Doctoral dissertation. Nuclear magnetic resonance study of selected Ruddlesden-Popper manganites

Transcription

1 AGH-University of Science and Technology Faculty of Physics and Applied Computer Science Charles University Faculty of Mathematics and Physics Doctoral dissertation Damian Rybicki Nuclear magnetic resonance study of selected Ruddlesden-Popper manganites completed at the Department of Solid State Physics Faculty of Physics & Applied Computer Science AGH University of Science & Technology, Cracow, Poland under supervision of prof. dr hab. Czesław Kapusta and at the Department of Low Temperature Physics Faculty of Mathematics and Physics Charles University, Prague, Czech Republic under supervision of Doc. RNDr. Helena Štpánková, CSc. Kraków, 2007

2 I thank all persons who contributed and have their share in this work. Above all I wish to thank my beloved wife for her patience and support. I warmly thank both supervisors, Prof. Czesław Kapusta and Doc. Helena Stepankova for their attention and guidance. I also express my gratitude to V. Prochazka,Z. Jirak A. Lemaski, D. Zajc, W. Tokarz, J. Przewonik and others.

3 Contents Contents: Polskie streszczenie i 1. Introduction 1 2. Properties of cubic and bilayered manganese perovskites Mixed valence manganese perovskites Structural properties Magnetic and electronic properties Phase segregation Bilayered manganese perovskites, La2 2 x Sr1 + 2 xmn2o Cubic manganese perovskites La1 xsrx MnO Nanoparticles of La1 xsrx MnO La1 xca xmno Sample preparation Cubic perovskites La1 x ( Sr, Ca) x MnO Bilayered perovskite manganites Nuclear Magnetic Resonance method Nuclear Magnetic Resonance Physical basis of the NMR Quantum mechanical description Classical description Spin echo technique and relaxation times NMR in magnetically ordered materials The effective field at nucleus Enhancement of the high frequency field NMR spectrometers and magnetometers Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO La Sr MnO 3 and La 0.85 Sr 0.15 MnO 55 3 Mn and 139 La NMR La Sr MnO 3-55 Mn NMR La 0.85 Sr 0.15 MnO 3-55 Mn NMR La Sr MnO 3 and La 0.85 Sr 0.15 MnO La La 0.9 Ca 0.1 MnO 3-55 Mn NMR results Nanoparticles of La 0.75 Sr 0.25 MnO Mn NMR results of La 0.75 Sr 0.25 MnO 3 nanoparticles Mn NMR spin echo spectra at 4.2 K and 77 K 61

4 Contents The spin-spin and spin-lattice relaxations at 4.2 K and 77 K The enhancement factor of 55 Mn at 4.2 K and 77 K La signal at 4.2 K and at no applied field Bilayered manganese perovskites, La 2-2x Sr 1+2x Mn 2 O Mn NMR of bilayered manganese perovskites, La 2-2x Sr 1+2x Mn 2 O Mn NMR results at 4.2 K Mn 4+ signal analysis Mn 3+ signal analysis Mn NMR at 77 K La NMR at 4.2K Heavily doped La 2-2x Sr 1+2x Mn 2 O Magnetic measurements of heavily Sr doped La 2-2x Sr 1+2x Mn 2 O 7, x Mn NMR results of heavily doped La 2-2x Sr 1+2x Mn 2 O Spin-spin relaxation times, T 2 in heavily doped La 2-2x Sr 1+2x Mn 2 O Conclusions References List of author s publications Publications related to thesis Other publications 110

