions of the cubic perovskite, quantified by the tolerance factor t =(A-O)/ 2 (B-O) (A, B, and O are the ionic radii within the ABO 3 perovskite). If the Ln ions in LnMnO 3 are replaced by larger Ak ions, the system Re (1-x) Ak (x) MnO 3 experiences decreasing tilt and rotation of the octahedral groups MnO6, with Mn-O-Mn bond angles approaching to 180. This leads to an increase of the hybridization among the Mn(3d) and O(2p) bands and of the bandwidth W, which depends on the Mn-O-Mn bond angle. With respect to the degree of Mn(3d)-O(2p) overlap, doped manganese perovskites are usually classified into three large groups: Low bandwidth compounds: In these compounds the insulating phase is especially pervasive through large regions of the phase diagram and the FMM phase can only be induced by external fields application. Pr 1-x Ca x MnO 3 can be considered the prototypical insulating DMP, being never metallic at zero temperature for x=[0,1]). Wide bandwidth systems: La 1 x Sr x MnO 3 is considered to be representative of the large bandwidth subset of manganese oxides. It is believed that in this compound the hopping amplitude for electrons in the e g -band is larger than in other manganites, as a consequence of the sizes of the ions involved in the chemical composition. The metallic phase of La 1 x Sr x MnO 3 at sufficiently large hole density seems quite properly described by double-exchange approaches, namely there is a simple relation between the resistivity and the magnetization in the metallic ferromagnetic phase [Tokura et al. 1994, Furukawa et al. 1998]. Intermediate bandwidth systems: Prototypical of this class is La 1 x Ca x MnO 3. This compound presents some characteristics of large bandwidth manganites, such as the presence of a robust ferromagnetic metallic phase. However, it also has features that 2

16 - 3 - INTRODUCTION indicate strong deviations from pure double-exchange behaviour, including the existence of charge/orbital-ordered phases. Not only the ground state but also the response (perturbation) properties of the DMP are a formidable challenge for experiments and theory alike. Indeed, these materials show an amazingly rich phenomenology caused by the extreme sensitivity to external fields that can easily induce metal-insulating transitions (MIT) often characterized by a dramatic change (several order of magnitude) in resistivity. The most celebrated of these gigantic responses is undoubtedly the aforementioned CMR (proper of many insulating DMP and especially remarkable in Pr 1-x Ca x MnO 3 ) that is a huge change of resistivity upon application of a magnetic field. More recent is the observation of the colossal electroresistance (CER), analogous to CMR, consisting on a huge change of resistivity with an applied electric field (recent works report large CER effects in Nd 0.7 Pb 0.3 MnO 3 [Ghosh et al.2004, Jain et al. 2007] although CER is probably a common properties of all the insulating DMP). The reasons of the extreme sensitivity to perturbations as well as the microscopic mechanisms driving the gigantic effects are still largely under investigation. Possible scenarios have been pictured and, in particular, the scenario which is based on the coexistence of different phases on micro or submicrometric scales is widely debated and experimentally well supported. Indeed, multiphase coexistence generically causes a sensitivity of physical properties to external perturbations: for a degenerate system, any perturbation is a large perturbation, and the most recent studies suggest that the largest magnetoresistance in these systems is associated with spatial inhomogeneity related to multiphase behaviour [Uehara et al. 1999, Moreo et al. 1999]. Remarkably, the proportions of two coexisting phases can be tuned by external parameters, like pressure, magnetic and electric fields, strain fields. The role of local strain in the balance between different phases has been treated with special interest. Local strain in manganites has been studied mainly in connection to point-like structural disorder, i.e. random local deviation from periodicity induced by doping at Re sites with chemical species of different size. Point-like defects introduce local distortions of the average structure which can promote electron localization and stabilize AFM insulating phases. Experiments show that, in presence of such kind of structural disorder, the long range 3

17 - 4 - INTRODUCTION magnetic ordered states are weakened and that a glassy window opens up at the AFMI/FMM boundary, with the spin glass probably consisting of an intricate texture of AFMI and FMM micro or nanodomains. Given the importance of strain fields, it is clear that the properties of a manganite are liable to be strongly dependent on the nature of the sample: the strain states and defects will vary between single crystals, powders, sintered powders and thin films. From some perspectives, the propensity for crystallographic twinning in the manganites reduces the value of single crystal studies in favour of free (non-sintered) powder samples since it is possible for each micron-sized grain to act like an untwinned single crystal. The possible extrinsic origin of the two-phase tendency in manganites and more in general in transition metal oxides has been in fact remarked in more than one occasion. One is more confident that if a phase separation is seen, for instance, in neutron powder diffraction, this is due not to surface effects at twin boundaries since, as known, each phase must extend for hundreds of Angstroms to be seen at all with neutrons. Conversely, in a twinned crystal, the local strain at twin boundary can create the conditions for the stabilization of a second phase even in the absence of specific intrinsic instability towards phase separation. Since, however, twinning can occur at nanosize length scale, and therefore may affects also powders, the role of the crystallographic texture in the two phase behaviour of doped manganites must be carefully considered and never underestimated. Twinning may be avoided by recourse to thin films. We note that the ability to prepare films and understand their properties is of prime importance in the case of manganite, since most technological applications require thin films on substrates. The scientific community have profited of different deposition techniques developed during the last almost 15 years for the synthesis of the first high-temperature perovskite-type superconducting oxide thin films. This resulted in the standardization of various methods, including sputtering, molecular beam epitaxy (MBE) and metal organic chemical vapour deposition (MOCVD), pulsed laser deposition (PLD). This latter method is used extensively to synthesize cuprates and HTSCs, which are now routinely made in laboratories, and it has been easily and rapidly adapted for manganites. 4

18 - 5 - INTRODUCTION As mentioned, the usual research approach in thin films of manganites tends to minimize twinning by deposition on oriented monocrystalline substrates. This kind of defect free substrate minimizes twinning by favouring one structural variant over the others by epitaxial stabilization. It can also stabilize non-bulk-like symmetries in the films via homogeneous strain accompained by changes in the magnetic, electronic, and magnetoresistive properties. The role of homogeneous strain in manganites thin films has been the object of hundreds of investigations. However, a different approach to thin films of manganites can be envisaged, aiming at inducing crystallographic twinning instead than at avoiding it, and along this route in this thesis we have explored the use of alternative substrates which are not monocrystalline, but naturally mesostructured from a crystallographic point of view. We were interested to explore the possibility that such mesostructured substrates can act as templates for the manganite films and induce in them a structural texture that may in turn have an electronic and magnetic counterpart. The chosen substrate for this study is lanthanum aluminate LaAlO 3. This perovskite is widely used as substrate for perovskite-type transition metal oxides like the herewith studied magnetoresistive manganites but also high Tc superconductors. However, its crystallographic peculiarities are not often remarked, at least in the field of manganites. At room temperature LaAlO 3 crystals used as substrates are heavily twinned, owing to a structural phase transition which breaks the cubic symmetry in favour of a rhombohedral one, leading to the formation of ferroelastic domains. The crystallographic texture due to twinning extends on micro or even sub-micrometric scale, i.e. on a mesoscopic scale. Twins disappear at the transition towards the cubic prototype which occurs at 540 K. We shall present experiments performed on thin epitaxial films of the wideband system La 1-x Sr x MnO 3 with x = 0.3 deposited on LaAlO 3 (001) substrates, using a pseudocubic notation. The manganite composition has been chosen for its high Curie temperature in the bulk state and for being well inside the stability region of the FMM phase: in the unperturbed bulk states there is no special evidence for a tendency towards phase separation. The samples discussed in this thesis have been deposited by Molecular 5

19 - 6 - INTRODUCTION Beam Epitaxy (MBE). The deposition temperature being above the ferroelastic transition of LaAlO 3, the epitaxial growth of the manganite took place on the untwinned paraelastic structure of LaAlO 3, i.e. on (100) cubic crystallographic facets. It is upon cooling down at room temperature that a crystallographic mesotexture appears in the substrate that can possibly affect the epilayer. We shall demonstrate that the twin structure of the LaAlO 3 substrate acts indeed as template for the films and has profound effects on the magnetic properties of the manganite, properties which can be discussed in terms of enhanced tendency towards phase separation related to the crystallographic texture due to the substrate-induced twinning. The thesis is organized as follows: in CHAPTER 1 we shall present the fundamental ingredients for understanding the physics of manganites, which will be useful for discussing the bulk phase diagram and properties of the system La1 -x Sr x MnO 3. The bulk phase diagram of La 1-x Sr x MnO 3 is then presented as a function of for hole doping level and temperature. In CHAPTER 2 the modifications induced by homogeneous strain on the bulk diagram of La 1-x Sr x MnO 3 are discussed, with reference to the fundamental results of Fang et al. The crystallography of the ferroelastic transition of LaAlO 3 is presented in CHAPTER 3, which also contains the experimental analysis of the domains structure of the used substrates by optical polarized light microscopy. CHAPTER 4 contains the structural characterization of the LSMO films on LAO, distinguished in a set of two partially relaxed films and a set of five totally strained (pseudomorphic) films. The X-rays structural results are completed by TEM images for the strained films. The same chapter contains also the results of the magnetic characterization, discussed in strict connection with the structural features of the films as determined by the diffractometric and electron microscopy analysis. 6

20 - 7 - INTRODUCTION CHAPTER 5 gives a concise summary of the work and the conclusions that were drawn. Moreover some suggestion about the development future of work are included. Furthermore two appendixes are included in the thesis. Appendix A contains the derivation of the Bragg law according to the Laue formulation. Moreover in the same appendix the diffractometer that has been used for structural characterization is presented and the different possible scans are visualized in the reciprocal space. Appendix B contains some details and informations on the other experimental techniques and instrumentation used for samples characterization: i.e. optical birefringence, transmission electron microscopy (TEM) and Superconducting QUantum Interference Device (SQUID). 7

21 - 8 - CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES CHAPTER 1 AN OVERVIEW OF DOPED MANGANITES In 1950 Jonker and Van Santen [Van Santen et al. 1950] reported about the first crystallization and magnetic characterization of the mixed-valence manganites belonging to the pseudo-binary systems LaMnO 3 -CaMnO 3, LaMnO 3 -SrMnO 3, LaMnO 3 - BaMnO 3 and LaMnO 3 -CdMnO 3. They used the name manganite to indicate all compositions containing both trivalent and tetravalent manganese, although, as they themselves stressed out, the term would be better reserved to phases of tetravalent Mn only. Experiments indicated antiferromagnetic ordering in most of the Mn +3 containing phases, like LaCrO 3 and LaFeO 3, in contrast to the ferromagnetic behaviour of LaMnO 3 which was at the beginning considered an exception. Deeper investigations allowed to ascribe the ferromagnetic ordering of LaMnO 3 to the presence of Mn in the mixed valence state Mn 3+/ Mn 4, likely due to oxygen off-stochiometry, which initiated the research on the peculiarities of mixed valence manganites. All manganites treated in this thesis crystallize in the perovskite structural type whose atomic arrangements was first described in the 1830s by the geologist Gustav Rose, who named it after the famous Russian mineralogist Count. Lev Aleksevich Perovski. The simple cubic perovskites of formula ABO 3 shown in Figure 1.1 has largest cation A at the corner of the cubic cell, B cation is in the centre of the cell and oxygen atoms in the middle of every face of the cube, with bond angles B-O-B all of 180 and all B-O distance equal. In the ideal case, the perovskite structure crystallises in cubic symmetry with space group Pm3m. A replica of the simple cell in the space shows a framework structure of regular corner sharing BX 6 octahedra, with the A cation located as in interstices surrounded by eight octahedral leading to a AO 12 polyhedra. 8

22 - 9 - CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES Figure 1.1-left panel: Unit cell of a simple cubic perovskite with A cation in green, the B-site in blue and the oxygen ion in red. Right panel: Perovskite structure peculiarity: corner sharing octahedra The atomic structure of the mineral perovskite, first found for CaTiO 3, exhibits a crystal lattice only approximately cubic, though it is actually slightly distorted orthorhombically. Distortions are widespread in perovskites and only few of them present a simple cubic structure at room temperature, recovering the cubic symmetry only at high temperature. To rationalize the tendency towards distortions, Goldschmidt introduced the so called tolerance factor of Goldschmidt t defined from the ionic radii of the atomic species of the structure [Galasso 1990] as follows: r t = 2 A r ( r + r ) with r A, r o and r B being the ionic radii for the A-site ion, oxygen and B-site ion respectively. For closest packing of atoms, t =1. Goldschmidt himself underlined that the perovskite structure is stable only if the t parameter lies between 0,9 and 1. As t approaches unity, the cubic structure becomes more stable. A deviation of t values from 1 indicates the likely formation of a perovskites structure distorted to respect to the ideal type. Generally in the manganites the tolerance factor is appreciably different from the unit leading to structures different from the cubic one. In particular, when a smaller than ideal A cation is situated in the close packed AO B o o 9

23 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES layers, the tolerance factor will be less than 1. In these cases the A cation relaxes towards a set of the surrounding O anions and by consequence the BO 6 octahedra will tilt in order to optimize space filling. Every specific distortion is due to a rotation (tilt) of the oxygen octahedra. Which structure is realized depends on both the magnitude and the relative rotation of the octahedra around the crystallographic axis. The notation used to indicate the particular tilt system is due to Glazer [Glazer 1972]. With this notation every tilt system is decomposed in three different octahedra rotations around the three original cubic directions [100] cub, [010] cub and [001] cub. The magnitudes of the rotation is indicated by mean a letter ( a, b. etc) : same letter means same amount of rotation, while a plus or minus sign as apex indicates in phase or antiphase adjacent octahedra rotations. Apex zero means no rotation at all. To the sake of clearness in table 1.1 some example of the Glazer notation with relative explanations are given, and in Figure 1-2 the more typical distortions from cubic for mixed valence manganites, together with the tilting system of Glazer, and the relation to the parent structure are shown : Table 1.1- Examples of Glazer notation for octahedra rotation and relative explanation Glazer notation a 0 a 0 a 0 a + b + c + a - a + c - a + b - b - Meaning No rotation about any axis: octahedra system for cubic structure An in-phase rotation of different magnitude about each axis An anti-phase rotation about x and z and an in- phase rotation about y; rotation about x and y have the same magnitude that differs from that that about z An in-phase rotation about the x axis and anti-phase rotations about y and z. Rotations about the y- and z-axes have the same magnitude which differs from the magnitude of rotation about the x-axis 10

24 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES Figure 1.2-Orthorhombic structure on the left and rhombohedral one on the right. Space group and Glazer system are shown together with the relation between the unit cell (dashed lines) and the ideal cubic phase. Mixed valence manganites have been given renewed attention from 1990s onwards, after the observation of the phenomenon called colossal magnetoresistence (CMR) in thin films of La 1-x Ba x MnO 3 and La 1-x Ca x MnO 3 [Von Helmolt et al.1993, Jin et al. 1994]. The gigantic resistance response to the application of a magnetic field encouraged the research efforts to find a possible use of manganites in a new technology based on the integration of magnetic and electronic properties, with application like read-heads in computer hard disks, magnetic field sensors, infrared detectors, microwave active components and in vivo application in biomedicine as well [Uskoković et al. 2006]. The following equation is generally used to define the MR: % MR = Δρ ρ H ρ0 100 = 100 ρ ρ0 where ρ H and ρ 0 are the resistivity with and without the applied magnetic field respectively. The difference between the ordinary MR (discovered by Sir William Thomson [Thomson 1857] and the CMR lies in the amount of resistance variation versus the applied magnetic field, which is few percents for the ordinary while reaches several magnitude orders ( up to 10 6 %) for the colossal effect. Anyway it is worth to note that a more fundamental difference exists, CMR being the result of quantum-mechanical 11

25 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES interactions specific of mixed valence transition metal oxides (TMO) with their strongly correlated electrons. The mixed valence state of Mn is the result of doping by heterovalent cationic species at Re site in the antiferromagnetic insulating end-member (x = 0) ReMnO 3 of the Re 1-x Ak x MnO 3 system. By partially replacing the trivalent rare earth for the divalent alkaline earth, the nominal valence of Mn can be gradually tuned between 3 + and 4 +. Doping introduces holes in the conduction band which is composed by the hybridized Mn3d and O2p orbitals. For specific chemical systems, in which the electron-lattice coupling is not too strong, at a certain doping level the holes become mobile and an insulator to metal transition (MIT) occurs in the temperature-composition (T,x) equilibrium phase diagram. The metallic phase induced by hole doping is ferromagnetic, which was suddenly interpretated in the framework of the double exchange magnetic interaction formalized by Zener in 1951 [Zener 1951]. The Curie temperature Tc coincides in many manganites with a MIT transition. However, this is not always the case, and a transition to a paramagnetic metallic phase with reduced carriers mobility may occurs instead. The application of a magnetic field at temperatures near T C drives the system into the ferromagnetic metallic state, which is the aforementioned CMR. The colossal effect is most pronounced for certain compositions of the phase diagram that are in proximity of a line of structural phase transitions. The structural transition may also be triggered by the magnetic field (magnetostructural transition), reflecting the strong relation between magnetic, electronic and structural degrees of freedom. In this CHAPTER we shall give a brief introduction to the main mechanisms which are thought to explain the physical behaviour of manganites. The complex physics of manganites is surprisingly contained in a limited set of factors, which are i) the energetic of Mn ions (which in the trivalent state are Jahn-Teller while as tetravalent species are not), that have a key role in the strength of the electron-lattice coupling, and ii) the magnetic interactions between the Mn ions, that determine the kind of magnetic ordering and in turn dictate the electronic (metallic vs insulating) character of the specific phase. It is from the coupling and interplay between these few factors that the richness of the physics emerges. Excellent reviews on this subject exist in the scientific literature [Dagotto et al 2001, Dagotto et al. 2003] to which we will often refer in the following. 12

26 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES 1.1 Energetics of Mn: Jahn-Teller effect When discussing about TMO like Re 1-x Ak x MnO 3, the common initial approach is to assume a purely ionic description of the chemical bonding and to assign to each chemical species an integral number of valence electrons. The neutral external configuration of Mn atoms is 3d 5 4s 2, so that after electrons transfer for bonds formation it becomes 3d 4 for Mn 3+ and 3d 3 for Mn 4+. For isolated Mn atoms, the fivefold degenerate 3d level are occupied by electrons according to the first Hund s rule of maximum spin multiplicity, owing to the strong intraatomic exchange coupling. The spins of the 3d electrons are parallel aligned in the ground state of the isolated ion and, in the spin-only approximation (valid for the 3d transition series) produce a total spin value S=2 for Mn 3+ and S=3/2 for Mn 4+ which corresponds to a magnetic moment of 4 and 3 Bohr magnetons, respectively. If the Mn ion is not isolated but put on the B site of a perovskite, the energetic of the d-electrons is governed by the Hamiltonian H 3d (r) which includes not only the potential of Mn 3+ ion core H (Mn), but also the electrostatic potential of the surrounding six oxygen atoms in octahedral coordination: H 6 ( Mn) ( oxy) 3d ( r) = H ( r) + V i i= 1 ( r R ) Simple electrostatic considerations allows to understand that the effect of the octahedral crystal field is to partially lift the orbital degeneracy and to separate the fivefold degenerate 3d states into three lower-energy levels t 2g (d xy, d xz, and d yz ) and two higherenergy levels e g (d 2 2 x -y and d z2 ) as shown in Figure 1.4, with Δ o ~ 1,5 ev being the separation e g - t 2g [Haghir-Gosnet et al. 2003]. 13

27 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES Figure 1.3- The five 3d-orbitals of a transition metal in octahedral environment. The six ligands are shown as green balls The resulting 3d energy levels are schematically shown in Figure 1.4. Figure 1.4- Crystal field splitting of 3d orbitals. The orbital filling refers to a 3d 4 ion. Jahn-Teller Effect: The electronic configuration of Mn 3+ is t 3 2g e 1 g, characterized by the presence of a single electron in the 2-fold degenerate e g levels. As such, Mn 3+ is a Jahn- Teller-active chemical species. According to the Jahn-Teller theorem, the Mn 3+ O 6 groups in Re 1-x Ak x MnO 3 are energetically unstable towards distortions aiming at reducing the total energy of the system, as a consequence of a the lifting of degeneracy of the twofold e g levels. The degree of distortion is determined by the competition between the gain in energy due to the eg splitting and the increase of the elastic energy associated to the lattice distortion itself. Referring to a tetragonal elongation along z-axis (Figure1.5) of the MnO 6 octahedron, the cost in elastic energy for a deformation δz along z will be proportional to (δz) 2. The splitting of the e g levels is proportional to δz, so that the energy gain for an electron which goes into the lower-lying level d(z 2 ) ( see Figure 1.6, left panel) is 14

28 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES proportional to δz. As a consequence the total energy E = α(δz) 2 -βδz is minimized by a finite distortion δz = β/2α. Figure 1.5- Tetragonal distortion from an ideal (all green atoms) to an elongated octahedron (white atoms along z), the elongation is δz Two possible distortions of the Mn 3+ O 6 octahedra are associated with the Jahn-Teller effect. The symbol Q 2 indicates the orthorhombic distortion, in which the four in-plane Mn-O distances are grouped into two long and two short ones. The tetragonal distortion with shortening of in-plane bond lengths and elongation of the out-of-plane bonds, or vice versa, is indicated as Q 3 [Kanamori 1960]. From a structural point of view, the main result of the distortions Q 2 and Q 3 is that the Mn-O distances become different. Figure 1.6 shows the effect of a tetragonal distortion Q 2 for the t 3 2g e 1 g electronic configuration of species like Mn 3+ [Jahn et al ]. Figure 1.6- Jahn Teller effect with tetragonal distortion. Left panel: elongation along z-axis, right panel: contraction along z-axis. The orbital filling corresponds to the case of high spin 3d 4 species. 15

29 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES The presence of Jahn Teller ions Mn 3+ in manganites means that the description of their behaviour is not accurately accounted for within the Born-Oppenheimer approximation, which, as known, is based on the assumption that in a solid the motion of electrons is independent of the motion of the atomic nuclei. The Born-Oppenheimer approximation amounts to assuming that the electronic motion is so rapid compared with the nuclear motion that the electronic potential V Q (q) is a function of the electron coordinates q only and is almost independent of the nuclear coordinates Q. If there is an orbital degeneracy of the electronic states (as in the case of Jahn-Teller species) then this approximation is no longer valid. Under these circumstances it is no more correct to refer to the crystalline modes as electronic or lattices modes. The term vibronic coupling is used to describe that mode which is mostly electronic in character but has some vibrational character too. Vibronic coupling describes the bridge between electronic and nuclear motions. The strength of the coupling is measured by the constant A which compares in the Jahn-Teller Hamiltonian H JT = AQSz where Sz is some electronic operator. If the different Jahn-Teller centres interact, at sufficiently low doping levels, we will have a correlated ordering of the local distortions which will lead to a macro-deformation of the crystal as a whole. New properties of the crystal arising from the correlation (ordering) of the Jahn-Teller centre distortions, including the formation of new crystal structures and structural phase transitions, are called the cooperative Jahn-Teller effect. A cooperative Jahn-Teller effect is found in the case of LaMnO 3 which undergoes an isostructural (orthorhombic O to orthorhombic O ) phase transition around 750K [Fazekas 1999]. Cooperative Jahn Teller effect occurs in manganites when the concentration of Mn 3+ ions is sufficiently high, i.e. at low and intermediate doping level. When Mn 3+ is diluted into Mn 4+ species by doping, the possibility of cooperative effects among Jahn teller active octahedra is reduced. Thus no static distortion will be observed. In opposition to the cooperative Jahn-Teller effects, averaged effects can be observed for high dilutions, called dynamic Jahn-Teller effects. The effect of cooperative and local Jahn-Teller effects in manganites is to localize the e g electrons on Mn 3+ sites, owing to the gained energy, and to stabilize insulating phases, either locally or at long range. 16

30 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES 1.2 Orbital ordering In recent years, the term orbital ordering has been preferred to denominate cooperative Jahn-Teller effect. Orbital ordering means an ordered pattern of occupied and unoccupied electronic orbitals in a crystal structure. The OO phase realized in orthorhombic LaMnO 3 below the cooperative Jahn Teller transition at 750 K in shown in Fig It is composed by an alternate occupancy of e g orbitals along x and y and is the result of an additional Jahn Teller Q 3 distortion of the MnO6 octahedra in the Pbnm phase. The Q 3 mode produces two different in-plane Mn-O distances, with the longer one corresponding to the more stable and occupied e g orbital. This leads to the OO with inplane (ab) alternation of d 2 3x r2 d 2 2 3y r orbitals. There is no alternation along the c axis as shown in Figure 1-7. The O orthorhombic structure is in fact characterized by alternating long and short MnO (2) distances in the ab plane that is a clear sign of orbital ordering. The OO in LaMnO 3 is of the so called C-Type orbital system, which is characterized by inplane antiferro-orbital ordering and out-of-plane ferro-orbital ordering. It is coupled with A-type antiferromagnetism, as it shall be described in the following Paragraph 1.4., with in-plane ferromagnetic and out-of-plane antiferromagnetic coupling of Mn spins. Figure 1.7- C-type orbital ordering in LaMnO 3 as a consequence of the cooperative Jahn-Teller effect 17

31 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES 1.3 Charge ordering Orbital ordering can be accompanied by ordering of electronic charges, giving rise to charge ordered (CO) phases. Charge ordering is most easily visualized for half doped manganites with equal concentration of Mn 3+ and Mn 4+. Usually CO is represented as an ordered alternation of manganese ions with different (Mn 3+ and Mn 4+ ) valence, or equivalently as a site-centred alternation of single electrons and holes localized within the Mn sublattice. As such, CO is often presented as a realization of the Wigner crystallization. In principle, however, these charges do not need to be necessarily localized on the Mn sites, and in fact they could sit on the bond centres as well, or, in the most general case, on some intermediate point between those two. Such an intermediate CO state can be more generally seen as a charge-density wave or orbital-density wave lacking inversion symmetry and then potentially capable to develop ferroelectric ordering. This is a further aspect of the already rich physics of manganites which we shall not discuss in this Thesis but that is being at present regarded with great interest. 1.4 Magnetic interactions: superexchange and double exchange The magnetic properties of manganites derive from Mn atoms, which are the only chemical species having a non zero magnetic moment. Two main types of magnetic interactions between localized magnetic moment are recognized in crystals: Direct Heisenberg exchange, which describes the direct interaction between the ions having the non-zero magnetic moment and is modelled by the Heisenberg exchange Hamiltonian H ex = 1 2 J ijsis j where J ij is the exchange coupling constant between spins S i and S j distributed on a regular lattice. Only nearest neighbours are usually included in the summation. ij 18

32 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES The magnetic properties of the crystal are thus dependent on the sign and strength of the interaction between spins: if J ij = J > 0 parallel orientation of the spins is favoured below the critical temperature TC, so that all spins are aligned giving a ferromagnetic state. If J ij = J < 0 the magnetic order is antiferromagnetic, with the spins antiparallel to their first neighbours. Superexchange interaction, which is the anion-mediated magnetic exchange. This interaction was first proposed by Kramers in 1934 to the aim of finding an explanation for the magnetic properties observed in insulating transition metal oxides [Kamers 1934], in which the magnetic ions are so distant that a direct Heisenberg interaction could not explain the presence of magnetically ordered states. The problem was thereafter treated theoretically by Anderson, who in 1950 gave the first quantitative formulation [Anderson 1950] showing that it favours antiferromagnetic order. The magnetic interactions in manganites are all mediated by the oxygen atoms lying between two Mn ions, i.e. they are all superexchange interactions. Therefore the insulating phases of manganites are expected to be antiferromagnetic. Different antiferromagnetic phases are possible for the simple cubic magnetic sublattice of the ideally undistorted manganese perovskite, as shown in Fig. 1.8: Figure 1.8- Different antiferromagnetic phases for the simple cubic Mn lattice: A-type constituted by ferromagnetic planes antiferro coupled along c axis; C-type constituted by an antiferromagnetic coupling along x and y axis and a ferromagnetic coupling along z axis and G-type where the interaction are antiferromagnetic along all axes 19

33 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES They are known as A-type, C-type and G-type antiferromagnets. A-type is constituted by ferromagnetic planes coupled antiferromagnetically along the c axis; C-type is constituted by in-plane antiferromagnetism with ferromagnetic out-of-plane coupling. G-type is the simplest antiferromagnetic structure in which all interactions favour antiparallel spin alignments. In manganites, the sign of the superexchange magnetic interactions between neighbouring manganese ions are determined by the kind of orbital ordering. The orbital ordering gives rise to anisotropy of the electron-transfer integrals Jij. This favours or disfavours ferromagnetic or antiferromagnetic interactions in an orbital direction dependent manner and hence gives a complex spin-orbital coupled state. The dependence of the sign of the superexchange interaction on the orbital occupation is summarized by the so-called Goodenough-Kanamori-Anderson (GKA) rules [Goodenough 1976]. According with these rules the exchange interaction between Mn 3+ -O- Mn 3+ may be either ferro or antiferro, such as in LaMnO 3 where both F and AF coexist. A-type antiferromagnetism is favoured at low doping, while C-type and G-type couplings are found at high level doping, when Mn 4+ ions predominates. 1.5 Ferromagnetic double- exchange To explain the close association of ferromagnetism with metallic conduction in manganites it is necessary to introduce the concept of double exchange mechanism (DE) first introduced by Zener in 1951 [Zener 1951]. Double exchange is the kind of exchange interaction between Mn 3+ and Mn 4+ in transition metal oxides. The double exchange mechanism is schematically depicted as: Mn O Mn Mn O Mn 1 2,3 1,3 2 [Cieplak 1978] 20

34 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES As such it can be thought as two simultaneous motions: the motion of a first e g electron from the Mn ion on the left to the intermediate oxygen and the motion of a second e g electron from the intermediate oxygen to the Mn ion on the right. It has been shown [Anderson P.W. et al. 1955] that the electron transfer integral t of the e g electron between Mn ions in the double exchange process depends on the angle Θ between the magnetic moment of the core (t 3 2g) Mn electrons: t = t o cos (Θ/2) Figure 1.9- Schematic view of the DE mechanism, the hopping probability is proportional to the angle subtended by the direction the core-spin moment. Figure 1.9 shows the schematic mechanism of DE, in which the parallel alignment of the core-spin moment favours the motion of e g electron between Mn 3+ and Mn 4+. Because of the strong intra-atomic Hund coupling between the e g electron and the Mn 3+ t 2g core, the motion of the itinerant e g electron favours the ferromagnetic alignment of the core-spin moments. In other words, the e g electron transfer process leads the degeneracy of the two states Mn 3+ -O-Mn 4+ Mn 4+ -O-Mn 3+ to be broken, with the consequent formation of two energy levels E ± t o cos (Θ/2). For a parallel spin configuration (Θ = 0) t is maximized to 21

35 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES respect to the antiparallel one ( Θ = π ) so that the energy gain leads to the ferromagnetic character of double exchange mechanism. The double exchange interaction contains the basic qualitative justification of the CMR. A magnetic field applied to a paramagnetic material (in which the magnetic moment are disaligned and the mobility of the e g electron is low) aligns the Mn t 2g magnetic moments and allows the e g electrons to move through adjacent Mn ions (from Mn 3+ to Mn 4+ ), leading to the observed dramatic decrease of resistivity. To give quantitative account of the experimental data of the resistivity changes, however, recent studies ascribes a crucial role of a strong interaction between carriers and lattice vibrations (the already described vibronic modes) that add their contribution to the pure double exchange interaction in those chemical systems in which the Jahn Teller Hamiltonian has particular influence [Millis et al. 1995, Röder et al. 1996]. 1.6 Low vs wide bandwidth systems: prototypical phase diagrams As pointed out in Introduction the family of DMP presents a very strong interplay among different degrees of freedom (spin, charge, orbital and structural degrees) that together contribute to determine which phase is realized for a specific value of hole doping. The three main phases which contribute to the richness and complexity of the phase diagrams of different DMP are a paramagnetic phase (PM) at high temperature, and, at low temperature, an antiferromagnetic insulator (AFMI) with possible orbital ordering (OO) and charge ordering (CO), and a ferromagnetic metal (FMM). The transition between the two magnetically ordered phases is first order, with possible phase coexistence for hole concentration near the AFMI/FMM phase boundary. The relative abundance of the three phases in a particular system is governed by several intrinsic and extrinsic factors. The argument most often invoked to explain the metal-insulating competition in manganites is the degree of structural distortions (oxygen rotations and/or Jahn-Teller effects) ruling charge localization and in turn the competition between superexchange and double- 22

36 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES exchange mechanism. The degree of distortion influences the width of the conduction band, with Mn e g -O2p character, which is at the basis of the itinerant vs localized character of the charge carriers introduced by doping. According to the width of the conduction band, manganites are subdivided into three classes: low, intermediate and wide bandwidth systems. Figure 1.10 shows the phase diagram of the system Pr 1-x Ca x MnO 3 up to half doping. This system is representative of the low-bandwidth class. The most interesting characteristic of the phase diagram is the complete absence of a thermodynamically stable ferromagnetic metallic phase in the whole doping range [0, 1]. In the phase diagram, canted insulating (CI) phases are stable for doping level between 0 and 0.1, followed by a region of insulating ferromagnetic (FI) phases (for x between 0.15 and 0.3) and a further region of antiferromagnetic (AFI) phases for x>0.3 which undergo a transition to a canted state (CAFI) upon cooling. In the paramagnetic region of this high-doping range, charge ordered insulating (COI) phases are also present. Figure 1.10-Phase diagram of the low bandwidth system Pr 1-x Ca x MnO 3 ; paramagnetic insulator (PI) phase and charge ordered insulator (COI) are present at high temperature. Moreover below the line of critical temperatures T N and T C canted, ferromagnetic, canted antiferromagnetic phases can be recognized (CI), (FI), (CAFI) and (AFI) 23

37 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES Figure Phase diagram of the intermediate bandwidth compound La 1-x Ca x MnO 3. Depending on the doping level several states: canted antiferromagnet (CAF), charge/orbital ordered phases (OO/CO), ferromagnetic insulator (FI), and antiferromagnetic (AF) La 1 x Ca x MnO 3, whose phase diagram is shown in Figure 1.11, is prototypical of the intermediate bandwidth systems. As already said in Introduction, this class of manganites shares some characteristics with low bandwidth systems, such as the pervasive presence of orbital-ordered and charge ordered states, indicating the persistent role of vibronic couplings. However, the class also shows a robust ferromagnetic metallic phase above a critical doping, which is typical of wide band systems as described below. Figure 1.12 shows the phase diagram of La1 -x Sr x MnO 3, which is the most studied representant of wide bandwidth systems. 24

38 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES Figure Phase diagram of the wide bandwidth system La 1-x Sr x MnO 3. At low temperature the system experienced insulating antiferromagnetism (AFI), insulating ferromagnetism (FI) and metallic ferromagnetism (FM). At high temperature paramagnetic phases are stabilized, either insulating (PI) or metallic (PM). As in other wide bandwidth manganites, a ferromagnetic metallic (FMM) state can be stabilized above a critical doping level, which is x = 0.17 in the La 1-x Sr x MnO 3 system. Above this composition, the eg electrons become mobile enough to give a metallic-like conduction in concomitance with the ferromagnetic alignment of the core t 2g spins of Mn ions. For Sr concentration above about 0.33, a quite high mobility of the e g electron is conserved also in the paramagnetic phase which still has metallic character (dr/dt>=0). Therefore in this composition range the Curie temperature does not correspond to a true metal insulator transition (MIT). At lower doping, on the contrary, the paramagnetic phase is insulating. One can note the absence of OO/CO phases (if not those derived from the OO phase of the end member LaMnO 3 at low doping), which indicates the weakness of the electron lattice interaction. More details on this diagram will be given in the next paragraph. 25

39 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES 1.7 Bulk properties of La 1-x Sr x MnO 3 A more complete phase diagram of La1 -x Sr x MnO 3 as function of Sr concentration and temperature is shown in Figure Figure Phase diagram of La1 -x Sr x MnO 3 as function of Sr concentration and temperature. Antiferromagnetic insulator (AFI) is realized for lower level of Sr doping and low temperature. Ferromagnetic metallic (FM) phase can be obtained increasing the doping level, while at high temperature paramagnetic phase are realize ( PI and PM). The gray line marks the line of structural transitions from orthorhombic (lower doping level) to rhombohedral structures for higher doping level. For x = 0.175, at which a structural and magnetoelectronic transition happens at the same time, the magnetoresistance effect has his maximum extent The undoped LaMnO 3 is an antiferromagnetic insulator ( AFI), with T Neel = 140 K and an orthorhombic structure stable below 140 K due to both small Goldschmidt tolerance factor and Jahn-Teller effect. The cooperative Jahn Teller effect between Mn 3+ ions produces the C-type orbital ordering giving in turn the A-type antiferromagnetic structure, according to the Goodenough-Kanamori-Anderson rules. 26

40 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES At high temperatures, for all Sr doping levels, the La 1-x Sr x MnO 3 system is in a paramagnetic state, denoted by P in the phase diagram. Doped phases undergo different transitions as a function of temperature. For low doping (0< x < 0,08 ) the system retains insulating properties with AFM ordering The AFM state is spin canted, which is sometime explained considering a gradual passage, with increasing Sr concentration, from the A-type structure of the undoped phase to the ferromagnetic state found above the concentration x=0,08: the sublattice magnetizations have in someway to gradually tilt with respect to each other as x increases, with relative angle passing from θ = π for x = 0 to θ = 0 for a certain value of doping. However, AFM with spin canting is hardly distinguished experimentally from a mixture of AFM and FM phases. To better understand what happens in the canting region let us consider the mean field energy density that can be written as [Fazekas 1999] : minimizing it with respect to θ we get E (θ) = Jcosθ - x [4t +2tcos (θ/2)] ϑ tx cos = 2 2J that shows the existence of a critical value x = x 2J cr = so that for 0 < x < x t cr the system experiences a transition from AFM to FM with canting until it becomes fully ferromagnetic for x > x cr. For 0,08 < x < 0,16 the system is still insulator but ferromagnetic. Spin canting is still present. Jahn-Teller distortion is also still present even if less effective, as can be seen observing a structural transition from orthorhombic (typical for Jahn-Teller distortion) to rhombohedral symmetry. In the 0.16<x<0.3 dopant regime, a phase transition from ferromagnetic insulator to ferromagnetic metal as well as a structural transition occurs. There is no more Jahn-Teller effect as the number of Mn 3+ Jahn-Teller active ions is too small to produce a cooperative 27

41 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES effect. As a consequence a rhombohedral structure with six equals Mn-O distances is stabilized. It is worth to note in fact that for x = we observe a structural transition ( the most important for this system) from orthorhombic to rhombohedral structure as well as a transition from a paramagnetic insulator (PI) to a Ferromagnetic metallic phase ( FM) leading the system to have for this concentration the colossal magnetoresistance at the highest level. For x > 0.3 the system is ferromagnetic at room temperature, and following an ideal line from low temperature to higher temperature the system experiences a transition from low temperature ferromagnetic metallic phase to high-temperature paramagnetic- less metallic phase. In fact even if the system is still metallic for T > Tc the transition from paramagnetism to ferromagnetism is accompanied by a large drop in the resistivity, while maintaining an overall metallic temperature dependence (Figure 1.14) [Urushibara et al. 1995]. The highest Curie temperature for Strontium-doped lanthanum manganite, LaMnO 3 :Sr (LSMO) is for x = 0.3 (Tc near 380 K) and this is the reason because this composition is the highly studied. Figure [From Urushibara et al. 1995] Temperature dependence of resistivity for La 1-x Sr x MnO 3 (0 < x < 0.4). The critical temperatures are indicated by an arrow, while open triangles indicates anomalies due to structural transition 28