5 Chapter 1: Introduction 1 1. Introduction Cubic and bilayered manganese perovskites belong to a very broad family of oxide compounds of transition metals crystallizing in the perovskite structure. They are a part of the Ruddlesden-Popper phases system which is described by the formula: ( A ) 1 xbx Mn n+ 1 no3n+ 1, where A and B are trivalent and divalent cations, respectively. The compounds studied exhibit intriguing magnetic and electronic properties and phenomena, including phase segregation. They also show magnetoresistance effect, which is very promising in terms of possible applications. Magnetic and electronic properties of these compounds are closely interrelated, due to the same (d) character of the magnetic and conduction electrons. The interplay of lattice, charge, spin and orbital degrees of freedom results in a variety of electronic and magnetic properties ranging from a metallic or insulating ferromagnetic, to antiferromagnetic insulating, or paramagnetic insulating behaviour. Manganese perovskites also offer a unique opportunity to study and verify concepts introduced by theoretical physicists and chemists, which can also be very useful in other fields of physics. In this work the effect of dimensionality of the compounds structure is studied. Cubic manganese perovskites with general formula ( A1 xbx ) MnO3 are considered as three dimensional compounds, while bilayered perovskites, ( A ) 1 xbx Mn 3 2O7 are considered as (quasi) two dimensional. Other important aspects and factors which influence properties of these compounds are also studied, such as: the effect of Sr or Ca doping, the influence of the grain size on the magnetic and electronic properties and how the applied magnetic field affects the local properties. Additionally, for some compounds the temperature changes of their properties are investigated. Namely, an attempt is made to check if the phase segregation picture is a common feature for various manganese perovskites, which differ in terms of their macroscopic properties. In order to study local properties of the compounds of interest, the Nuclear Magnetic Resonance (NMR) method was employed and complemented with bulk magnetic measurements. NMR uses nuclear magnetic dipole moments and electric quadrupole moments as local probes of electronic and magnetic states of their parent atoms with the selectivity to the individual isotope of the element. Nuclear magnetic dipoles probe magnetic hyperfine fields produced by electrons and the nuclear electric quadrupoles probe electric field gradients produced by an electric charge density of aspherical distribution around the nucleus. It provides the information on the magnetic and electronic state of an element at the individual structural and magnetic sites. Fluctuations of the hyperfine fields and electric field gradients contribute to the nuclear relaxation. Performing the NMR experiment in an applied magnetic field enables us to study the local arrangement of magnetic moments and their coupling.

6 Chapter 2: Properties of cubic and bilayered manganese perovskites 2 2. Properties of cubic and bilayered manganese perovskites 2.1 Mixed valence manganese perovskites Mixed valence manganites with the perovskite structure (see subsection 2.2 Structural properties) with the general formula ( A1 xbx ) MnO3 became for the first time the subject of interest of physicists in the fifties of the last century. Many features of those compounds were described by Jonker and van Santen, namely ceramic sample preparation process, crystal structure and magnetic properties etc. [Jonker 1950, 1956, van Santen 1956]. When a trivalent cation, A 3+ is substituted with a divalent cation B 2+ with oxygen ion maintaining O 2- state, the relative fraction of Mn 3+ to Mn 4+ decreases with increasing doping x. In the fifties of the last century many different systems were studied and a rich variety of possible magnetic type orderings and first evidence of phase separation in those compounds were found, see for example in [Wollan 1955], where La 1-x Ca x MnO 3 system was studied by neutron diffraction technique. The interest of the experimental physicists was followed by theoretical physicists and the theories established by C. Zener, J. Kanamori, J. Goodenough and the others are used by scientists today. The interest in manganites revived in the 1990s, when large magnetoresistance (MR) effects were found in Nd 0.5 Pb 0.5 MnO 3 [Kusters 1989]. Magnetoresistance is an effect in which the electrical resistivity of the material changes when this material is placed in an external magnetic field. The effect was first predicted by E. Hall [Hall 1897] and the MR is usually defined as: RB R0 MR = R0 where R B is the resistivity of material at applied external magnetic field and R 0 is the resistivity at zero field. Example of such effect for La1.4Sr1.6 Mn2O7 compound is presented in Fig Fig Temperature dependence of the electrical resistivity measured on single crystal of La 1.4Sr1.6 Mn2O7 at various applied magnetic fields, the resistivity was measured along two different directions [Perring 1998].