42 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES 1.8 Orthorhombic and rhombohedral distortions of the perovskite structure in La 1-x Sr x MnO 3 phases The orthorhombic and rhombohedral variants are the most important ones in strontiumdoped lanthanum manganite La 1-x Sr x MnO 3. In fact as already observed in the previous paragraph, at room temperature the system La 1-x Sr x MnO 3 experiences a crystal structure transition from orthorhombic (space group Pbnm, Z = 4) to rhombohedral ( space group R3c, Z = 2) through the critical doping level x = In Figure 1.15 the room temperature lattice parameters of La 1-x Sr x MnO 3 for [Urushibara et al. 1995]. x between 0 and 0,4 are reported Figure Lattice parameter at room temperature for La 1-x Sr x MnO 3 The most important difference between the two symmetries is that the rhombohedral space group does not allow static Jahn Teller distortion of the MnO 6 groups: it admits in 29

43 CHAPTER 1-AN OVERVIEW OF DOPED MANGANITES fact only one Mn-O distance. The cooperative Jahn Teller effects (OO) are therefore forbidden. Rhombohedral phases are generally more itinerant of the orthorhombic ones, because of the absence of Jahn-Teller localization effects. In Figure 1.16 the rhombohedral (grey dashed line) and orthorhombic (black line) variants are shown together with the ideal cubic perovskite. Figure Comparison between the rhombohedral (dashed grey line) and orthorhombic (black line) variants to respect to the perovskite cubic cell (thin grey line). The double cubic unit cell is also represented. Rhombohedral and orthorhombic parameters can be expressed in terms of cubic lattice parameter: a r = b r = c r = a c. 2 α r 60,38 a orth a c. 2 ; b orth a c. 2 ; c orth 2. a c At room temperature the system La 0.7 Sr 0.3 MnO 3 has therefore a rhombohedral structure with a r Å and α r 60,38, even if the pseudocubic approximation with a c = b c = c c Å will be often adopt. 30

44 CHAPTER 2- PROPERTIES OF EPITAXIAL THIN FILMS OF LA 1-X SR X MNO 3 CHAPTER 2 PROPERTIES OF EPITAXIAL THIN FILMS OF LA 1-X SR X MNO 3 In this thesis we are dealing with epitaxial films of La 1-x Sr x MnO 3 with Sr concentration of 0.3. Generally speaking thin films (with thickness at least less than 1 μm but even more, around several nanometers) are essential for microelectronics. Going from bulk to thin film in several cases some properties change, in strict connection both to the reduced dimensionality (finite thickness), to interface effects and to possible novel characteristics due to strain-stabilized non-bulk symmetries. 2.1 Mismatch and relaxation degree in epitaxial films To obtain good epitaxial films it is of paramount importance the choice of a suitable substrate that must have chemical composition, structure and lattice parameters similar to the material we want to deposit. In the case of manganites it has been widely discussed [Maurice et al. 2003, Haghiri Gosnet et al. 2003, Millis et al. 1998] that a small epitaxial distortion of the unit cell can deeply influences the physical properties of the bulk, as it affects Mn-O length and Mn-O- Mn angles which (mainly through double exchange mechanism) affect in turn electrical and magnetic properties. Different distortions can be obtained with the opportune substrate. Among the most common used substrates for manganites there are SrTiO 3 and LaAlO 3, both perovskites with different lattice parameters: SrTiO 3 is cubic with a = 3,905 Å, while LaAlO 3 is pseudocubic (actually rhombohedral as we shall discuss later in CHAPTER 3) with pseudocubic lattice parameter of a pc = 3,786 Å. 31

45 CHAPTER 2- PROPERTIES OF EPITAXIAL THIN FILMS OF LA 1-X SR X MNO 3 Here we deal with epitaxial films of La 0.7 Sr 0.3 MnO 3, that as already explained in 1.8, is rhombohedral with only a slightly distortion from cubic, so that the pseudocubic approximation with a pc = 3,873 Å can be used. The definition of lattice mismatch δ at the interface between substrate and layer is given in terms of the lattice parameters in the plane of the deposition: δ = a bulk a a bulk L = Δa a where a bulk and a L are the in-plane lattice parameters of the substrate and the film respectively. Considering a pseudocubic approximation of a cube on cube growth we have a positive mismatch of 0, 81% for La 0.7 Sr 0.3 MnO 3 (001)/ SrTiO 3 (001) and a negative mismatch of 2,2% for La 0.7 Sr 0.3 MnO 3 (001)/LaAlO 3 (001). The sign of the mismatch indicates the nature of the isotropic strain (ε xx = ε yy ) induced by the substrate on the layer: i.e. positive mismatch leads to tensile strain in the plane of deposition (as for La 0.7 Sr 0.3 MnO 3 on SrTiO 3 ) while negative strain leads to in-plane compressive strain (as for La 0.7 Sr 0.3 MnO 3 on LaAlO 3 ). In the same way we can also define an out of plane mismatch: δ = a bulk a c bulk L = Δc c leading to an out of plane strain ε zz. The in-plane and out-of-plane strain are linked by the following relation: ε 2 ν = 1 ν zz ε xx being ν the Poisson ratio for the material constituting the layer. For small layer thickness usually it can be expected that the in-plane lattice parameter of the manganite is determined by the substrate. Once a critical thickness is reached, relaxation mechanism recovers the bulk structure. 32

46 CHAPTER 2- PROPERTIES OF EPITAXIAL THIN FILMS OF LA 1-X SR X MNO 3 The degree of relaxation is defined in terms of the lattice parameter of the substrate and the film in the deposition plane [ Holy et al. 1999]: a R = a L, strained L, bulk it naturally follows that R can assume all values between the two extremes 0 and 1 corresponding respectively to a fully strained layer if R = 0 ( a L, strained = a bulk ) and fully relaxed layer if R = 1 (a L, strained = a L,bulk ). Fully strained films are also called pseudomorphic layers. For La 0.7 Sr 0.3 MnO 3 films the critical thickness as well as the relaxation mechanisms depends on the deposition technique and on the substrate. In case of Pulsed Laser Deposition it has been shown that full relaxation occurs roughly above 30 nm for La 0.7 Sr 0.3 MnO 3 on LaAlO 3 and above 80 nm for La 0.7 Sr 0.3 MnO 3 on SrTiO 3 [Angeloni et al. 2004]. This difference can be easily understood considering that the density of elastic energy stores in a strained film depends on the square of the strain and is therefore higher for La 0.7 Sr 0.3 MnO 3 on LaAlO 3 relative to La 0.7 Sr 0.3 MnO 3 on SrTiO 3. Relaxation mechanisms have been experimentally observed for La 0.7 Sr 0.3 MnO 3 on SrTiO 3. Pseudomorphic growth of La 0.7 Sr 0.3 MnO 3 on SrTiO 3 is tetragonal and the recovering of the bulk rhombohedral symmetry implies both shear strain relaxation and lattice parameter relaxation. It has been shown that shear strain relaxes with the formation of twins at the film substrate interface [Maurice et al. 2003], while the bulk lattice parameters is reached through the creation of dislocations near the interface. For La 0.7 Sr 0.3 MnO 3 on LaAlO 3 is has been observed that different films having the same thickness close to the critical value and grown in the same condition can have different degrees of strain relaxation from almost fully relaxed to almost fully strained [Angeloni et al. 2004]. However, we note that the results concerning La 0.7 Sr 0.3 MnO 3 on LaAlO 3 must be taken with prudence and reconsidered in the light of the crystallographic peculiarities of the substrate that will be explained in details later in CHAPTER 3: apparently unusual behaviours of such films become in fact comprehensible when a proper description of their structure is kept into account. a a bulk bulk 33

47 CHAPTER 2- PROPERTIES OF EPITAXIAL THIN FILMS OF LA 1-X SR X MNO Strain effect on phase equilibria in La 1-x Sr x MnO 3 x = ( 0 1 ) It is widely accepted that epitaxial strain is an effective method to control and stabilize novel non-bulk electronic and magnetic phases for thin film of DMP. Strain effect in ferromagnetic metallic manganites has been modelled [Perroni et al. 2003], by properly taking into account the modification it induces in the Mn-O-Mn bond angle ϑ and in the Mn-O bond length d, which both appear in the empirical formula for the hopping of e g electrons between two neighbour Mn sites, which controls T C : t d 3.5 sin ϑ/2 [Medarde et al. 1995]. It was found that also for compressive strain (as it is for La 0.7 Sr 0.3 MnO 3 on LaAlO 3 ) a reduction of the transition temperature T C can occur, in contrast to the simpler interpretation in terms of contraction of the in-plane Mn-O bond length d alone, which should lead to an increase of the electron in-plane hopping t and thus T C. The same result is obtained considering two sources of the strain: a uniform compression that tends to increase the hopping electron transfer amplitude reducing the importance of the electron-lattice coupling and a biaxial distortion leading to an increase of the Jahn-Teller splitting in e g levels that in turns lead to an increase of the tendency of the electron to be localized. The dependence of Tc on the epitaxial strain according to the two sources of strain can be represented by means of the formula [Millis et al.1998]: ( ) ( 0) 1 * 1 T c ε = T c ε = αε B Δε, with, 2 α = dtc T d c ε and 1 d Tc Δ = * 2 B Tc dε where ε B = ε zz +2 ε xx and ε*= 1/2( ε zz- ε xx ) are two parameter that keep into account the bulk strain and the biaxial (Jahn-Teller) strain respectively. As the bulk contribution can be either positive or negative depending on the sign of the biaxial strain (positive in case of compressive strain and negative for tensile strain), while the Jahn-Teller contribution is 34

48 CHAPTER 2- PROPERTIES OF EPITAXIAL THIN FILMS OF LA 1-X SR X MNO 3 always negative, the variation on T c value can be either positive or negative. The actual variation is therefore dependent on the particular used substrate. For the system La 1-x Sr x MnO 3, the effect of strain due to different substrates SrTiO 3, LaAlO 3, LaAlO 3 ) 0.3 -(SrAl 0.5 Ta 0.5 O 3 ) 0.7 has been studied by first principle density functional calculations [Fang et al. 2000, Konishi et al. 1999] and compared with X ray diffraction, magnetic and magnetotransport analyses [Konishi et al. 1999]. The results are summarized in the phase diagrams of Figure 2.1. Figure 2.1- [From Konishi et al. 1999] Left panel: The extended phase diagram of La 1-x Sr x MnO 3 (LSMO) as a function of lattice strain c/a and doping level x. The dashed line represent the results for LSMO bulk, the result s for LSMO on LaAlO 3 and on SrTiO 3 are represented by means black triangles and black circles respectively. Right panel: The corresponding calculated magnetic phase diagram, the magnetic structures corresponding to the (c/a, x) coordinates marked with x are represented ion Figure 2.2 In the left panel of Figure 2.2 the experimental magnetic phase diagram of La 1- xsr x MnO 3 (as a function of lattice strain c/a and doping level x) is shown, which has to be compared with the correspondent calculated magnetic phase diagram shown in the right panel. The large variation of biaxial strain or of the c/a ratio due to highly strained growth onto different substrates can induce phase transitions accompanied by magnetic and magneto transport properties variations. These changes can be justified in terms of orbital ordering/disordering induced by the strain. 35

49 CHAPTER 2- PROPERTIES OF EPITAXIAL THIN FILMS OF LA 1-X SR X MNO 3 For La 1-x Sr x MnO 3 films with x = 0.3 the effect of strain induced by SrTiO 3 substrate is not strong enough for the stabilization of an antiferromagnetic orbital ordering with A-type or C-type antiferromagnetism. In case of deposition on SrTiO 3, films on La 0.7 Sr 0.3 MnO 3 retain ferromagnetic properties exactly as in the bulk. On the other side, for highly strained samples (c/a = 1.06) of La 0.7 Sr 0.3 MnO 3 on LaAlO 3 a C-type antiferromagnetic phase is stabilized. Figure 2.2 -[from Konishi et al.1999] Electron density distribution for the energy window of 0.6 ev width just below the Fermi level for the magnetic structure to the x in the left panel of Figure 2.1. The up-spin component and low spin component are shown separately. Manganese and oxygen atoms are denoted respectively by black and white spheres. In Figure 2.2 the electron density distribution calculation relative to the magnetic structures marked with x in Figure 2.1 are shown. Manganese and oxygen atoms are represented by means of black and white spheres respectively. The up spin component and the down spin component are shown separately. In the A-type phase the preferentially occupied orbitals are d x2-y2, so that in-plane conduction can occur, while in the C-type one, with preferentially occupied d 3 z2-r2 orbitals, the conduction within the ab plane is not permitted. The previous model has been used to justify the anisotropic behaviour of the resistivity observed in epitaxial La 0.7 Sr 0.3 MnO 3 films [Orgiani et al ]. 36

50 CHAPTER 2- PROPERTIES OF EPITAXIAL THIN FILMS OF LA 1-X SR X MNO 3 It can be noted that the representative point for highly strained La 0.7 Sr 0.3 MnO 3 on LaAlO 3 is very close to the transition line separating the F ferromagnetic region and C-type antiferromagnetic region. Therefore a competition between the two magnetic phases in this kind of films has to be expected [Aruta et al. 2006]. 37

51 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION CHAPTER 3 CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION LaAlO 3 is commonly used as substrate for the deposition of CMR doped manganites epitaxial films. The reason lies in the fact that it has a perovskite like structure with a well fitted pseudocubic lattice parameter. It also has good chemical stability under growth conditions. LaAlO 3 experiences a symmetry breaking of the crystal system upon cooling through a critical temperature and therefore is a ferroelastic material. The crystallographic transition in LaAlO 3 was firstly reported by Wood in 1951 [Wood 1951] and then by Geller and Bala in 1956 [Geller et al. 1956]. They all indicated a transition temperature T F = 435 C lower than the actual one, which has been recently redetermined by Hayward to be T F = 813 K [Hayward et al. 2005]. Upon cooling through the critical temperature, the structure transforms from cubic Pm 3 m to rhombohedral R 3 c. The rhombohedral structure corresponds to the Glazer system a - a - a - and is due to antiphase octahedra rotation around the ternary cubic axis [111]. Due to the smallness of the rhombohedral distortion, however, it is common to consider a pseudocubic cell with a pc = 3,79A and α pc ~ [Bueble et al. 1998] useful to simplify the discussion on the relationships between substrate and overgrown manganite epilayer, for which a pseudocubic description can be and usually adopted as well. The ferroelastic symmetry change of LaAlO 3, corresponding to the ferroic species m3mf3m in Aizu notation [ Aizu 1970], leads to formation of a number of energetically equivalent rhombohedral variants (domains), given by the order of the prototype symmetry group divided by the order of the derived symmetry group. At the transition, LaAlO 3 is therefore characterized by the formation of four kinds of rhombohedral domains. For a better understanding of the ferroelastic transition, we can think to the high temperature cubic cell and to the possible ways of deforming it by stretching or 38

52 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION compressing along the directions [111]. The four rhombohedral variants come from the four equivalent triad axes <111> of the m3m class. The rhombohedral domains are labelled as I, II, III, IV in Figure 3.1, in which the domains (in red) are shown within the cubic cell, with the [111] rhombohedral axis parallel to the <111> cubic direction. Figure 3.1-Four ferroelastic rhombohedral domains (in red) each with the [111] rhombohedral axis parallel to the <111> of the original cubic cell. The domains can be described using the hexagonal setting as well, and the transformation matrix to change the representation from cubic to hexagonal and from cubic to rhombohedral are: 39

53 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION 1 ( α, b,c) hex = ( α,b, c) cub ( α, b,c) r homb = ( α, b, c) cub Figure 3.2- Hexagonal, rhombohedral and cubic cell on the left; on the right: relation between hexagonal, cubic and rhombohedral unit cells. In Figure 3.2 the hexagonal, rhombohedral and cubic cells and their relationships are shown. Table 3.1 gives the lattice parameters of the three possible representations of LaAlO 3 : 40

54 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION Table 3.1: Lattice properties for the three representations of the LaAlO 3 cell. structure Lattice parameter ( Å)* α, β, γ ( ) hexagonal a h = b h = (4) c h = (1) α = β = 90 γ = 120 rhombohedral a r = b r = a r =5.3547(3) α = β = γ = (4)* (pseudo) cubic a c = b c = c c = (3) α = (1)* * Data from Bueble et al The strain matrices corresponding to the formation of the four domains are given in Table 3.2, together with the axis about which the octahedra rotation occurs. Table 3.2: The four domains due to ferroelastic transition with correspondent strain tensor and unique threefold axis of rotation. domain I II III IV Strain tensor 0 e e Axis of rotation [ ] e 0 e e e 0 0 e e e 0 e e e 0 0 e e e 0 e e e 0 0 e e 111 [ 111] [ 111] [ 111] e 0 e e e 0 The four pure domains can be coupled in six different ways leading to the generation of the domain structure. With reference to the pseudocubic cell, domain walls can be of two types, {100} pc {110} pc, so that there are twelve physically distinguished couples of twin domain orientations. The possible domain walls for the different couples of domain are reported in table 3: 41

55 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION Table 3.3: Possible domain wall for each couple of domains. Couple of domains I, II I, III I, IV II, III II, IV III, IV Allowed domain wall (101), (010) (011), (100) (110), (001) ( 110) (001) ( 110), (001) ( 10 1), (010) The coexistence in the same region of all the four domains produces the typical chevron tiling. A schematic draw of a chevron tiling is shown in Figure 3.3 in which the possible domain walls separating different domains are also indicated. Figure 3.3- Schematization of a typical chevron tiling structure originated by the four different domains in the same region. 42

56 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION 3.2 Optical microscopy on LaAlO 3 substrates Polarized light microscopy (PLM) In this section we show the room temperature optical micrographs of the as-received substrates and of the same substrates after the deposition of La 0.7 Sr 0.3 MnO 3 films. For the optical observation the LAO substrates have been freely mounted on the rotary stage of a Leinz Orthoplan Pol microscope with crossed polars. Samples were mechanically polished and cleaned with suitable solvents. After polishing, to the aim of releasing possible strain due to the mechanical polishing itself, they were annealed for several hours at quite low temperature of 623 K. It is worth to note that the used deposition temperature (973 K) was above the ferroelastic transition temperature (873 K) of LaAlO 3. It is also below the maximum temperature of 1173 K up to which La 0.7 Sr 0.3 MnO 3 retains a rhombohedral distortion [Wenbin et al. 1999]. This is schematically drawn in Figure 3.4. Figure Schematic of what happens during the deposition procedure. 43

57 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION From the scheme depicted in Figure 3.4 it follows that during deposition a rhombohedral La 0.7 Sr 0.3 MnO 3 film grows onto the cubic LaAlO 3 substrate. This latter in turn transforms and subdivides into domains upon cooling down to room temperature. Domains, as confirmed by optical birefringence, are present in the LaAlO 3 substrates before and after the thermal cycle experienced during deposition As received substrate In Figure 3.5 the typical domain pattern of an as-received LaAlO 3 substrate is shown with a magnification of 10x. Different coloured stripes, parallel to the crystallographic direction [100] and [010], are present, that can be identified as different domains separated by domain walls of {110} pc type, having their traces parallel to [100] and [010] pseudocubic directions but inclined by 45 to respect to the deposition plane [Bueble et al ]. Figure 3.5-(magnification 10x)-Domain structure on an as-received (001) LaAlO 3 substrate at room temperature. PLM image shows strongly birefringent lamellas oriented approximately along [100] pc and [010] pc.different coloured stripes correspond to different domains. The width of these domains lies between 5 μm and 50 μm. In the upper middle part of the sample, some so-called needle domains are visible at the interception of stripes along [100] pc and [010] pc, typically formed when incompatible perpendicular systems of lamellar {100} pc boundaries approach each others. 44

58 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION In Figure 3.6 the as-received substrate has been rotated by 45 with respect to the analyzer and polarizer. Most domains appear dark even if there are regions with residual birefringence in correspondence of the highly strained areas when incompatible chevron types join. As in the previous image, lamellar stripes ascribed to domains separated by domain walls with traces along [100] and [010] pseudocubic directions are evident. Figure 3.6 -(magnification 10x)- As received LaAlO 3 substrate under crossed polars in nearly extinction position, the traces of domain wall running along [100] and [010] pseudocubic directions are visible; residual birefringence is evident in highly strained area. 45

59 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION Substrate after the deposition of LSMO 20 nm film Figure 3.7- Upper panel: (magnification 10x) Optical micrograph of LaAlO 3 substrate after deposition of a 20 nm thin layer of LSMO. The domains pattern is still present and well recognizable as well as an area where domain with domain walls oriented perpendicular to each other approach. The marked region, at higher magnification (20 x) and after a rotation of 45 under the microscope is shown in the bottom panel. Domain wall running along [010] pc direction is well recognizable and a not flat deposition surface can be noted by this image. 46

60 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION Figure 3.7 shows the optical micrographs of the substrate after the deposition of a thin (about 20 nm) layer of LSMO. In the upper panel the domain structure is well visible an composed by two differently oriented chevrons, identified as adjacent different coloured stripes along [100] and [010] pseudocubic directions, that approach each others giving rise to a chevron boundary [Harrison et al. 2004] recognizable as the highly strained region oriented along [110] direction in the middle part of the images. In the upper left region the presence of some needles is also evident. In the lower panel, to the aim of better evidencing the domains structure which gives rise to the coloured stripes, the marked region of the upper panel is shown at higher magnification and after a clockwise rotation of 45. These coloured stripes can be identified as domains of type I and type II (due to the deformation of the original cube along the threefold direction [111] and [-111] respectively) separated by domain wall of (100)-type perpendicular to the growing plane. As a result of this crystallographic description, the surface of the substrate will be not flat as schematically explained in Figure 3.8. Figure 3.8-Schematic representation of domain of type I and type II separated by domain wall of (100) type, giving rise to a non flat surface. 47

61 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION Figure 3.9- (magnification 10x) Substrate with 20 nm LSMO film under crossed polars. Stripes running along [100] and [010] directions with width as small as 5 m are visible. Figure (magnification 20x) Substrate with 20 nm LSMO film under crossed polars, the complex microstructure is evident. 48

62 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION Figure The marked region of Figure 3.9 is shown at higher magnification (32x); the complicated microstructure of the substrate can be observed. Domain walls running along [100], [010] and [110] can be observed, the typical chevron tiling structure is also recognizable. Other optical micrographs are given in Figures 3.9, 3.10, 3.11, showing almost the same region at increasing magnification 10x, 20x and 32x respectively. A complicated microstructure of the substrate is observed: stripes running along [100] and [010] pseudocubic directions but also along [110] are revealed, this latter to be related to {110} pc domain walls perpendicular to the layer deposition surface, i.e. to the (100) pc. As in the optical micrographs with only the substrate also now needles structure are present, being this a clear sign of interception of two incompatible chevron, the interpenetration of chevron of domains of different orientations is in fact often mediated by needles twins formation [Harrison et al. 2004]. In the bottom left part of Figure 3.10 highly strained region brighter to respect to other region is present at the interception of different oriented incompatible chevrons. In Figure 3.11 the marked region of Figure 3.9 is shown at 32x magnification. At this magnification the typical chevron tiling structure is recognizable, this structure, as previously explained, origins from the coexistence in the same region of the four rhombohedral domains. 49

63 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION Figure Optical micrograph of LaAlO 3 substrate with 20 nm LSMO layer, beside of the wider coloured striper running along [010] direction a smaller microstructure with stripes running along both [100] and [010] direction is visible, and the narrower recognizable domains ( marked by white arrows) have dimension down to 2 μm. In Figure 3.12 a region of LaAlO 3 substrate with 20 nm LSMO film is shown. Different coloured wide stripes with traces running along [010] direction are evident, but at this magnification an adding microstructure is recognizable. Littler domains are segnalated by the white arrows in Figure 3.12, the dimension are down to 2 μm Substrate after deposition of 9 nm film In Figure 3.13, 3.14 optical micrographs on LaAlO 3 substrate with overgrown 9 nm LSMO layer are shown. Again the complicated twin microstructure of the substrate is clearly evident. In Figure 3.13 upper panel - made with a 4x magnification- an overview of the substrate is given. 50

64 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION Chevron oriented mainly along [100] and [010] pseudocubic direction are evident, and the two orientations approach both with needles formation (upper right part) and with a highly strained chevron boundary. To better evidentiate the chevron boundary the marked region has been rotated by 45 anti-clockwise and observed at higher magnification (10 x) in Figure 4.13 bottom panel. Figure LaAlO 3 substrate with 9 nm LSMO layer under crossed polars. Upper panel- (magnification 4x) Overview of the sample with two different chevron orientation running parallel to ] [010] direction, the marked region with the so-called chevron boundary is rotated by 45 and shown at 10x magnification in the bottom panel. 51

65 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION At this magnification the two chevron orientation are well evident as well as the way in which they approach, the brighter region is the most strained. The red arrows mark traces of domain walls of {110} pc type, as a result a typical stair-step surface is formed in that region. Figure 3.14-(magnification 10 x) Optical micrograph of LaAlO 3 substrate with overgrown 9 nm LSMO film. At least in Figure 3.14 a further image of the same sample is shown. Domain wall traces are mainly recognizable as coloured stripes along [010] direction, moreover additional traces along [100] are visible, at the interception between different twin domains type a strained brighter region is evident. 52

66 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION 3.3 AFM on LAO substrate We conclude this CHAPTER giving a further evidence of the presence of twinning in the substrate after the deposition process of the manganite epitaxial films. One image obtained by scanning probe atomic force microscopy (AFM) is shown in Fig. 33. The image refers to the substrate with deposited LSMO20. From this image two chevron orientations running parallel to the sample sides (along [100] and [010] directions) are clearly visible. Figure AFM on a 10 μm x 10 μm region of LaAlO 3. The presence of two different chevron orientation is evident, with chevron domain wall oriented along [100] and [010] pseudocubic directions. 53

67 CHAPTER 3- CRYSTALLOGRAPHY OF FERROELASTIC LAALO 3 : THEORY AND EXPERIMENTAL CONFIRMATION Figure 3.16 AFM on a 5 μm x 5 μm region of LaAlO 3. The presence of two different chevron orientations is evident, with chevron domain walls oriented along long [100] and [010] pseudocubic directions. In Figure 3.16 the same features are visible for a smaller area: 5 μm x 5 μm. In the region of the sample where the two chevron orientations approach a chevron boundary is clearly visible. 54

68 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION CHAPTER 4 EXPERIMENTAL RESULTS AND DISCUSSION In this chapter we present and discuss the experimental results concerning the structural and magnetic characterization of several La 0.7 Sr 0.3 MnO 3 grown on ferroelastic LaAlO 3. The discussion will focus on the effect of the structural details on the magnetic behaviour. The films were epitaxially deposited through Molecular Beam Epitaxy (MBE) at the University of Salerno. Some details on the deposition technique can be found in Appendix B. The CHAPTER is divided in two sections. The first section (paragraph 4.1 and subparagraphs) contains the experimental results for two relaxed LSMO/LAO layers, the first one of nominal thickness of 9 nm, which will be referred to as LSMO 9r, and the second one of nominal thickness of 20 nm (LSMO 20r). The second section (paragraph 4.2 and sub-paragraphs) contains the experimental results relative to five fully strained films: two of them have nominal thickness of 40 nm and the other three have decreasing thicknesses of 20 nm, 10 nm and 5 nm. Hereafter these samples will be referred to as LSMO40, LSMO40a, LSMO20, LSMO10 and LSMO5. The LaAlO 3 substrate is often referred to as LAO. For the two relaxed films we shall discuss the structural and magnetic characterization, performed by means of high resolution X ray diffraction and SQUID magnetometry. High resolution x-ray diffraction measurements have been performed by means a D8 Discover Bruker diffractometer. A brief overview on X-ay diffraction, as well as some information about the instrument, are given in Appendix A. Magnetic measurement have been performed using a SQUID magnetometer, which is included in Appendix B. For the fully strained samples, in addition, high resolution transmission electron microscopy measurements will be also presented. These measurements have been 55

69 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION performed at the Queen s University of Belfast with a TEM TECNAI FEI Tecnai F20 200kV microscope. Details on the microscope are reported in Appendix B. 4.1 Results on relaxed films High resolution X-ray diffraction To investigate the effect of the substrate ferroelastic transition on the structure deposited LSMO20r and LSMO9r films, room temperature high resolution X-ray analyses were performed. In particular we performed rocking curves (also called ω-scans) and reciprocal space maps (RSM), two of the typical reciprocal space scans in thin films characterization by X-ray diffraction. Both these scans are powerful tools for the study of twinned crystals in which the reciprocal lattice vectors related to a set of equivalent lattice planes in different twins are not parallel. To perform a rocking curve, as clearly explained by Harrison [Harrison et al. 2004], a suitably oriented crystal of LaAlO 3, with an overdeposited LSMO film, is placed close to the diffraction condition for a selected Bragg reflection, with the reciprocal lattice vectors of different twins lying within the scattering plane. The crystal is then rotated by an angle ω about an axis perpendicular to the scattering plane, to bring into the diffracting condition one twin at a time (Figure 4.1). 56

70 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure 4.1-Schematic representation of the general principle of rocking curve for a twinned crystal containing two domains (A and B). By rotating the crystal, one domain at time can be brought consecutively in diffraction position. A rocking curve, which is a plot of integrated intensity as a function of ω, will show individual peaks corresponding to each of the twin domains. The angular difference between the peak positions in the rocking curves is related to the angular difference between the reciprocal lattice vectors in different domains. The complex crystallography of ferroelastic LaAlO 3 is the reason for the complex rocking curve that can be obtained. As we explained in CHAPTER 3, the ferroelastic transition in LaAlO 3 produces four pure domains that can be coupled in six different ways leading to domain wall formation, which can be of two types for each couple. The coexistence in the same region of all the four domains, with three mutually compatible domain walls, gives rise to the typical chevron tiling structure, and six different type of chevron can be recognized [Bueble et al. 1999]. Since each chevron contains four domains, there must be 24 distinguishable domain orientations. The number of the peaks and the angular different between them is strictly dependent on the geometry of the aggregates in the ferroelastic crystal under diffraction condition at the same time and for slight variation of incident angle. Simulated rocking curves of LaAlO 3 crystals in (001) pc orientation have been reported for different twin structures [Harrison et al. 2003], i.e. for crystals containing different aggregates of ferroelastic domains, and can be compared with our X-ray experiments. The collection of a reciprocal space map consists of iterated ω scans at fixed 2ϑ values, for a certain range of ω/2ϑ, around a given reciprocal node of the pseudocubic phase of 57

71 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION LaAlO 3, or, alternatively, of iterated q x scans (transverse scan) for a certain range of the q z coordinate (longitudinal scan) around the corresponding point (q x, q z ). The resulting twodimensional map will contain the scattered intensity associated with the Bragg nodes of the twins. When the paraelastic cubic phase of LaAlO 3 undergoes the transformation to the ferroelastic symmetry, some of the Bragg node will split into more, each one related to one particular domain. This splitting will appear in the reciprocal space map. Figure 4.2 shows the rocking curve made on the (002) pc reflection of the substrate LaAlO 3 for the sample LSMO20r. The letters Ds have been used to mark the four recognizable domains. Figure 4.2- Rocking curve of LaAlO 3 substrate of LSMO20r made around the (002) pc reflection. Four domains marked as D are visible. The analysis of LSMO20r has been made without inserting in the primary optics the V- groove monochromator, with the aim of obtaining more intensity. The doubling of every peak in the rocking curve of Fig. 4.2 is therefore the consequence of the simultaneous presence, for each domain, of the Bragg peaks for kα 1 and kα 2. The reciprocal space map of LSMO20r made around the (002) pc reflection of the substrate is shown in Figure

72 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure 4.3- Reciprocal space map around the (002)pc reflection of the LAO substrate of LSMO20r sample. As can be seen, the reciprocal space map of Fig. 4.3 has Miller indexes H,L as (x,y) coordinates. The relation between H and L and the scattering vector q x and q z are : q z 2π 2π = L q x = H a a where a is the lattice parameter in pseudocubic approximation. Different domains D of the substrate can be appreciated along a one-dimensional section at L = cost 2. The LSMO20r diffusion around the (002)pc node is recognized at a lower L value. It can be noted that the LSMO20r diffuse scattering is anomalously wide along H, with a full width at half maximum FWHM value mainly influenced by the twin structure of LaAlO 3 substrate. This result is analogous to what found in case of Ca-doped La 0.7 Ca 0.3 MnO 3 film deposited on LaAlO 3 by RF magnetron sputtering, also twinned [Song et al. 2001]. This indicates the presence of different crystallographic orientations in LSMO20r, as in the substrate, not well resolved due to the complex structure of the substrate rocking curve. The diffusion of LSMO9r extends orientatively between the value 59

73 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION L= 1.90 and L =1.95 with a maximum around L = 1.93 that is closer to the L value for relaxed film than that for strained film as can be estimated considering a pseudocubic lattice parameter of Å. Therefore the LSMO20r film has to be considered relaxed. This conclusion is supported by the observation of the reciprocal space map made around the (103) pc asymmetric reflection, presented in figure 4.4. Figure 4.4-Reciprocal space map around the (103) pc reflection of LaAlO 3 substrate for LSMO20r. Along the longitudinal direction (represented by a dot-dashed line) there are the intensity nodes due to diffraction from the (32 1 ) and (431) planes of LaAlO 3 for both kα 1 and kα 2 components (marked as D 1 and D 2 respectively), while following the transversal direction from the D 2 node a ferroelastic domain can be observed, marked as D 3. The presence of the diffusion due to LSMO20r film in longitudinal direction (evidenced by means a dashed blue ellipse) indicates that the film is relaxed. In correspondence of the coordinate H = 1 and L = 3, one finds the reciprocal lattice node of the substrate, which splits for the presence of the kα 1 and kα 2 components and of domains. In fact, even if we are using the pseudocubic approximation for simplicity, we must remember that the monocrystalline LaAlO 3 has actually a rhombohedral structure and is divided into ferroelastic domains. From the reciprocal space map of Figure 4.4. both the 60

74 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION rhombohedral symmetry and the domain structure can be observed and rationalized as follows: if we consider the correct rhombohedral description for LAO, we cannot disregard that the (103) pc (or equivalently (310) pc ) family of planes splits into two. In Figure 4.5 and 4.6 the simulations of powder pattern for LaAlO 3 in the two non equivalent descriptions (pseudocubic and rhombohedral) are shown [the simulations have been made by means the simulation program Powdercell version 2.4, W. Graus, G. Nolze]. Figure 4.5- Simulation of the powder pattern of LaAlO 3 using cubic description. 61

75 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure Simulation of the powder pattern of LaAlO 3 using rhombohedral description. Let us focus the attention on the cubic (310) Bragg peak, that splits into two rhombohedral components (32 1) (431) going from lower to higher angles (Figure 4.7), and Figure 4.7- Splitting of the (310) cubic reflection (on the left) when the rhombohedral description for LaAlO 3 is adopted (on the right). In rhombohedral description the two peaks correspond to (32 1 ) and (431) planes. 62

76 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION let us observe again the reciprocal space map of Figure 4.4: along the longitudinal direction we find intensity nodes due to diffraction from the (32 1 ) and (431) planes for both kα 1 and kα 2 (marked in Figure as D 1 D 2 respectively), while following the transversal direction from the D 2 nodes we find a ferroelastic domain (marked as D 3 ). The diffusion from the LSMO20r film can be recognized (evidenced in Figure 4.4 by means blue dashed ellipse) along the longitudinal direction on the reciprocal space map, which proves the film to be relaxed. For the thinner sample LSMO9r, the rocking curve of the (002) pc reflection of the substrate, collected with the use of a 2-bounces V-groove monochromator, is shown in Figure 4.8. Its simpler profile constituted only by two well resolved peaks means that the same Bragg condition is valid for two domain states at a time. Figure 4.8- Rocking curve of LaAlO 3 substrate of LSMO9r. Two ferroelastic domains marked with D are recognizable as two peaks with comparable intensity. The fact that the intensity of the two peaks is comparable is connected to the comparable volumetric fraction of each domain [Harrison et al. 2004]. The two peaks are separated by ~ 0.1 and their FHWM is of ~0.04, indicating a high degree of crystallization for each domains. Figure 4.9 shows the corresponding reciprocal space map around (002) pc reflection of LaAlO 3 for LSMO9r. 63

77 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure 4.9-Reciprocal space map around (002) pc reflection of the substrate for LSMO9r. The domains are clearly visible and well resolved for both the substrate and for the film. It is worth to remark that the domain separation along H direction in LSMO9r film is the same as in the substrate and this is a clear sign of the strict connection existing between twin domains in the substrate and those in the film. The formation of the observed twins must have taken place in La 0.7 Sr 0.3 MnO 3 films when domains raised in LaAlO 3 substrate just below the cubic to rhombohedral transition temperature T F. The domain structure of the substrate acted as template for the manganite film, a result which is in agreement with recent findings concerning the role of the substrate ferroelastic transition on the presence of twinning in La 0.7 Sr 0.3 MnO 3 films [Laviano et al. 2005, Chiodoni et al. 2005]. Therefore we suggest that the substrate transformation acts as a driving force for the transformation of the La 0.7 Sr 0.3 MnO 3 film towards its bulk rhombohedral symmetry and that the twin law for the Pm3m R3 c symmetry change is respected in the film, as it would have been in the bulk. If this would be the case, the observed domains in the manganite films would be correctly called transformation twins. This is different to what happen La 0.7 Ca 0.3 MnO 3 on SrTiO 3 when this latter undergoes the cubic-tetragonal ferroelastic transition at 105 K [Vlasko-Vlasov et al. 64

78 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION 2000]. Also in this case domains are formed in the manganites film, however without crystallographic correlation with those of the substrate. The origin of the herewith discussed twinning differs also from that of the domains found in La 1 x Sr x MnO 3 coherently grown on untwinned substrates, like (001)-oriented SrTiO 3 [Maurice et al.2003, Farag et al. 2005], which are explained in terms of strain relaxation mechanisms. According to this explication, the part of the elastic energy due to the lattice mismatch is reduced by the formation of misfit dislocations at the film/substrate interface, while the part which is related to the shear strain, and which results from the rhombohedral symmetry of La 0.7 Sr 0.3 MnO 3 at room temperature, when it is matched onto a cubic substrate, is diminished by the formation of structural domains with an alternating sign of shear. Such a structural domain pattern can be also called a twin pattern, since the crystallographic orientation of neighbouring domains is similar to common twins. However, these domains are more similar to mechanical twins than to transformation twins Magnetic properties On the light of the structural characterization which showed the complex microstructure of both substrate and film, it is interesting to investigate which is the influence of this peculiar structure on the magnetic properties. In particular, the presence of twin boundaries in the LSMO films introduces into them a high degree of structural disorder (planar defects) and a variation of the lattice strain level near the boundaries. One can suppose, therefore, that the magnetic behaviour will display features connected to defects and deviations from full periodicity. It is well known that different disordered systems, as spin glass (SG) and cluster spin glass (CSG) are characterized by a separation in the ZFC FC magnetization curve at an irreversibility temperature (T irr ) which indicates the starting of the irreversibility. Moreover the zero field curve (ZFC) magnetization (M ZFC ) of this disordered system has a 65

79 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION cusp indicating the freezing temperature of the spins, being the freezing temperature determined as the maximum of M ZFC [Mydosh 2003]. Before starting to see the magnetic response of our sample we shall show what has to be expected in the case of the bulk. Figure 4.10 shows the ZFC-FC magnetization curves for a LSMO single crystal, grown by the floating-zone method, at applied field of 20 Oe (simple solid lines) and 5 koe (solid lines + symbols) [ Liu et al. 2004]. The absence of irreversibility in the ZCF-FC branches at low applied field, as well as the absence of anomalities like cusp in the ZFC curve shows a typical ferromagnetic behaviour, as it is expected for this wide-band Zener phase without any structural disorder. The presence of rhombohedral twins does not disturb the ferromagnetic properties of the crystals. Other investigation, using a magneto-optical indicator film and imaging technique and an X-ray topography, showed a strong correlation between magnetic and twin domains in LSMO crystals [Khapikov A. et. al 2000] which reflects itself on the crystal magnetic anisotropy and gives as easy axis the [100] cubic direction. Figure [From Liu et al. 2004], ZFC FC magnetization curve at 20 Oe evidencing a non spin glass behaviour of the sample To the aim of probing the presence of some kind of thermomagnetic irreversibility induced by the disorder due to the twinning structure, ZFC FC magnetization measurement versus temperature were performed on our sample for 4 K < T < 400 K. The magnetization measurements were performed using a Quantum Design MPMS5 XL5 SQUID magnetometer, equipped with a superconducting magnet producing fields up to 66