7 Chapter 2: Properties of cubic and bilayered manganese perovskites Structural properties Due to similar crystal structure to that of the mineral CaTiO 3 (perovskite), the compounds studied are called perovskites. Ideal cubic perovskite structure is shown on Fig It consists of the transition ion (small cation) at the centre of the cube, which is coordinated by six oxygen atoms in octahedron, the corners of the cube are occupied by large cations, which can be for example La, lanthanides, alkaline earths or elements from first group of the periodic table like K or Na. Only in ideal case the crystal structure is of cubic symmetry; if one has a mismatch of ionic radii between small and large cations, the symmetry is reduced to orthorhombic or tetragonal. Fig. 2.2 The unit cell of the ideal cubic manganese perovskite. The studied compounds belong to the Ruddlesden-Popper phases with a general formula( A ) 1 xbx Mn n+ 1 no3n+ 1, the n parameter can be equal to 1, 2, 3, and, x is the doping, A is a trivalent cation and B is a divalent cation. When n= one obtains formula( A1 xbx ) MnO3, which are so called three dimensional cubic perovskites. If n=2 the general formula is ( A ) 1 xbx Mn 3 2O7, compounds from this series are sometimes referred as two dimensional bilayered perovskites, which is due to their quasi two dimensional crystallographic structure. Both crystallographic structures are presented in Fig The crystallographic structure of the "cubic" perovskites is no longer of cubic symmetry, but has orthorhombic symmetry due to rotations of the oxygen octahedra and due to the cooperative Jahn-Teller distortions (octahedra can be compressed or elongated along various axes), Fig 2.3a or a rhombohedral symmetry at higher doping (not presented). The crystallographic structure of bilayered perovskite presented in Fig 2.3c is tetragonal. Fig 2.3b presents the Mn-O bonds arrangement in cubic perovskites. The medium bond length is between Mn and apical oxygens, the short and long bonds are between Mn and planar oxygens and they alternate on going to neighbouring octahedron. Fig. 2.3d presents a scheme of Mn-O bonds arrangement in bilayered manganites. Depending on the doping parameter x, the short and medium bonds can be exchanged.

8 Chapter 2: Properties of cubic and bilayered manganese perovskites 4 Fig. 2.3 a) Crystallographic structure of cubic manganese perovskite with Pbnm orthorhombic symmetry; b) bonds arrangements in cubic manganese perovskite with orthorhombic symmetry (L-long, M-medium, S-short, trivalent or divalent cations were omitted for clarity); c) crystallographic structure of bilayered manganese perovskite with I4/mmm tetragonal symmetry; d) bonds arrangements in bilayered manganese perovskite with tetragonal symmetry. 2.3 Magnetic and electronic properties Before going into more detailed information on electronic and magnetic properties of perovskite manganites with mixed valence a brief and essential introduction to basic physics related to manganese compounds with perovskite structure is presented. As was mentioned earlier, when substituting a trivalent cation A with divalent cation B the valence of Mn increases from Mn 3+ to Mn 4+. Both these ions have their valence electrons in the 3d band, the splitting of the atomic 3d energy levels by the crystal field and by the Jahn-Teller effect in Mn 3+ is presented in Fig 2.4.

9 Chapter 2: Properties of cubic and bilayered manganese perovskites 5 Fig 2.4 Energy levels of 3d band of the Mn 3+ in a free ion (five-fold degenerate levels) and splitting of levels by the crystal field (10Dq) in the octahedral symmetry into t 2g and e g levels and further splitting by the Jahn-Teller distortion ( JT ). One of possible modes of the Jahn-Teller distortion is also presented. The meaning of used symbols is described in text. In the free Mn 3+ cation five 3d orbitals are degenerated, but the crystal field resulting from six oxygen anions in vertices of octahedron surrounding Mn 3+ cation in the centre, splits energy levels into three lower energy levels, t 2g ( d, d xy xz, d ) and two higher energy levels, e yz g ( d, d ). The crystal field 2 2 x 2 y 3z r 2 splitting (10Dq) amounts to 2-3 ev. The t 2g and e g levels are further split by the Jahn-Teller distortion ( JT ), which is typically one order of magnitude smaller than the crystal field splitting energy. One of possible modes of the Jahn-Teller distortion is presented in Fig 2.4. In the presence of the Jahn-Teller distortion the e g orbitals differentiate their energy, which leads to many interesting phenomena like orbital ordering in manganese perovskites [van den Brink 2002]. The large Hund s coupling (J H ) leads to the high spin state of the Mn ions (either three electrons on the t 2g band and one electron on the e g band for Mn 3+ or only three electrons on the t 2g band for Mn 4+ ). For understanding the physics related to manganese perovskites it is also essential to introduce possible magnetic interactions, which can occur between Mn ions i.e. the super-exchange (SE) and double exchange (DE) interactions. Both these interactions are indirect exchanges with mediation of the oxygen, which is located between two Mn ions. The SE interaction occurs between two magnetic ions of the same valence through the occupied oxygen 2p orbital (Fig. 2.5). The SE interaction is a virtual exchange between electrons of magnetic ions with electrons from the same 2p orbital of oxygen, which are antiparallel according to Pauli exclusion principle. Therefore the orientation of spins of magnetic ions is also antiparallel and leads to antiferromagnetic ordering of the material. In some cases the SE interaction can lead to ferromagnetic ordering, it happens, when electrons from magnetic ions interact with electrons from