80 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION 50 koe and calibrated using a Pd standard; the sensitivity for the magnetic moment is 10 8 emu. The measurement protocol used for such measurement is the following: ZFC magnetization curve The sample is cooled down to the lowest measurement temperature ( 4 K) without any applied magnetic field and then once the temperature is stabilized the magnetization is recorded versus temperature up to 400 K (that is above the bulk Curie temperature). FC magnetization curve A constant applied magnetic field which is switched on at 400 K and the magnetization vs temperature is recorded on cooling down the sample to 4 K. In Figure 4.11 the ZFC-FC magnetization curves versus temperature for the LSMO20r sample are plotted, for applied field parallel to the film plane. Three different magnetic fields of 5 Oe, 1 koe and 10 koe were used. For the lower field (5 Oe) M ZFC curves has a peak at T f = (260 ± 5) K. A separation between ZFC and FC curves is present below a slightly higher temperature T irr. The FC curve shows that the magnetization slightly decreases until a broad minimum corresponding to the inflection point of the ZFC curve, below which it starts to increase again going to lower temperature. From the ZFC-FC magnetization curves at higher applied field (1 koe and 10 koe) it can be seen that the peak in the ZFC curve tends to disappear with increasing the field. The separation between ZFC and FC curves is still present at 1 koe and for temperature below T irr = 70 K, while an applied field of 10 koe is such to remove any separation between the ZFC and FC curves. 67

81 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure ZFC-FC magnetization curves vs. temperature for LSMO 20r.The magnetic field is applied parallel to the deposition plane, being the magnitude 5 Oe, 1kOe and 10 koe respectively. Figure 4.12 shows the ZFC-FC magnetization curves of LSMO20r with an applied field of 5 Oe and 50 Oe, this time perpendicular to the film plane. The separation ZFC-FC is qualitatively similar to that obtained for H parallel. The peak of the ZFC magnetization curve at 50 Oe is at T = (205 ± 5) K, while the thermomagnetic irreversibility has already started around T irr = 250 K. 68

82 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure ZFC-FC magnetization vs temperature curves with 5 Oe ( left panel) and 50 koe (right panel) magnetic field applied perpendicular to film plane for LSMO 20r. The Curie temperature (T C ) for LSMO 20 is 289±1 K, as evaluated from the low field magnetization (with H = 5 Oe) fitted by the mean field theory expression M (T) = A (T C T ) 1/2 in the vicinity of the transition [Zijlstra 1967]. The Curie temperature is notably lower than the bulk value of 378 K. Its reduction can be related to the disorder due to twin boundaries and to other extended defects (dislocations) which may be present, because the LSMO20r thickness is above the critical value for pseudomorphic growth. In addition, the effect of epitaxial strain on T C should be considered. Different strain effects in manganites can induce variation on the value of the Curie Temperature compared to that of the bulk. Strain effect in manganites has been modelled [Perroni et al. 2003, Yuan cond/mat], and already explained in 2.2. In the present case however, since our samples have been proved to be structurally partially relaxed, we expect that strain plays a minor role on T C. Last, an important factor to be considered for the decrease of the Curie temperature T C in thin films is the finite size effect [Fisher et al 1972, Barber 1983] which results because of the finite film thickness d that limits the divergence ξ of the spin-spin correlation length at T C. This causes a decrease of T C with respect to the bulk value for d < ξ. For instance, the finite size scaling of T C has been reported for the lanthanum cobaltite La 0.7 Sr 0.3 CoO 3 thin films [Fuchs et al. 2005] for thickness between 2.6 nm and 42 nm. 69

83 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION The ZFC and FC magnetization of the LSMO9r film for H parallel and H perpendicular to the deposition plane are shown in Figures 4.13 and 4.14 respectively. The first peculiar feature that can be noticed for this sample and for H perpendicular is that with applied field up to 1 koe, the ZFC-FC irreversibility is observed almost in the whole measured temperature range. We notice that the more evident splitting between M ZFC and M FC takes place in the low temperature range, i.e. below the major rising of the magnetization (Figure 4.13). Figure ZFC-FC magnetization curves vs. temperature for LSMO9r. The magnetic field is applied parallel to the film plane, being the magnitude 5 Oe, 1kOe and 10 koe respectively. 70

84 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure ZFC-FC magnetization vs temperature curves with 500 Oe ( left panel) and 1 koe (right panel) magnetic field applied perpendicular to the film plane for LSMO 9r. Nevertheless, the two curves remain separated up to about 350 K. This feature is more evident for the case with H perpendicular to film plane (see Fig. 4.14), but is also present for H parallel (Fig. 4.13). The high temperature irreversibility is not more detectable for H = 10 koe. The second salient feature of this thinner film is that, for H parallel to the film plane with H = 5 Oe, the peak at 140 K of M ZFC is associated with a coincident peak of M FC ; this behaviour is still observable at 1 koe, with the peak temperature shifted to about 100 K. The peaks disappear with an applied field of 10 koe. For H perpendicular to the film plane, the M ZFC curves show the peak with fields up to 1 koe, but there is no observable concomitant anomaly in the FC curves. Concerning the value of the Curie temperature for the LSMO9r film, the data analysis described for LSMO20 would lead to T C = 186 ± 1 K. Since this sample presents irreversibility, for fields as high as 1 koe, up to 350 K, we prefer to indicate this temperature as, in order to emphasize that it is the temperature that marks the passage between two magnetic ordering regimes. This point will be discussed in more detail in the following. * T C The more evident feature of the low field behaviour of both LSMO20 and LSMO9 is the presence of irreversibility between the FC and ZFC magnetization curves. A separation between M ZFC and M FC has been already reported for La 0.7 Sr 0.3 MnO 3 film grown on LaAlO 3 by sputtering [Xiong et al 2002] with thickness of 600 nm and ascribed to a spin- 71

85 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION glass like behaviour caused by the competition between ferromagnetism and antiferromagnetism, as a direct consequence of the random distribution of Mn 3+ and Mn 4+ ions, without mention to the possible role of the substrate-induced twinning on the observed lacking of true magnetic long range order. To the best of our knowledge, the magnetism of thinner films has not yet been discussed in this contest. A cusp in the M ZFC at T f, and a separation between M ZFC and M FC at T irr are both present in the magnetization curves of LSMO20 (see Figures 4.11, 4.12). Even though not conclusive, these features make a strong case in favour of spin-glass-like properties of LSMO20. Moreover, because it is also possible to identify a Curie temperature T C above both T f and T irr, we suggest that the irreversible magnetic behaviour of LSMO20 can be ascribed to a re-entrant spin glass (RSG). As described by Ito [Ito 2000], a RSG has to be considered a mixed phase of the long range ferromagnetic phase and the SG phase. The mechanism of the RSG transition is that, when the long range order is established at T C, some amount of disordered (not aligned) spins exists in the long range ferromagnetic network. With decreasing temperature, even some of the spins participating to the long range order escape from the ordered network, resulting in an increasing amount of the frustrated spins. On further lowering temperature, the frustrated spins freeze at T f. We propose to relate the observed magnetic behaviour to the microstructure of LSMO20r. We may suppose that double-exchange couplings are dominant inside each structural domain and that frustration appears in a transition region between them, which we identify with the twin walls. In other words, a coreshell-type structure is proposed, in which the core is ferromagnetic and metallic while the shell is spin disordered and insulating. This picture has already been used for La 0.7 Sr 0.3 MnO 3 nanoparticles with surface spin-glass layers formation [Zhu et al. 2001] and for polycrystalline films of La 0.7 Ca 0.3 MnO 3 which, beside the ferromagnetic core, display spin glass phases related to grain boundaries and grain surfaces [Wu et al. 2005]. The depicted micro-structural description of the twinned La 0.7 Sr 0.3 MnO 3 film is reminiscent of the two-phase scenario, according to which FM regions (in our case inside the twins) and AFI regions (induced in our case by locally enhanced strain at twin boundaries) coexist in manganites with CMR [Dagotto et al. 2006]. In particular, this description refers to the model of Ahn et al. [Ahn et al. 2004], in which the insulating phase has a short- or long-wavelengths lattice distortion, and the metallic 72

86 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION phase is undistorted, with emphasis put on the primary importance of structural aspects in causing the multiphase coexistence. The same coreshell model is also useful to explain the irreversibility observed in the thinner LSMO9r film well above * T C. The observed high temperature thermomagnetic irreversibility in LSMO9r is consistent with the formation of frozen FM clusters within the undistorted metallic core of the structural domains at T irr = 350 K. This temperature is not far from the bulk Curie point, a result that seems to indicate that the inner part of the twins is almost free from defects due to relaxation, as it should prevents the occurrence of a long range ferromagnetic ordering between the clusters for * T C < T < T irr. A global ferromagnetic state develops in the film only at * T C, as evidenced by the strong increase of the FC magnetization. The presence of ferromagnetic clusters in manganites for temperatures above T c has been recently predicted [Burgy et al. 2001], thus introducing different temperature regimes: a high-t regime where the system is magnetically disordered, an intermediate-t range with preformed ferromagnetic clusters with uncorrelated order, and a low-t regime where the clusters grow in size giving a globally ferromagnetic behaviour. The observation of the intermediate-t regime in La 1 x Sr x MnO 3 phases has been reported in the case of single crystal with Sr doping up to x = 0.16 and discussed in terms of a Griffiths phenomenon [Deisenhofer et al. 2005], suggested to a generic feature of manganite systems, not restricted to the weakly doped regime, when the structural distortions are sufficiently strong to allow for the bond disorder to be completely quenched. Actually, previous observations on optimally doped (x = 0.3, 0.4) single crystals have been claimed to be consistent either with a two phase scenario [Dagotto et al. 2001] or with the existence of the intermediate-t regime [Mannella et al. 2004]. As it concerns the anomalous behaviour of the M FC at low field H parallel, we note that the same feature has been already reported for La 0.7 Sr 0.3 MnO 3 films on LaAlO 3 [Tsui et al. 2000] and ascribed to a spin reorientation transition, an interpretation which stands on the assumption of a substrate induced compressive in-plane strain. This assumption is correct for defect free heteroepitaxial system, but questionable for heavily twinned substrate and microstructured epilayer, which can not be treated as single crystals. Moreover, at a closer look, also LSMO20r exhibits this kind of anomaly, even though much less evident (Figure 4.11), with the shallow minimum of M FC at 225 K. This result contrasts with the predicted 73

87 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION thickness dependence of the spin reorientation transition temperature, which has been shown to decrease for increasing film thickness [Pappas et al. 1990]. Since the anomaly in the M FC curve is only observed for LaAlO 3 substrate [Tsui et al. 2000], while it is absent for untwinned SrTiO 3, we wonder if this feature could be instead related to the substrate induced microstructure of the manganite film and in particular to a crystallographictexture-driven phase separation, an hypothesis that, we remark, that for Ca-doped films has already received some consideration [Moskvin et al. 2003, Park et al.2004, Fath et al. 2004]. Further investigations are needed to clarify this point Comparison with LSMO films on SrTiO 3 To make the previous discussion more clear and the related conclusions more robust we shall present the magnetization behaviour of a LSMO film grown on SrTiO 3 that, in contrast to LAO, has a cubic perovskite structure stable down to 105 K, temperature at which it undergoes a transformation towards a tetragonal phase with formation of three kinds of ferroelastic domains [Cao L. et al. 2000]. The ferroelastic transition temperature is about 200 K below the typical ferromagnetic Curie temperature of LSMO samples and, moreover, it is also well below the film deposition temperature. This means that the ferromagnetic transition of LSMO takes place without the presence of twin boundaries and related structural disorder which, as previously discussed in the case of LSMO/LAO, causes the competition between the AFM and FM interactions giving rise to the spin-glass features. Figure 4.15 shows the ZFC-FC magnetization curves at H= 5 Oe (applied parallel to the deposition plane) of a relaxed LSMO/STO sample whose thickness is 20 nm. The relaxation degree has been verified by means of X-ray diffraction measurement not reported here. 74

88 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure ZFC-FC magnetization curve on a 20 nm thickness film of LSMO deposited on STO substrate A dramatic difference with respect to the behaviour of LSMO/LAO samples can be observed: there is no cusp in the ZFC curve, which follows the FC one with only a small separation due to the smallness of the applied field. This kind of behaviour has nothing to do with the one expected for the canonical spin-glass and is instead typical of a ferromagnetic material. We can also note that the substrate transition al 105 K has no effect on both ZFC and FC magnetization branches, which is probably due to the structural elastic decoupling between film and substrate owing to the relaxed state of the epitaxial layer Conclusion on relaxed film We have shown that the structural and magnetic properties of relaxed La 0.7 Sr 0.3 MnO 3 grown by MBE on LaAlO 3 are strictly connected. High-resolution X-ray diffraction has shown that twins are present in the La 0.7 Sr 0.3 MnO 3 epitaxial films at room temperature, clearly resolved in reciprocal space maps and in direct crystallographic connection with those of the substrate. Both the analyzed films are therefore characterized by extended planar defects, whose orientation is fixed by the same twin laws valid for the substrate. The correlated quenched disorder due to twinning has been shown to reflect itself in the 75

89 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION magnetic behaviour, leading to a thermomagnetic irreversibility which has been discussed in terms of coexisting ferromagnetic and spin disordered regions within domain cores and domain walls, respectively. The previous results on twinned epitaxial films stress out the connection between quenched structural disorder and phase inhomogeneity in La 0.7 Sr 0.3 MnO 3 which, for the large width W of the e g band, is often described as a canonical double exchange system. Our results can be compared with the already mentioned observations concerning single crystals of the same composition [Deisenhofer et al. 2005], also claimed to be consistent either with the phase separation scenario, in contrast to the canonical description, or with the presence of an intermediate-t regime with the formation of a Griffiths phase: since the rhombohedral phase of La 0.7 Sr 0.3 MnO 3 derives from a paraelastic prototype, single crystals should also be twinned, which invites to a reflection upon the origin of the observed electronic and magnetic inhomogeneity. 76

90 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION 4.2 Results and discussion on strained LSMO films High resolution x-ray diffraction The structural characterization of the strained samples have been made in the high resolution configuration, using both monochromator (2 bounces V-groove) and collimator (Göbel mirror), to evidence and differentiate at best the different ferroelastic domains. Rocking curve on the (002) pc reflection and reciprocal space maps on both symmetric (002) pc and asymmetric (103) pc reflections have been performed. Figures 4.16, 4.17, 4.18, 4.19 and 4.20 show, on the left, the rocking curve made on the (002) pc symmetric reflection for the LSMO5, LSMO10, LSMO20, LSMO40 and LSMO40a films and, on the right, the reciprocal space map made aligning on the (002) pc symmetric reflection of the substrate. The symmetric reciprocal space maps reveal that all the La 0.7 Sr 0.3 MnO 3 films contain a replica of the ferroelastic domains structure formed in LAO at Tc = 813 K [Hayward et al 1998] during cooling to room temperature after deposition. We note in fact that in the maps every peak of the substrate has his own correspondent peak of the film, as can be clearly seen following the longitudinal direction with H = constant starting from each node of the substrate. Therefore a coherent growth of the domains of the film on the domains of the substrate can be deduced. Rocking curves on (002) pc pseudocubic reflections of the films provide a clear proof of their subdivision into domains. For the thinner film LSMO5, the shape of the Bragg node is the more elongated along the longitudinal direction L (q z ), which is clearly due to the finite size effect. It is known, in fact, that the shape of a reciprocal lattice node is assimilable to a point only in the ideal case of an infinite crystal, but it is an ellipsoid in any real case. This ellipsoid is subject to several broadening in different direction depending on the particular characteristic of the sample. The so called finite size effect leads to an elongation of the reciprocal lattice node in longitudinal direction when the sample size is finite perpendicular to that direction. This effect is more evident in the thinnest film. 77

91 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION The high resolution also permits to see the thicknesses fringes, marked in the reciprocal space maps with the letter F. Such fringes, which are indicative of a good quality of the film, are particularly evident for the LSMO10 and LSMO20 samples (Figure 4.17 right panel and Figure 4.18 right panel respectively). Figure 4.16-left panel: Rocking curve on LSMO 5 film. Four rhombohedral domains marked with D are recognizable; right panel: Reciprocal space map around the (002) pc reflection of the substrate for LSMO5. The same domain structure of the substrate is re-proposed also by the film. Figure left panel: Rocking curve on LSMO10 film, two well resolved rhombohedral domains marked with D are recognizable; right panel: Reciprocal space map around the (002) pc reflection of the substrate for the LSMO10 film. For lower L values the same division in domain as that of the substrate can be appreciated also for the film. Also thickness fringes marked with F are visible. 78

92 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure 4.18-left panel: Rocking curve on LSMO20 film, at least four domains marked with Ds are recognizable; right panel: Reciprocal space map around the (002) pc reflection of the substrate for LSMO 20, four domains of the substrate are visible along L = 2, and as many perfectly aligned in longitudinal direction also for the LSMO20 film. Thickness fringes marked with F are visible. Figure 4.19-left panel: Rocking curve on LSMO 40 film; right panel: Reciprocal space map around the (002) pc reflection of the substrate for the 20 nm LSMO film, four domains of the substrate are visible along L = 2, and as many perfectly aligned in longitudinal direction also for the LSMO film. 79

93 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure left panel: Rocking curve on LSMO40a film deposited onto LaAlO 3 (001) substrate, in which different domains are marked by Ds; right panel: Reciprocal space map around the (002) pc reflection of the substrate for the LSMO40a film, with along horizontal direction L = 2 several intensity nodes due to different domains of the substrate, and corresponding domains for the LSMO film perfectly aligned in longitudinal direction. To the aim of evaluating the relaxation degree of the five films, reciprocal space maps have been recorder around an asymmetric reflection. Being the analyzed samples constituted by La 0.7 Sr 0.3 MnO 3 (001) grown on LaAlO 3 (001), the (103) planes (having non zero first and third Miller index) are not parallel to the deposition surface as such they can be chosen to produce an asymmetric reflection. Such reflection enables to extrapolate information related to in-plane and out-of-plane lattice parameters. In a pseudocubic on pseudocubic approximation if we have a relaxed material grown on the substrate we expect to have reciprocal space nodes of both substrate and layer aligned in longitudinal (ω-2theta) direction, that for a asymmetrical reflection is represented by the line connecting the origin of reciprocal space (000) to the (103) reflection of the substrate (exactly what happens for the relaxed film LSMO20r presented in the previous section Figure 4.4). If the lattice parameter of the substrate is smaller than that of the film (in case of compressive strain as in the present of La 0.7 Sr 0.3 MnO 3 on LaAlO 3 ) starting from the reciprocal space origin we meet first the reciprocal space node of the layer and then that of the substrate. On the other side, a fully strained layer means that it has the same in-plane lattice parameter of the substrate, which in turn implies a perfect alignment in H direction 80

94 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION of the node of the layer and that of the substrate. If we consider an elastic deformation, a compression of the parameter in the deposition plane leads to an elongation in the out of plane lattice parameter, that leads to a consequent variation also of L value (a L decrease for in-plane compressive strain, a L increase for in-plane tensile strain). Figure left panel: Scheme of the reciprocal space for the two extreme situations: fully relaxed layer and fully strained layer, and relaxation line in the right panel All the positions between the two extreme ones - correspondent to totally relaxed and totally strained case - give rise to the so called relaxation line as shown in Figure 4.21 (the concept of relaxation line is explained in more details in Appendix A). The reciprocal space map made around the (103) pc asymmetric reflection of the substrate are shown for all the five samples in Figure As can be understood by the observation of the maps (Figure 4.22), all La 0.7 Sr 0.3 MnO 3 films are fully strained. In correspondence of the value L = 3, reciprocal lattice nodes of the substrate can be noted. The presence of more than one node in transversal direction (rocking direction) is again a clear proof of the presence of ferroelastic domains in the substrate. Going vertically down from each node we find for lower value of L a one to one correspondence between nodes belonging to the substrate and nodes belonging to the film. The black lines in Figure 4.22 are an eyes guide for better evidence the coherent 81

95 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION strained growth of LSMO domains on LaAlO 3 domains: the perfect alignment in H direction indicates the full degree of deformation for each domain. To appreciate the high degree of in-plandirection) where the nodes of the film are supposed to be if they would be relaxed, are deformation, the longitudinal direction (ω-2θ shown as dashed line in Figure

96 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure Reciprocal space map on (103) pc asymmetric reflection of the substrate for four thickness film: 40 nm, 20 nm, 10 nm and 5 nm. All films are fully strained as can be deduced from the perfect alignment in H direction of reciprocal lattice nodes of LSMO films and LAO substrate. The black arrows are an eyes guide for better see that alignment. The longitudinal direction where the reciprocal lattice node of the film is supposed to be in case of relaxation is represented with a dashed line HRTEM results High resolution transmission electron microscopy cross-section images on thin film of LSMO deposited onto ferroelastic LaAlO 3 have been performed. For the TEM cross section observation a TEM TECNAI FEI Tecnai F20 200kV high resolution TEM has been used. The aim of the transmission electron microscopy measurement was to get information about the nanostructure of La 0.7 Sr 0.3 MnO 3 film and to see if and how the structural properties of the substrate influence the structure of the overgrown film. For cross section observation under Transmission Electron Microscopy, thin electron transparent lamellae (tens of nanometers) have been prepared by means a Focus Ion beam FIB (see Appendix B). In Figure 4.23 a HRTEM image of the cross section of a LSMO (001) film deposited onto (001) LAO in shown. The interface is evidenced by means of the dashed white arrows and the [001] crystallographic orientation is also marked. 83

97 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION LSMO [001] LAO 5 nm Figure 4.23 HRTEM cross section image of 10 nm (001) La 0.7 Sr 0.3 MnO 3 film on (001) LaAlO 3 substrate. The crystallographic [001] orientation is shown; the interface is marked with white dashed arrows (magnification: 1 Mx) The structure of the substrate appears to be regular and well defined, while for the film La 0.7 Sr 0.3 MnO 3 a nano-texture can be observed. To the aim of better reveal and to enhance the periodic features of images, Fast Fourier Transforms have been performed. A fast Fourier transform is a special algorithm for quickly calculating a Fourier transform on a source image having dimensions that are powers of two (i.e. 2, 4, 8, 16, 32, 64, etc.). Once this size requirement is fulfilled, Fast Fourier Transforms (FFTs) are significantly faster than straightforward calculation of the discrete Fourier Transform (DFT). Fourier masking allows to remove unwanted noise by select in the complex image only the desired frequencies. The next step is to perform an inverse fast Fourier transform extended only in the masked area. In the so obtained new real image we have an enhancement of the periodic characteristic. For FFT analysis the software package DigitalMicrograph (TM) for GMS (by Gatan software team) has been used. The just explained method is been applied to the image shown in Figure 4.23 and the result is shown in Figure 4.24, in which the white dashed arrows indicate the interface between film and substrate. 84

98 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION LSMO LAO Figure Inverse Fast Fourier transform (IFFT) obtained from the image of Figure Differently oriented regions leading to a texture in the film can be recognized. This texture is driven by the structure of the substrate. After Fast Fourier transform, differently oriented region can be recognized in the film. Two of those regions have been evidenced in blue and yellow. These two regions have line of atoms inclined by 45 anti-clockwise (the blue one) and clockwise (the yellow one) with respect to the [001] direction, which lies in the plane of the image perpendicular to the interface. Texture is composed of very small regions which extent even over only 7 atomic lines. Let us comment the observed texture and film substrate interface with reference to what happens during the film deposition, schematically shown in Figure 4.25 (left panel). 85

99 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure left panel from [Bueble et al 1997]: Schema of mechanism that leads to have roughness at the interface. (a) Cubic prototype at high temperature, (b) twin domain formation after cooling down through ferroelastic transition temperature, (c) cutting an polishing procedure leading to a nearly flat surface, (d) Twin disappearance during deposition procedure and (e) new twin domain formation; Right panel: HRTEM cross section image of 10 nm (001) LSMO film onto (001) LAO (magnification: 1 M x), black arrows are a eyes guide to better evidenced the roof-like interface. In a) the substrate is at high temperature above T F, i.e. in the cubic prototype point group m 3 m. When it is cooled down to room temperature through T F = 544 C, the point symmetry is broken to 3 m with twins formation as shown in b). After that, the substrate is cut parallel to a crystallographic plane of the cubic prototype, and polished to obtain a flat surface suitable for film deposition, as shown in c). In d) the substrate is ready for the deposition during which, inside the deposition chamber, it is warmed up to the deposition temperature that is well above T F, so that - being the ferroelastic transition reversible - it experiences a change of point symmetry from 3 m to m 3 m. Twin disappears, but traces of them can be recognized as roughness that occurs on the surface. The film is now deposited, and after that the whole system (substrate and overgrown film) is cooled down to room temperature, crossing again T F with a new formation of the twin 86

100 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION structure. The result of this mechanism as far as it concerns the substrate is schematized in e). A roof-like interface is therefore to be expected. In Figure 4.25 right panel a HRTEM image of 10 nm (001) LSMO film onto (001) LAO is shown with a magnification of 1 M x. The crystallographic [001] cubic orientation is shown; near the interface LAO/LSMO dark regions alternate with brighter regions, and the profile drawn by this dark regions is very similar to the substrate profile shown in (e) of the left panel. As a confirmation of what so far observed for La 0.7 Sr 0.3 MnO 3 on LaAlO 3 and to be sure that the La 0.7 Sr 0.3 MnO 3 microstructure is without doubt to be ascribed to the particular substrate, HRTEM on cross section has been performed also on La 0.7 Sr 0.3 MnO 3 film deposited onto SrTiO 3 (STO). STO has been chosen because of its simple cubic perovskite structure. LSMO (001)/SrTiO 3 (001) samples have been prepared with Molecular Beam Epitaxy exactly under the same condition used for La 0.7 Sr 0.3 MnO 3 on LAO. LSMO (001)/SrTiO 3 (001) samples have been also characterized by HRXRD which showed highly strained samples. The crystallinity of the substrate has been analyzed by means rocking curve. In Figure 4.26 a rocking curve performed around the (002) reflection of STO substrate is shown. The presence of a sharp (FHWM of 0.04 ) single peak is a clear sign of a well crystallized substrate. Figure Rocking curve on SrTiO 3 substrate of LSMO 5nm/ STO sample. A single peak with FWHM of 0.04 is indicative of a high degree of crystallization. 87

101 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION In Figure 4.27 HRTEM on cross section of a 5 nm LSMO film deposited onto STO substrate made at 1 M x is shown together with the IFFT of the marked region around the interface between LSMO and STO. Even from the real image a regular structure of the film can be observed, but the simple structure as well as a sharp interface are better evidenced in the IFFT in the box in the bottom right panel of Figure The nanostructure observed for LSMO film grown on LAO is not observable in the case of deposition on STO. LSMO STO 5 nm Figure 4.27-Upper left panel: HRTEM cross section image of LSMO 5 nm film deposited onto STO substrate, the magnification is 1 M x. Bottom right panel: IFFT of the region in the box, the sharp interface is marked with dashed red line. 88

102 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION In conclusion, for the LSMO/LAO the HRTEM characterization has shown a strict connection between the structure of the substrate and that of the overgrown film. In particular, a texture composed by differently oriented region extended over some nanometers scale has been observed in La 0.7 Sr 0.3 MnO 3 film deposited onto LAO substrate. This texture has surely to be ascribed to the presence of ferroelastic twin domain in the substrate Magnetic properties The dependence of magnetization on temperature was studied by zero field cooling (ZFC) and field cooling (FC) measurements in the interval 5 K < T < 395 K. In the measurements of the temperature dependence of the ZFC magnetization (M ZFC ), the sample was cooled from 395 K to 5 K in zero field, then the measuring field was applied at 5 K and the magnetization was recorded on heating the sample. The FC magnetization (M FC ) curves were recorded on cooling, keeping the sample in the same applied field. The isothermal thermoremanent magnetization (TRM) as a function of time and the evolution of the magnetization in a constant applied field (M (t)) were also measured for some chosen samples. For these measurements, the samples were field cooled (H = 25 Oe) starting from 395 K down to the desired measurement temperature T m, the field was kept constant for a certain waiting time t w, then it was cut off and the magnetization was recorded as a function of elapsed time to obtain the TRM curves. The relaxation of the magnetization M(t) in constant field was recorded during the waiting time. Both for temperature and time dependence magnetization measurements the magnetic field was applied parallel to the film plane (H ). The ZFC-FC curves for the LSMO 40 sample are reported in Figure 4.28 for 25 Oe, 50 Oe and 10 koe applied field. The low field M ZFC curves (at 25 Oe and 50 Oe) show a clearly observable peak at 85 K which broadens and shifts to 60 K at 1 koe. A second structure is present at higher temperature (around 220 K) in the low field curves and 89

103 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION disappears at 1 koe. In all the three curves at 25 Oe, 50 Oe and 1 koe, the M FC curve presents a shoulder at the temperatures corresponding to the peak in the M ZFC curves. A considerable separation between ZFC and FC curves, indicating irreversibility, can be observed below T irr = 320 K for the lower field curves, while T irr is slightly higher (around 350 K) in the curves recorded at 1 koe. Figure ZFC-FC magnetization curve for LSMO40 for different applied field ( 25 Oe, 50 Oe and 1 koe) parallel to film plane Figure 4.29 shows the ZFC and FC magnetization for LSMO 20 film. The behaviour is similar to that observed in the sample LSMO 40, but it can be noticed that in this case the peak observed at T = 90 K in the M ZFC curve at 25 Oe is considerably broader, while the second structure around 220 K is more pronounced. For this film, irreversibility can be observed below 300 K.. 90

104 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure ZFC-FC magnetization curve for LSMO 20 for different applied field ( 25 Oe, 50 Oe and 1 koe) parallel to film plane A very broad peak centred at 170 K can be observed in the low field M ZFC for LSMO 10 sample (Figure 4.30). Also in this case, the maximum in the M ZFC corresponds to a shoulder in the M FC curve. This film exhibits irreversibility in the whole measurement temperature range The low field ZFC-FC magnetization curves for the LSMO 5 sample are reported in Figure This measure appears very noisy, since this sample exhibits a very weak magnetization owing to its small thickness. In spite of this, even though an irreversibility temperature can not be precisely determined, a peak in the M ZFC is still detectable at T = 70 K, and a clear separation between the ZFC and FC branches can be observed below this temperature. 91

105 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure ZFC-FC magnetization curve for LSMO 10 for 25 Oe applied field parallel to film plane. Figure ZFC-FC magnetization curve for LSMO 5 for 25 Oe applied field parallel to film plane. As it concerns the transition towards a high temperature paramagnetic phase, a Curie temperature T C can be identified at about 300 K for the 40 nm thick film and at 350 K for the 20 nm thick film. The Curie temperature has been evaluated from the low field magnetization (with H = 25 Oe) fitted by the mean field theory expression M(T) = A(T C - T) 1/2 in the vicinity of the transition [Zijlstra 1967]. The two thicker samples therefore develop long range magnetic order, although with Curie temperatures notably lower than the bulk value of 378 K. For the 10 nm and 5 nm thick films, conversely, the spontaneous magnetization does not vanish up to the highest measured temperature (400 K, which is the upper limit of the magnetometer). The absence of an instrumental offset in the magnetic moment values is confirmed by the data recorded during the zero field cooling, which fluctuate around zero within the estimated error. This suggests that the transition 92

106 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION towards a ferromagnetic phase for the LSMO 10 at 25 Oe occurs only at temperature higher than 395 K and therefore well above the bulk Curie point. A similar conclusion can be drawn for the thinnest sample (LSMO 5), despite of the poor signal to noise ratio related to the low magnetic response of the film. The magnetization vs. time measurements, both relaxation M(t) and TRM, were performed at T m = 50 K ( T m = 0.4 T f ), well below the maximum in the M ZFC curve. Figure 4.32 (a) reports the TRM curve for a 40 nm thick film LSMO 40 with t w = 0 s (120 s). The time decay is monotonic and can be well fitted with a simple logarithm. The decrease of the magnetic moment is of few % during the observation time interval, indicating an extremely long relaxation time [Rivadulla et al. 2004]. The curves with t w = 1200 s or greater (Figure 4.32, b, c, d, e) show a remarkably more complex behavior. The decay is nonmonotonic, presenting a series of fluctuations, during which the magnetic moment, albeit showing a global decrease, exhibits sudden decreases and increases. In particular, in all the decay curves a characteristic feature is present, i.e. a marked dip centered at about 5x10 3 s after the external field has been switched off. This structure is particularly noticeable in the curve with t w = 10 5 s (Figure 4.32 (e)). Also the relaxation curves M(t) exhibit a very complicated behavior. As it can be observed, during the waiting time the magnetic moment never shows a monotonic increase with time. The curve with the longest waiting time (t w = 10 5 s) exhibits the most peculiar behavior, showing a slow initial increase of the magnetic moment lasting about 2.5 x 10 4 s, followed by an abrupt decrease. The magnetization reaches a minimum for t = 4 x 10 4 s, then it starts to increase again. Around t = 5.5 x 10 4 s it stops increasing and a plateau is reached, with an almost constant magnetization value up to t = 10 6 s, when finally the field is switched off. 93

107 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure Thermoremnant (TRM) magnetization decay measurements for LSMO 40 performed at 25 Oe at Tm = 50 K for different waiting time (a) t w = 0, (b) 1200s, (c) 5000 s, (d) s and (e) s 94

108 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Discussion on strained films ZFC-FC magnetization curves The presence of a cusp in the M ZFC recorded in low applied field is a typical feature of several spin disordered system, such as spin glasses (SG), cluster spin glasses (CSG) and superspin glasses (SSG), and the temperature corresponding to this peak is considered as the freezing temperature (T f ) for the spin glass. The very slow relaxation with time of the magnetization is another fingerprint of these disordered magnetic systems [Xiong et al. 2002]. Both these characteristics appear in our measurements, leading us to consider our samples as containing a spin-glass-like phase. Moreover, it is also possible to identify a Curie temperature T C above both T f and T irr. The presence of a ferromagnetic phase is confirmed by the sudden jump of M(t) when the applied field is removed, as expected for a long range ferromagnet relaxing to its residual magnetization value, and by a negative magnetoresistence in the temperature range 4 K < T < 400 K indicative of a double exchange (DE) ferromagnetic phase present at all temperatures. Therefore we suggest that the low temperature magnetic behaviour of our samples can be ascribed to a re-entrant spin glass in which long range ferromagnetic order coexist with the frozen SG phase. This description of the RSG agrees with several recent experiments which unambiguously demonstrate that long range ferromagnetism persists below T f for specific re-entrant systems [Kimura et al. 2000, Kaul et al. 1998, Kundu et al. 2005]. The DC magnetization curves are consistent with this interpretation, which permits to rationalize the presence of the two structures appearing in M ZFC just below Tc and at T f, respectively: the former is due to the ferromagnetic phase transition and the latter is originated from the formation of the spin-glass state. With increasing H, the hightemperature peak is smeared (Figure 4.29, 1000 Oe) or quenched (Figure 4.28, 1000 Oe) indicating the saturation of the ferromagnetic moment. The RSG picture also helps to interpret the depletion of the ferromagnetic moment in the low field M FC between T C and T f (Figure 4.28 and 4.29 with 25 Oe and 50 Oe applied field) as due to fluctuations of the unfrozen spins in the PM clusters which escape the FM network [Ito 2000]. 95

109 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION As it concerns the origin of the two phases which are mixed in the RSG for LSMO/LAO films, we propose that the ferromagnetic component rises from the double exchange DE interaction, while the spin glass component originate from competing FM and antiferromagnetic interactions. Actually, in the case of manganites, in addition to DE interaction, Mn core spins may also interact via a direct superexchange with a sometimes positive exchange coupling, in which case superexchange competes with the DE mechanism. With reference to the structural and microstructural characterization reported in and 4.2.2, we may suppose that double-exchange couplings are dominant inside each structural domain and that frustration appears in the twin walls therefore in a ''transition region'' between domains. The depicted microstructural description of the twinned LSMO films is reminiscent of the two-phase scenario, according to which FM regions (in our case inside the twins) and AFI regions (induced in our case by locally enhanced distortions at twin boundaries) coexist in manganites with CMR [Dagotta et al. 2001], with emphasis put on the primary importance of structural aspects in causing the multiphase coexistence [Ahn et al. 2004] Comparison with strained film of LSMO/STO As already done in the case of relaxed films, it is useful to compare the ZFC-FC magnetization curve of LSMO/LAO films with films of LSMO epitaxially grown under the same conditions on SrTiO 3 (001) substrate. Figure 4.33 shows the ZFC-FC magnetization curves at H= 5 Oe (applied parallel to the deposition plane) of a LSMO/STO sample whose thickness is 12 nm. 96

110 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION Figure 4.33-ZFC-FC magnetization curve for LSMO film with thickness of 12 nm deposited onto SrTiO 3 substrate. The magnetic field of 5Oe is parallel to the deposition plane. An evident difference with respect to the behaviour of LSMO/LAO samples can be observed also for the strained sample, with no cusp in the ZFC curve which follows the FC one with only a small separation due to the smallness of the applied field. We can also note that the substrate transition al 105 K has the same clear effect in both magnetization branches leading to a magnetization increase which can be ascribed to a magnetoelastic coupling between film and substrate due to the pseudomorphic growth of the former. We can conclude that if the ferromagnetic transition of LSMO takes place without the presence of twin boundaries and related structural disorder, no spin-glass behaviour arises in the manganite epilayer The time evolution of the magnetization In the light of the previous discussion, we shall analyze the time evolution of the magnetization when recorded below the spin glass freezing temperature. Let us first briefly recall the mechanism of the re-entrant spin glass transition. When the long range order is established at T C, some amount of disordered spins exists in the long range ferromagnetic network. Between T C and T f the fluctuations of the not aligned spins in the PM twin walls are so rapid that they have a little influence on the FM network and their 97

111 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION effect is only to reduce the net FM moment. On approaching T f the thermal fluctuations of the spins in the PM regions become slower and the coupling between these spins and the FM network becomes significant. Below T f, the situation is reached in which the molecular field from the frozen spins acts on the FM as a random magnetic field. The non equilibrium relaxation of a ferromagnet subject to a random field has been discussed by Kornyei in the model case of an Ising square lattice whose initial state is generated switching on a Gaussian random field [Kornyei et al. 2005]. An unusual time re-entrance of magnetization is found, in contrast to the monotonic (logarithmic, stretched exponential and power law) time evolution predicted by the common treatment of spin-glass-like systems. The nonmonotonic behaviour, and in particular the re-entrance of magnetization, is due to competing processes of dissolution and subsequent reorganization of domains, which lead to successive magnetization decrease and increase. In Figure 4.34 the typical evolution of magnetization predicted by Kornyei in his model in a double logarithmic scale is shown. Figure 4.34-[from Kornyei 2006] Typical evolution of magnetization in a double logarithmic scale. A first decrease ( 1) due to the dissolution of ferromagnetic cluster disturbed by the random field is followed by non equilibrium reorganization (2) and by an equilibrium relaxation (3).The four insets show the spin configuration system in different regimes. 98