10 Chapter 2: Properties of cubic and bilayered manganese perovskites 6 different oxygen orbitals [Goodenough 1955]. Since SE is only virtual exchange it does not affect the mobility of electrons. The DE interaction occurs between two Mn with different valence also through the 2p oxygen orbital, but unoccupied (Fig. 2.5). The DE interaction occurs when the electron from the e g orbital (of Mn 3+ ion) can hop to a neighbouring site (to Mn 4+ ion), when there is a vacancy of the same spin [Zener 1951]. As a result of the first Hund s rule and strong exchange interaction of the e g electron and three t 2g electrons all electrons are aligned. Therefore the hopping of the e g electron from one site to other site with t 2g electron spins antiparallel to e g electron spin is not energetically favourable. As a result, ferromagnetic alignment of neighbouring magnetic ions is required to maintain the high spin state of both ions. The DE and the electron hopping ability reduce kinetic energy and the system aligns ferromagnetically to minimise the total energy. Another result of electron hopping is the appearance of itinerant electrons in the system, which results in metallicity of the material. If the manganese spins are not parallel or if the Mn-O-Mn bond is bent the electron transfer is more difficult and electron mobility decreases. Fig. 2.5 The schematic diagram of mechanism of the double exchange and super-exchange interactions in the case of two Mn cations. It was proposed by Anderson and Hasegawa [Anderson 1955] that the transfer integral, t follows following relation: θ t = t0 cos (2.1) 2 where t 0 is the normal transfer integral, which depends on the spatial wave functions and the term cos(θ/2) is due to spin wave function where θ is the angle between two spins directions (Fig. 2.5). An important factor, especially

11 Chapter 2: Properties of cubic and bilayered manganese perovskites 7 for nuclear magnetic resonance, is also correlation time of the electron hoping, τ which is smaller than 10 ps, in La 1-x Na x MnO 3 (x= ) compounds τ was found to range from s (at 60 K) to s (at 300 K) [Savosta 1999]. 2.4 Phase segregation Due to the strong competition between the DE and SE interactions and electron-phonon interactions (i.e. Jahn-Teller effect) in manganites a rich variety of possible types of magnetic (paramagnetic, ferromagnetic, antiferromagnetic, canted antiferromagnetic) and electronic (metallic, insulating) phases can occur. Moreover, in manganites ferromagnetic metallic (FMM) phase can coexist with ferromagnetic insulating (FMI) or antiferromagnetic insulating (AFI) phases. If one also keeps in mind the possible charge order (Mn 3+ and Mn 4+ ions) and orbital order of the Mn 3+ 3d e g orbitals ( d or d ) the number of physical parameters, which has to be taken into account, when explaining observed properties of manganites, is very high. x y 3z r Fig. 2.6 An atomically sharp boundary separates an insulating charge-ordered phase (left, pink) from a weakly conducting charge-disordered phase (right, purple), as shown in this room-temperature STM image of Bi 0.24 Ca 0.76 MnO 3, inserts present I-V curves for both regions [Renner 2002, Mathur 2003]. First observations of phase coexistence in manganese perovskites date to 1950s and were done with neutron diffraction, but nowadays imaging techniques provided much more detailed information on the nature and the length scales of this phases. The first experiment with imaging technique (transmission electron microscopy) revealed coexistence of the FMM phase and charge ordered insulating (COI) phase in compounds La 5/8-y Pr y Ca 3/8 MnO 3 [Uehara 1999]. The authors also proposed a model, which explained the fact that observed saturation magnetisation, M S was smaller than it was supposed to be according to the compound s stoichiometry and related theoretical spin magnetic moment. The model assumed that due to DE interaction between Mn 3+ and Mn 4+ ions, FM