112 CHAPTER 4-EXPERIMENTAL RESULTS AND DISCUSSION It can be observed that the magnetization reaches a minimum at a time t min (the value of which depends on the degree of disorder and the initial magnetization), increases up to a t max, and finally decreases again towards equilibrium in the large time scale. These three regimes are indicated in Figure 4.34 with (1), (2) and (3). The intriguing time re-entrance can be quenched by increasing the strength of the random field. Such behaviour is very similar to what we observe, even if we are aware that the FM Ising square lattice is oversimplified to directly represent the experimental situation. However, it is now understood that RFIM describes the essential physics of a rich class of experimentally accessible disordered systems. These include structural phase transitions in random alloys, commensurate charge-density-wave systems with impurity pinning, binary fluid mixtures in random porous media, and the melting of intercalates in layered compounds such as TiS 2. In particular, in the case of manganites the FM DE Hamiltonian r r H DE = t ci αcjα JH S i ci ασ αβciβ i, j α iαβ binding band of e g electron interacting with Mn 3+ t 2g core spins S by a Hund exchange, which comprises a single nearest neighbours tightinteraction (J H >>t), can be mapped onto an effective nearest-neighbour Heisenberg model H = J SS rr 2 where J = t /4S and t is the average kinetic energy per bond, model F i j ij which, in mean field approximation, is not much different from the Ising one [ Shannon et al. 2002]. The effect of a random field on a Heisenberg FM has been studied both for square and simple cubic lattice, and it was found that the ferromagnetic transition takes place for a wide range of random field strengths with a renormalization of the Curie temperature [Albuquerque et al. 2002]. Therefore, in our opinion the Kornyei results may constitute a useful starting point for the analysis of the experimental results here reported. To the best of our knowledge, the previous description has not been used for any magnetic system in which a nonmonotonic time relaxation of the magnetization has been observed, such as granular superferromagnet [Co 80 Fe 20 /Al 2 O 3 ] 10 [Chen et al. 2003] and complex phases in the series YBaCo 4-x Zn x O 7 [Valldor 2004], for which two magnetic subsystems with different relaxing mechanisms and time evolution have been hypothesized. 99

113 CHAPTER 5- CONCLUSION CHAPTER 5 CONCLUSION AND FUTURE DEVELOPMENT In this PhD thesis work we have investigated thin epitaxial La 0.7 Sr 0.3 MnO 3 films grown through Molecular Beam Epitaxy (MBE) onto ferroelastic substrates of LaAlO 3. In particular the results onto two partially relaxed film of nominal thickness 20 nm and 9 nm and onto five fully strained films : two of nominal thickness of 40 nm and the others with thickness of 20 nm, 10 nm, and 5 nm respectively have been presented and discussed. The first step has been to prove the ferroelastic domains division of the substrate, this has been made by means optical characterization (CHAPTER 3). It has been shown that, as expected the ferroelastic transition of LaAlO 3 is totally reversible, as matter of fact we showed evidence of ferroelastic domains in the substrate before and after the thermal cycle that the substrate experienced during the film deposition procedure inside the MBE chamber. The deposition temperature is in fact well above the ferroelastic transition temperature, but after the deposition the sample is cooled down to room temperature. To the aim of investigating the influence of the structure of the substrate on that of the overdeposited manganites films diffraction measurements ( i.e. reciprocal space maps on both symmetric and asymmetric reflections and rocking curves) have been performed with a high resolution X-ray diffractometer on all samples (CHAPTER 4). Moreover the structural characterization of the strained films has been completed also by means High resolution Transmission electron microscopy on cross section. We confirmed that manganites films are very sensitive to the microstructure of the substrate. The films in fact showed to have a similar division in crystalloghaphic domains to that of the substrate. Therefore the effect of the LaAlO 3 substrate on La 0.7 Sr 0.3 MnO epitaxial films is not only to induce a compressive strain in the plane of deposition as usual reported in literature disregarding the real structural peculiarity of LaAlO

114 CHAPTER 5- CONCLUSION A crystallographic domains structure constituted by regions of different orientation on nanoscale extent has been observed. The same film deposited on a different substrate (SrTiO3) does note present the same nanotexture. The correlated quenched disorder due to twinning has been shown to deeply influence the magnetic behaviour. From the study of the magnetization as a function of temperature by means Zero field cooled (ZFC) and Field cooled (FC) magnetization curves we observed thermomagnetic irreversibility as well as the presence of a cusp in the M ZFC recorded in low applied fields. Both characteristic are typical of spin disordered systems therefore in the present case these peculiarities been discussed in terms of coexisting ferromagnetic and spin disordered regions. The proposed explanation is that the ferromagnetic component rises from the double exchange DE interaction, while the spin glass component originates from competing FM and antiferromagnetic interactions. As it concerns the origin of the two phases, which are mixed giving rise to a so-called reentrant spin glass (RSG), in the case of manganites, in addition to DE interaction, Mn core spins may also interact via a direct superexchange with a sometimes positive exchange coupling, in which case superexchange competes with the DE mechanism. On the light of the structural and microstructural characterization, we may suppose that double-exchange couplings are dominant inside each structural domain while a disordered phase can appear in the twin walls as a consequence of the frustration present in these ''transition region'' between domains. The presence of a disordered phase coexisting and interacting with a ferromagnetic phase has been proved also by the observation of the very slow time evolution of the magnetization when recorded below the spin glass freezing temperature. A nonmonotonic evolution of the magnetization and in particular the presence of a reentrance in time has been observed and explained in terms of to competing processes of dissolution and subsequent reorganization of domains, which lead to successive magnetization decrease and increase. Such behaviour has been explained, considering the molecular field due to the frozen spin of the spin glass phase acting on the ferromagnetic component as a random field. 101

115 CHAPTER 5- CONCLUSION The importance of the LAO substrate in inducing structural peculiarities in the manganites films has been proved by comparison of low field magnetization measurement of LSMO film onto STO, for which, in particular, no the ZFC-FC irreversibility with a ZFC maximum has been observed. On the light of the results obtained and presented in this PhD Thesis, some natural developments of the work can be proposed. First of all, as it is clear that the ZFC-FC irreversibility below T irr and the ZFC maximum at T f are not conclusive for a spin-glass phase; more investigations are needed to prove it. To this aim, the influence of the external magnetic field H on the reentrant temperature can be studied. As known, in the case of direct paramagnetic to spin glass instability, different H dependence of the freezing temperature are predicted, depending on the model: within an Ising model, T f should vary following the so called de Almeida- Thouless line in the (T, H) plane, while the so called Gabay-Thouless line should be followed in the case of isotropic model of m-component spins. Conversely, the case of a reentrant state with coexisting spin glass and ferromagnetic order parameters has been understood in the mean field theory, according to which the reentrant temperature should vary linearly on H. The measurement of the reentrant temperature at various applied fields and the analysis of the (T, H) plane could in principle allow to distinguish between the three cases. Observation of dynamic behaviour based on low filed ac-susceptibility at various observation times should also be performed, by studying the temperature dependence of the in-phase and out-of phase linear and non linear susceptibility components at various fields above and below the reentrant temperature, i.e. in the pure ferromagnetic phase and in the supposed mixed phase. Fundamental differences between the magnetic behaviour of LSMO film on LAO and STO, observed already from the comparison of the ZFC-FC curves, should be studied more carefully by following the time evolution of the magnetization for the untwinned films on STO above 105 K or of the same films below 105 K, in order to analyze the possible role of the STO ferroelastic transition in the magnetic behaviour. Last, a further interesting complementary study of the herewith presented work would be a set of low-field (of the order of Oe instead of Tesla) magnetoresistance 102

116 CHAPTER 5- CONCLUSION measurements. It is known, in fact, that in manganites films with structural discontinuities (like those present in films in films deposited on bicrystals or in polycrystalline films at grain boundaries), and an extrinsic component of the magnetoresistence can be present, which is of tunnel-type through the discontinuity. This extrinsic component has considerable value at low magnetic fields, which constitutes an advantage with respect to the intrinsic colossal component of single crystal films and much more interesting that this one for potential applications. We may suppose that twin boundaries in LSMO/LAO films can play the role of potential barriers between different domains and promote a low field magnetoresistive response. 103

117 - 104 APPENDIX A X-RAY DIFFRACTION APPENDIX A X-RAY DIFFRACTION A.1 Laue formulation of Bragg law X-ray diffraction which has been first discovered by Max Von Laue in 1912 is a wellestablished powerful tool for structural characterization of crystalline material, no matter if they are thin layer, massive bulk or powder. Basically when x-rays beam interacts with a crystalline material it can be elastically scattered by the atomic planes constituting the material in a way that is strictly connect to the atomic distance as well as to the incident angle. A crystal can be considered as a periodic array of atomic planes regularly spaced as shown in Figure A.1. Figure A.1- Schema showing constructive interference of x-rays wave planes according to Bragg s law This periodic lattice diffracts x-rays according to the well known Bragg law, which is simply the condition for constructive interference of different x-rays wave planes: n λ = 2d sinθ, n = 1, 2, 3,

118 - 105 APPENDIX A X-RAY DIFFRACTION where d is the distance between atomic planes and Θ is the angle at which the scattered beam can be detected. Therefore it is clear that, from Bragg law, once Θ is been measured if λ is known the lattice parameter can be deduced, permitting so to obtain structural information. In the next the Bragg law will be deduced using the Von Laue derivation [Kittel 1998]. In the Laue derivation the crystal is seen in the reciprocal space. Figure A.2- Geometry for x-ray diffraction: k and k are the incoming and scattered wave respectively, the position of the detector to respect to the origin O is R while to respect to the scattered atom is r Let consider an incoming plane wave with frequency ω and wave vector k, and let assume that incoming and outgoing radiation have same frequency and same magnitude of wavevector: ω = ω k = k The origin O of the reciprocal space is in x = 0. The incoming wave in the free space is described by: F(x) = F 0 exp [i (k. x ωt)] So that the incident wave in d is given by: 105

119 - 106 APPENDIX A X-RAY DIFFRACTION F(d) = F 0 exp [i (k. d ωt)] If we consider only t =0 the previous relation becomes: F(d) = F 0 exp [i (k. d)] We are interested in what is seen by the detector, so let consider the scattered wave in R to respect to the origin O, this will be given by the product of two factors: F (R) = F 0 exp i ( k. d) exp [ i ( k r)] = F 0 exp [i ( k. d + k r)] Being R >> r as in any real case it is possible to make the following approximation: r R d cos ( d, R ) so that the scattered wave can re-written as: F (R) = F 0 exp [i ( k. d + k. R k d cos (d, R)] If R is parallel to k and considering that k = k we can write: k. d cos (d, R ) = k d cos ( k, R) = k. d Considering again the exponential we can write: exp[i(k. R)] exp [i(kd- k d cos ( k, R)] = exp [(i (k. R)] exp[i (k. d - k. d) = exp [(i (k. R)] exp[-i d Δk] being Δk = k k All so far said is valid if one single scattering center is considered (in this case that was in d), so now let consider all possible lattice points: d = m a + n b + p c where assuming that crystal has M unit cell in any direction the integer m, n, p has to be summed from zero to M-1, so that the second exponential of the last relation cab be written as: m, n, p exp[ i (m a + n b + pc) Δk] The condition to have a diffraction maximum is: 106

120 - 107 APPENDIX A X-RAY DIFFRACTION a Δk = 2π h d Δk = 2π N where N is an integer b Δk = 2π k c Δk = 2π l These are the so called Laue equations lattice. also used to introduce the concept of reciprocal The constructive interference Laue conditions are in fact satisfied only if the scattering vector Δk point a reciprocal lattice point. 2π Therefore Δk (whose magnitude is d ) is nothing other than a reciprocal lattice vector and as such it has the property to be perpendicular to the family of atomic planes having distance d, being this atomic planes nothing other than the Bragg planes encountered earlier to first introduce the Bragg law. Figure A.3- Relation between the scattering vector and the atomic planes having distance d From Figure A.3 we can obtain the relation Δk = 2k senθ and being also Δk = law is can obtained combining these two relation. 2π Bragg d 107

121 - 108 APPENDIX A X-RAY DIFFRACTION A.2 Ewald sphere construction A really useful concept in diffraction analysis is the Ewald sphere construction in reciprocal space (Figure A.4). Thanks to this construction is it possible to have clear understanding of the geometry of the different scan in the reciprocal space. Let consider a family of atomic planes with miller index (h, k, l) having distance d hkl and let k and k ( k = k ' 2π = ) respectively the wave vector of the incident and scattered λ radiation, the Ewald sphere is defined as that sphere with radius 2π /λ which has is centre in the incident point C of the radiation on the sample, (Figure A.4). Figure A.4- Ewald sphere: any reciprocal nodes that falls on it gives rise to Bragg diffraction peaks Being Δk = k k from Figure A.4 can be deduced the relation: 2π Δk = 2 sen θ λ combining this relation with the Bragg law we deduce 2π Δk =. d hkl Any family of plane is in the right position to give rise to Bragg diffraction peaks if and only if the correspondent reciprocal node falls on the Ewald sphere. 108

122 - 109 APPENDIX A X-RAY DIFFRACTION In any diffraction experiment we have a Ewald sphere depending on the used radiation and a reciprocal lattice associated to analyzed sample. To bring a reciprocal node in Bragg position one method is the Laue diffraction method that is historically the oldest method which has been proposed to obtain diffraction patterns and this is based on a fixed crystal and a variable spectrum of wavelength, this way permits to change the radius of the Ewald sphere keeping the sample in a fix position; otherwise, the wavelength can be fix while the sample is rotated in a opportune way. The diffraction measurement presented in this thesis have all been made with the first method, therefore by means a diffractometer equipped with an Eulerian Cradle ( A.3.3) that is a really useful system for orientation of the sample. Lastly a short note on the limiting sphere is due. Let imagine to make the Ewald sphere rotate about the origin of the reciprocal lattice, in this way the sphere with a radius that is double to respect to that of the Ewald sphere is obtained, this sphere is the so-called limiting sphere and it contains all reciprocal lattice nodes that can be observed once that the wavelength of the radiation is fixed. In particular, once the wavelength is fixed only reciprocal space nodes correspondent to atomic family planes with distance d < λ/2 can be observed as can be easily deduced from the Bragg law being sen θ 1 always. 109

123 - 110 APPENDIX A X-RAY DIFFRACTION A.3 D8 Discover (BRUKER-AXS) High resolution diffractometer All diffraction measurement presented in this thesis have been performed using a D8 Discover (Bruker AXS) Diffractometer (Figure A.5) It is a triple axes high resolution diffractometer mainly thought for thin film analysis. The expression triple axis refers to the presence of the following constituting elements: the x-ray source together with the beam conditioning primary optics ( constituted by both the Gobel mirror and the V-Groove monochromator) which represent the 1 st axis the Eulerian Cradle where the sample holder is mounted which represents the 2 nd axis the detector which represents the 3 rd axis as shown in Figure A.5. Figure A.5- D8 Discover (Bruker); high resolution triple axes diffractometer The x-ray source is an x-ray tube with Cu anticathode; the working setting is 40 KV and 40 ma. Primary optics for beam conditioning is constituted by Göbel mirror to collimate the beam and a V-Groove monochromator to compress the beam and to eliminate the k α2 component of radiation. 110

124 - 111 APPENDIX A X-RAY DIFFRACTION A.3.1 Göbel Mirror Just in front of the housing of the X-ray source a Göbel Mirror is opportunely mounted to the aim of collimate the beam. This is a parabolic, laterally graded multilayer mirror which converts the divergent beam projected by the line focus of the x-ray tube into a quasimonochromatic and highly parallel (divergence 0.03 ) beam of high intensity. White radiation and k β lines are eliminated. The choice of this particular mirror is due to the fact that x-ray cannot be deflected by ordinary mirror as visible light. Gobel mirror is constituted by a stack of typically alternating nanometer-thick layers made from two different chemical elements. The parabolic shape is fundamental for obtaining the collimation as it is well known that a parabola deflects the radiation coming from its focus in a parallel beam, so as shown in Figure A.6 the x-ray source is positioned in the focus of the parabola. Figure A.6- Göbel mirror which converts the divergent beam coming from the x-ray tube into a quasi-monochromatic and highly parallel (divergence 0.03 ) beam of high intensity The deflection of the radiation is due simply to a Bragg reflection, and considering that Bragg reflection has to be fulfilled by the multilayer at each point of the parabola the period d has to vary over the length of the parabola according to the following equation [Schuster et al.1995]: λ d(f) = 2f 2sen arccot p 1 1/ 2 111

125 - 112 APPENDIX A X-RAY DIFFRACTION Where f is the distance the distance between the focus F and the incidence point A (i.e. focal length) in the parabola so that every x-ray impinging on the mirror is scattered in parallel direction with a divergence less than A.3.2 V-groove compressor monochromator To obtain more resolution, after the Gobel mirror a V-groove compressor monochromator is often mounted. The name V-groove refers to its V-shape and it is basically made up of a crystal of Ge cut parallel to (022) planes. Figure A.7- V-Groove monochromator: eliminates of kα 2 component and reduces five times the lateral dimension of the beam With suitable orientation of the Ge crystal to respect to the incident beam, the elimination of the kα 2 component of the radiation can be obtained as the Bragg condition for (022) planes is fulfilled for different incident angles by kα 1 and kα 2 component. Moreover the V-shape allows to the beam to be compressed by a factor 5. Therefore the width beam that is ~1.1 mm after the Gobel is reduced to a ~ 0.25 mm after the monochromator. The divergence of the beam exiting from the V-Groove is less than

126 - 113 APPENDIX A X-RAY DIFFRACTION A.3.3 Eulerian Cradle The diffractometer is composed by a high precision goniometer with two circles, one with radius that is the double of the other. The ¼ centric Eulerian cradle is mounted on the smaller circle (whose angular movement is given by θ), while the detector can be moved (2θ ) on the bigger circle. Once the sample is perfect aligned in the centre of the of the Eulerian cradle each movement among the 6 permitted ( x, y, x, chi, phi,θ ) does not damage the alignment, therefore thank to all this freedom degrees the sample can be moved in such a way to bring into the diffracting Bragg position the desired family of planes. In Table A.1 the range of operation of all six motors are reported Table A.1- The six allowed movements in the Eulerian Cradle with the respective range of operation motor Range of operation chi phi x y z Unlimited, ± - 40 mm 40 mm - 40 mm 40 mm mm 1.2 mm θ A.4. Different scans and their visualization in reciprocal space Every diffraction experiment can be understood thanks to the representation of it in the reciprocal space. Every crystalline sample has associated its own reciprocal lattice that is a real finger print for every material: to obtain information about the reciprocal lattice and the 113

127 - 114 APPENDIX A X-RAY DIFFRACTION shape of the reciprocal lattice node allows obtaining at the same time informations about the analyzed material. In Figure A.8 the reciprocal space accessible region in a diffraction experiment is shown. The yellow area is the accessible one, and this is delimitated by the limiting sphere ( A.2) moreover there are two more region that cannot be observed because of limitation due to instrumentation geometry, it would be necessary to impinge from below the sample (therefore transmission geometry) or otherwise change the wavelength of the used radiation and this is not allowed in the used diffractometer. Figure A.8- Accessible reciprocal space region in a diffraction experiment The typical diffraction measurements commonly used in thin film analysis are [Holy et al.1999]: Longitudinal scan (ω-2θ scan) than can be both a specular scan on symmetric reflection or a non specular scan on asymmetric reflection Rocking curve ( also called ω-scan or transverse scan) Reciprocal space map 114

128 - 115 APPENDIX A X-RAY DIFFRACTION As sake of clearness it is worth to underline that the terms symmetric and asymmetric have a clear meaning only once the crystallographic orientation of the sample is known, So for example if we consider a (0 0 1) oriented (cubic) layer grown on a (001) oriented substrate a symmetric reflection is every reflection concerning family of planes parallel to the deposition plane, i.e. all (0 0 l), while on the opposite an asymmetric reflection is every reflection concerning crystallographic planes inclined by a certain angle to respect to the deposition plane i.e. every (h k l) planes provided h, k 0. Rocking curve ( w-scan) This kind of monodimensional scan also called transverse scan is used to get information about crystal texturing and mosaicity of thin film as well as twin domains detection. To perform a rocking curve the sample is brought in the right Bragg position for the crystallographic family of plane we want to investigate. Then once θ and 2θ position are fixed the sample is rotated of some degree by means θ movement so that if the sample have no defect (i.e. perfectly crystallized without any texture and/or twins) only a unique sharp peak is obtained, while the peaks will be broader for sample with some degree of mosaicity, moreover if there are a twin structure this kind of measurement allows to bring consecutively in diffraction position the different domains so that each domain have a corresponding peak. In such a measurement what varies is the direction of the scattering vector relative to the family planes under investigation to respect to the surface normal. During a rocking curve therefore in the reciprocal space an arch of circumference with its origin coincident with the origin of reciprocal space (000) is drawn by the scattering vector ( in blue in Figure A.9 ). w-2θ scan This kind of measurement is used to get information concerning crystal orientation of substrate and overgrown layer, lattice parameter and thickness. 115

129 - 116 APPENDIX A X-RAY DIFFRACTION Sample ( θ ) and detector (2θ ) are simultaneously rotated being always 2θ the double of θ, so that all family of planes having same crystallographic orientation ( but different atomic planes distance) are brought one after the other in the right Bragg position. This kind of measurement can be made on both family of planes parallel to the physical surface of the sample (specular scan on symmetrical reflection) or on family of planes inclined by a certain angle to respect to the physical surface of the sample (non specular scan on asymmetrical measurement the scattering vector relative to the family planes under study has always the same orientation to respect to the physical surface of the sample, what is varied is the magnitude of that vector. As a consequence in the reciprocal space straight line connecting the origin to the reciprocal space node relative to family on planes under investigation will be drawn (green line in Figure A.9). Reciprocal space map A reciprocal space map is a bidimensional map of integrated intensity. Basically once the reflection is been chosen such map around a certain reflection (both symmetric o asymmetric) can be obtained making for each position on a ω-2θ scan a rocking curve. This means that the scattering vector scans a nearly rectangular region of the reciprocal space. In Figure A.9 the different scan are seen in the reciprocal space: the ω-2θ direction is the green one while the ω-scan (transverse direction) is the blue one. In Figure A.10 an example of how a reciprocal space map can be obtained is shown. 116

130 - 117 APPENDIX A X-RAY DIFFRACTION Figure A.9- Different scans in reciprocal space, to perform reciprocal space map iterative ω-scans and ω-2θ scans have to be performed. Figure A.10- Reciprocal space map. 117

131 - 118 APPENDIX A X-RAY DIFFRACTION A.5 Epitaxial film description in reciprocal space and concept of relaxation line As in a diffraction experiment we obtain nothing other than a monodimensional or bidimensional image of the reciprocal space it is useful to see how we expect the reciprocal lattice of the samples as to better understand and comment the diffraction measurement. The samples are thin films of manganite deposited onto a substrate ( LaAlO 3 in the present case). We have so the overlapping between the reciprocal space lattice of both substrate and layer. In figure A.12 it is shown a section (hh0) (00l) of the reciprocal space in a simple case of a fully relaxed layer of (001) Al x Ga 1-x As on (001) GaSs. Figure A.11 -Schematic representing the film on the substrate and some crystallographic direction identifying two sections in the reciprocal space. The reciprocal lattice nodes (of the considered section) of the film are represented in red, while reciprocal lattice nodes of the substrate are the black ones. 118

132 - 119 APPENDIX A X-RAY DIFFRACTION Figure A.12-Right panel: Section of the reciprocal space showing nodes of reciprocal lattice of a fully relaxed layer (red) onto a substrate (black) left panel. From Figure A.12 left panel it can be deduced that the layer has lattice parameter both in plane and out of plane bigger than that of the substrate as in the case of deposition of film of La 0.7 Sr 0.3 MnO 3 (LSMO) on LaAlO 3 (LAO) substrate. The position of the node in Qx and Qz direction is inversely proportional to the lattice parameter in the conjugated direction. Therefore a variation of the lattice parameter leads to a variation in the position of reciprocal lattice nodes on the layer. If the growth is pseudomorphic it means that the layer assumes exactly the same lattice parameter of the substrate in the deposition plane and leading the reciprocal lattice node of the layer to assume the same Qx coordinate of the substrate as shown in Figure A.13. Figure A.13- Right panel: Section of the reciprocal space showing nodes of reciprocal lattice of a fully strained layer (red) onto a substrate (black) (left panel). The perfect alignment of the reciprocal lattice nodes of the layer with that of the substrate in Qx direction for all reflection except of those of (00l)-type is the proof of the pseudomorphic growth. 119

133 - 120 APPENDIX A X-RAY DIFFRACTION If we consider for example the two extreme situations (relaxed layer and pseudomorphic layer) for a reflection relative to a family plane inclined to respect to the deposition plane (that as such has both an in-plane and a component) the concept of relaxation line can be introduced. This concept is really useful for strain degree investigation in epitaxial film, and it has been used in Chapter 4 the analysis of the diffraction reciprocal space map on asymmetric reflection. Let consider the reflection of the planes (103) for a LSMO (001) film deposited onto LAO (001) substrate. In pseudocubic approximation the situation we have to expect is shown in Figure A.11. Figure A.14 -Relaxation line relative to (103) reflection for a LSMO (001)/LAO (001). In table A.2 the lattice parameter and correspondent H and L values for the two extreme situations of a fully relaxed LSMO (001) film on LAO(001) and fully strained LSMO (001) on LAO(001) for the (103) pseudocubic reflection are shown. The values of L for the two extreme situations of fully relaxed layer and fully strained layer have been estimated considering an elastic deformation with volume conservation. 120

134 - 121 APPENDIX A X-RAY DIFFRACTION Table A.2- Lattice parameter and correspondent H and L value for a LSMO relaxed and fully strained film on LAO substrate LAO a = 3,786 Å H = 1 L = 3 LSMO fully relaxed a = b = c = Å H = 0.98 L = 2.93 a = b = Å LSMO fully strained c = Å H = 1 L = 2,80 The values in table A.2 have to be considered only as an indicative estimation, in particular because the shape of the reciprocal space nodes is not punctiform as it would be in a ideal case of crystal with infinite extension in all direction but there are several causes of broadening due to lowering of the dimensionality (finite thickness effect) and to defects of the sample (mosaicity, roughness) as well as instrumental effect. A.5.1 Concept of Truncation rod In all classical derivation of Bragg condition the scattering intensity from a parallelepiped with M 1 M 2 and M 3 unit cell in the three directions and having a 1 a 2 a 3 as lattice parameter is proportional to the square of the structure factor: F( k 1, k 2, k ) sen ( 2 M 1k1a1) sen ( 2 M 2k2a2 ) sen ( = sen ( k a ) sen ( k a ) sen M1 M 2 M 3 = j1 = 1 j2 = 1 j3 = 1 i( k ) 2 1a1 j1 + k2a2 j3 + k3a3 j3 e ( M 1 2 = 3 k k 3 3 a 3 a ) 3 ) If M 1 M 2 and M 3 are large this oscillating function has sharp peaks ( the more large M 1 M 2 and M 3 are the more sharp they are) at Bragg point having intensity (M 1 M 2 M 3 ) 2 whenever 121

135 - 122 APPENDIX A X-RAY DIFFRACTION the Laue condition for reciprocal lattice definition are satisfied k 1 a 1 =2ph, k 2 a 2 = 2pk and k 3 a 3 =2pl If one of the Laue condition is not perfectly satisfied: i.e. k 3 a 3 2pl the structure factor for large limit of M 3 is: 2πh 2πk F (,, k a a M M sen 2 ) 2 1 ( 1 2 = M k a ) M sen ( 2 M 3k3a3) 2 1 sen ( k a ) that means that all sharp Bragg points are no more well separated each other but there is diffuse streaking connecting all the Bragg nodes. The scattering is sharp only in two directions while in the other there is a broadening like a rod, known as truncation rod [Robinson 1986]. A rod broadening arises every time there is localization in some direction: being the width of maximum proportional to 1/M 1 (or 1/M 2 1/M 3 ). Therefore in the present case where we can assume to have an infinite crystal in the two in-plane ([100], [010] direction) and the break of the condition of infinite crystal is in [001] direction we aspect the truncation rod (a broadening of the reciprocal lattice nodes) perpendicular to the growth plane. An elongation (thickness effect) of reciprocal lattice node of the films in longitudinal direction has to be expected and has been observed in reciprocal space maps performed on the sample analyzed in this Thesis. The elongation appeared to be more evident for the thinner films. 122

136 APPENDIX B-EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION APPENDIX B EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION This appendix contains information regarding the different techniques used for the characterization of the samples. These are: Optical microscopy for the observation of the domain structure of the substrates High resolution X ray diffraction for the characterization of films La 0,7 Sr 0,3 MnO 3 ( reported in Appendix A) High resolution transmission electron microscopy (TEM) for the study of the La 0.7 Sr 0.3 MnO 3 nanostructure SQUID magnetometry for the magnetic characterization of the La 0.7 Sr 0.3 MnO 3 films All samples presented in this thesis have been prepared at Salerno University by means molecular beam epitaxy, using a codepostion procedure in which the elemental rates of Molecular Beam Epitaxy (MBE) also called element-by-element technique is an Ultra-High- Vacuum (UHV)-based technique for producing sequential high quality epitaxial thin film. The main peculiarity of the MBE is the possibility to achieve in-situ formation of the perovskite at very low oxygen pressure without post-annealing treatment. In the present case, a mixture of O 2 + 5% ozone at total pressure of P = 2.63 x 10-2 Pa have been employed. Basically during the MBE deposition procedure what happens is that the solid source of the elemental species needed for the deposition are e-beam co-evaporated inside the Knudsen effusive cell onto a heated substrate. All the deposition time long the substrate is continuously rotate as to assure the homogeneity of the deposition onto the surface. All the process happens in a Ultra-High-Vacuum regime to be sure that the free mean path λ of the atomic specie is bigger than the geometric dimension of the deposition chamber, and therefore to be sure that the atomic species can reach the surface of the heated substrate. This condition is generally fulfilled if the internal pressure in 10-5 Torr (~ 1.33 x 10-3 Pa ) [ Annual Report 2002, Optoelectronics Department, University of Ulm] 123

137 APPENDIX B-EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION Figure B.1-Basic principle of molecular beam epitaxy showing co-evaporation of atoms or molecules from different sources onto a heated substrate. It is worth to note that with this technique the growth rates are typically on the order of a few Å/s and the beams can be shuttered in a fraction of a second ( normally ~ 0.1 s), so that a nearly atomically abrupt transitions from one material to another is allowed. Being the time to grow a monolayer typically of 1 5 s it is clear that this technique allows a very precise monolayer control. One of the main advantages (due to the ultra high vacuum regime) of this method is the possibility to control the growth in real time thanks to the in situ use of the reflection high energy electron diffraction (RHEED). During a RHEED monitorization a high energy beam (3-100 kev) is directed at the sample surface at a grazing angle. As a consequence the electrons are diffracted by the crystal structure of the sample and then impinge on a phosphor screen mounted in front of the electrons source. The resulting pattern is constituted by a series of streaks. The streaks become sharper and more pronounced upon the completion of a unit cell, and the distance between the streaks is an indication of the surface lattice unit cell size. The grazing incidence angle ensures surface specificity despite the high energy of the incident electrons. If a surface is 124

138 APPENDIX B-EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION atomically flat, then sharp RHEED patterns are seen. If the surface has a rougher surface, the RHEED pattern is more diffuse. B.1 Optical Microscopy B.1.1 Optical birefringence Among the different experimental techniques developed for twin domains distinction, optical microscopy with polarized light is the most common, because, despite the quite limited spatial resolution, it permits to have a clear idea of the crystallographic texture due to the coexistence of different domains inside the same sample. With respect to their response to incidence visible light ( Å), transparent crystals are classified depending upon whether or not their main crystallographic axes are equivalent, and two classes can be enumerated: Crystal optically isotropic in which monochromatic light travels with the same speed regardless of the direction of vibration. Being the speed of light propagation the same in all direction, also the refractive index is the same in all directions throughout the crystalline lattice of the substance. Glasses, liquids, gases and isometric (cubic) crystals all belongs to this category. Crystal optically anisotropic, in which the crystallographic axes are distinct and the interaction with light depends upon the orientation of the crystalline lattice with respect to the direction of the incident light. The light travels with different speeds along different directions. In these materials indeed the refractive index is not unique but different for different propagation directions of light. The anisotropic material can be in turn divided into two subgroups, i.e. uniaxial materials, which encompass all minerals with tetragonal, trigonal, hexagonal symmetry, called 125

139 APPENDIX B-EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION uniaxial because they have a single optic axis, and biaxial materials to which belong all minerals with orthorhombic, monoclinic, triclinic symmetry, so called because they have two optic axes. In uniaxial materials one direction is the optic axis: the light travelling in that direction feels the crystal as it would be isotropic, and does not experience any change concerning its polarization state. Rhombohedral LaAlO 3 belongs to this group of crystals. The unique axis is its ternary axis. Therefore a LaAlO 3 single crystal cut normally to the ternary axis will appear dark between crossed polars. It is common to characterize the optical anisotropy of a crystal referring to the optic indicatrix (otherwise called index ellipsoid) defined as x n 2 2 p y + n 2 2 q z + n 2 2 r = 1 in which n p n q and n r are the principal refractive index. For the sake of clearness let us imagine to draw all vectors whose directions correspond to the vibration direction of light, and whose lengths correspond to the refractive index of the material for light with that vibration direction, their tips will define an imaginary surface called the indicatrix (Figure B.2) described through the previous equation, in which n p n q and n r principal semi- axes. represent the Figure B. 2: Optic indicatrix or index ellipsoid for uniaxial crystal n p = n q n r. With reference to Figure B.2 where the optic indicatrix for a uniaxial crystal is represented, a ray p, propagating along y, vibrates parallel to the z-axis and its refractive index (n p ) is 126

140 APPENDIX B-EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION plotted as radii along z; a ray q propagating along x vibrates parallel to y being its refractive index (nq) plotted along y. For any other ray propagating along an arbitrary direction different from the principal axes it is possible to define two refractive indexes, given by the two semi-axis of the interception ellipse between the plane through the origin that is perpendicular to the direction of propagation and the index ellipsoid. An incoming ray polarized in arbitrary direction is so usually split into two rays corresponding to two different refractive indexes: n o for the so called ordinary ray and n e for the extraordinary ray, and this is what is called optical birefringence. For isotropic crystal the refractive index are the same in all direction and the optical indicatrix is a sphere, for uniaxial crystal n p = n q = n o and n r = n e, while for biaxial crystal the index are different in all directions n p = n q = n r. Between crossed polars domains polarized in the viewing direction appear dark for all direction of rotation about the polar axis, while domains polarized in any other direction appear birefringence and appear bright provided the polar axis of the crystal and the polarizes axis are not coplanar. B.2 Transmission electron microscopy The local structure of thin films of strained La 0.7 Sr 0.3 MnO 3 deposited onto LaAlO 3 ferroelastic substrate has been studied also by high-resolution electron microscopy. This technique enabled us to get more information about the microstructure of La0.7Sr0.3MnO3 film and LaAlO 3 substrate with particular regard to the interface between film and substrate. For the transmission electron microscopy characterization a FEI Tecnai F20 Field emission high resolution transmission electron microscope has been used. 127

141 APPENDIX B-EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION Beside the functioning principle of a TEM that basically is the same of that of optical microscope the peculiar characteristic of a TEM is the possibility to reach resolution and magnification much better than that of optical microscopy. This resolution is smaller than the size of most atoms and therefore the image produced by means TEM show the true structural arrangement of atoms in the sample material. Information about the morphology, crystal structure and defects, crystal phases and composition, and magnetic microstructure can be obtained. As a matter of fact the TEM image are formed using electrons instead of visible light so that being the wavelength of electron shorter that of visible light if they are properly accelerated and focused on a transmitting sample they can produce magnification of details up to 1 M x with resolution of nanometer scales. B.2.1 Basics of Transmission electron microscopy Basically a transmission electron microscopy is composed by a source of electrons (the electron gun, not shown in the picture) and a series of electromagnetic lens for deviation and focalization of the electron beam. To the aim of obtaining wavelength much smaller than that of the light the electron are accelerated at several hundred kv: i.e. 200kV electrons have a wavelength of 0.025Å. 128

142 APPENDIX B-EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION Figure B.3- Schema of a TEM: objective lens and projective lens are shown. Essentially the final image in the TEM is formed by means three types of lenses: Condenser lens which concentrates and focuses the beam of electrons coming over from the electrons source onto the sample to give a uniformly illuminated sample Objective lens ( objective and intermediate lens in Figure ) which form the diffraction pattern in the back focal plane or image in the image plane, what eve is obtained in this plane can be further enlarged by means the projector lens Projector lens which form the final image / diffraction pattern on the screen By means the objective diaphragm we can take the diffraction pattern in the back focal plane as object for the objective lens, in this way we obtain the diffraction pattern as final image on the screen (diffraction mode). Otherwise if we take the image plane of the 129

143 APPENDIX B-EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION objective lens as the objective plane of the intermediate lens and projector lens, we will form image on the screen and this is the image mode. The two basic images modes of TEM operation are the bright-field mode (BF) and the dark-field imaging mode (DF). Bright field mode means that the image is constructed starting from the transmitted electrons, while in dark field mode the transmitted electron are excluded and the image is constructed by means the diffracted or scattered electrons. Figure B.4- Bright field mode and dark field mode; in bright field mode the image is created by means transmitted beam while in dark field mode the final image is created by the diffracted beam. B.2.1 Sample preparation for TEM cross section observation One typical method to prepare thin lamellae for electron microscopy is to thin the specimens to electron transparency down to nanoscopic dimension by means a fine energetic beam of Gallium ions of a Focus Ion Beam (FIB). For the preparation of the samples for TEM observation a FEI FIB200TEM (shown in Figure B.5) with a Ga ions at 30 kv is been used. 130

144 APPENDIX B-EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION Figure B.5- FEI FIB200TEM used from TEM thin lamellae preparation (Queen s University Belfast). After the deposition of a thin protective layer of Al (or carbon) on the surface, the sample is positioned in the sample holder inside the FIB chamber where a Pt addictive layer is deposited in order to minimize any ion damage during subsequent FIB milling. Inside the FIB chamber is possible to tilt and rotate the sample to mill it at different angle as to reach the desired dimension and shape of the lamella. Cross-sectional samples were prepared in standard trench geometry. The beam current can be varied from 10 pa to 5000 pa depending on the the dimension of the trench that has to be milled. It is very important the correct balance between the duration of the cut and the energy of the beam. For the same cut, if the beam is more energetic the duration of the cut is reduced therefore also the possibility for the sample to move and so the risk to mill undesirable areas decreases- but on the other side if the beam is too much energetic it could remove the protective layer and in the worst cases even damage the sample under the protective layer. Basically after the Pt deposition a clean area of the sample is identified and a first standard cut is made as schematically shown in Figure B.6 upper part as to obtain a first bar shown in plan view in the right part. 131

145 APPENDIX B-EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION Figure B.6- Upper panel: Schematic representation of the first phase of lamella preparation, a first bar is obtained by milling trenches of material from each side; bottom panel: plan view of the bar. Then after the so-called U-cut made tilting the sample by 45 (as shown in Figure B.7) the thinning procedure can start. This procedure consists on iterative milling from each side until the desired thickness (typical around 50 nm) is achieved. Figure B.7- The U-cut which is made before starting the fine thinning procedure. 132

146 APPENDIX B-EXPERIMENTAL TECHNIQUES FOR SAMPLES CHARACTERIZATION Trenches of material are removed alternatively from each side slightly tilting the sample alternatively in positive and negative direction. The lateral dimension as well as the depth of the cut are reduced at every step until a lamellae with 50 nm a thickness in the middle part is obtained (Figure B.8 bottom panel) Then two cuts on the edges still attached to the rest of the sample have to be made so to permit in a second moment the lamellae to be lifted out. FigureB.8- Upper panel: one step in the thinning procedure is shown: the removed area is that in the yellow rectangular. Bottom panel: image of the lamellae after the thinning procedure before the final cut on the lateral edges. To lift out the thin lamellae the sample positioned under an optical microscope, where with the help of a glass needles micromanipulator the thin lamellae were lifted out by means electrostatic forces and then positioned in the carbon grid ready for TEM observation. 133