12 Chapter 2: Properties of cubic and bilayered manganese perovskites 8 clusters (domains) are formed, their size depends on the distortions and doping. However, there are also regions characterized as charge ordered and insulating, which are responsible for smaller M S of the sample. The picture of phase separation obtained by scanning tunnelling microscope (STM) spectroscopy combined with the atomic resolution STM imaging for Bi 0.24 Ca 0.76 MnO 3 is presented in Fig In the charge-ordered phase, the I-V curve displays insulating behaviour, whereas the chargedisordered phase shows an ohmic, metallic regime near zero voltage. The origin of this difference appears to be related to the structure. In the charge-ordered phase, the Mn 3+ and Mn 4+ ions arrange themselves in a regular, repeating pattern that doubles the unit cell [Renner 2002, Mathur 2003]. The phase separation problem has recently been studied by other imaging techniques. E.g. Loudon et al. [Loudon 2002] reported the electron holography and transmission electron microscopy results on La 0.5 Ca 0.5 MnO 3 at 90 K. The authors found the phase exhibiting simultaneously charge ordering and ferromagnetic properties, which were prior believed to be mutually exclusive. J.H. Yoo et al in [Yoo 2004] studied La 0.81 Sr 0.19 MnO 3 compound by means of the electron holography and the effect of the applied magnetic field on the coexisting paramagnetic and ferromagnetic phases was presented. Their studies revealed that well separated ferromagnetic domains located in paramagnetic matrix are connected by the formation of the channels of magnetic flux, while the previous works considered the interaction between the substantially close FM domains. When phase separation was found by experimentalists it also attracted interest of theoretical physicists. First computational results presented in [Yunoki 1998] with Kondo Hamiltonian have taken into account the DE interaction and Jahn-Teller distortions and the results showed strong tendency for phase separation in hole doped manganese perovskites. The models were further extended [Moreo 1999, 2000, Dagotto 2001, 2002] but the common feature was assuming a cluster state with FM islands (droplets etc.), which were aligning their magnetic moments on applying external magnetic field. However, such models had problems with explaining the experimental values of the resistivity. This problem was solved in [Burgy 2004] by adding into considerations the cooperative nature of Mn-O lattice distortions. In [Khomskii 2003] it was shown that in percolation picture, not only the total fraction of one or another phase, but also distribution of these phases in size and shape can be crucial. Also NMR measurements revealed electronic phase separation in manganese perovskites. First such results were presented in [Allodi 1997, Papavassiliou 1999, 2000, Renard 1999, Kapusta 2000a, 2000b]. Phase separation observed with the NMR method manifests itself with distinct resonant lines in the frequency swept NMR spectra. Resonances around 330 MHz or higher than 400 MHz are due to Mn 4+ and Mn 3+ ions in the

13 Chapter 2: Properties of cubic and bilayered manganese perovskites 9 ferromagnetic insulating phase. Signals between MHz are due to the resonance of Mn 4+ ions in the antiferromagnetic insulating phase. The resonance around MHz is due to manganese ions with averaged valence (between 3+ and 4+) as a result of the ferromagnetic coupling resulting from the DE interaction [Matsumoto 1970]. Observation of this resonance indicates that the characteristic time of electron hopping due to the DE interaction is shorter than the precession period of the nuclear magnetic moment, i.e. it is much shorter than the difference in precession periods in the two states (3+ and 4+) when the direction of hyperfine field does not change, i.e. << s. A schematic plot of the frequency swept spectrum with possible resonant lines is presented in Fig In [Allodi 1997] results of 55 Mn and 139 La NMR measurements, showed coexistence of antiferromagnetic and ferromagnetic subsystems in Ca doped LaMnO 3 compounds. Coexistence of FMM and FMI regions is also possible as was concluded in [Papavassiliou 2000] for La 1-x Ca x MnO 3 (with x ranging from 0.2 to 0.5). In low hole doped La 1-x Sr x MnO 3 system coexistence of insulating and metallic phases was found as well [Renard 1999]. Fig Schematic plot of the frequency swept NMR spectrum with possible resonant lines and their attribution to various phases.

14 Chapter 2: Properties of cubic and bilayered manganese perovskites Bilayered manganese perovskites, La2 2 x Sr1 + 2 xmn2o7 The general formula of bilayered manganites can be written as La2 2 x Sr1 + 2 xmn2o7. The magnetic and structural phase diagram for doping parameter x ranging from 0.3 to 1, determined by neutron powder diffraction [Mitchell 2001] is presented in Fig 2.8. Fig. 2.8 Magnetic and structural phase diagram of La2 2 x Sr1 + 2 xmn2o7 determined by neutron powder diffraction [Mitchell 2001]. Solid markers represent magnetic transition temperature (T C or T N ), open markers the tetragonal to orthorhombic transition. The abbreviations mean: FMM (ferromagnetic metallic), AFI (antiferromagnetic insulating), LRO (long range order), CAF (canted antiferromagnet), CO (charge ordered), types of magnetic order are shown in Fig As was stated earlier the compounds studied have tetragonal I4/mmm symmetry at low temperatures, which does not change with doping up to x=0.8. Their body centred tetragonal structure consists of bilayers of MnO 6 octahedra separated by (La,Sr) 2 O 2 layers. MnO 6 octahedra, similarly to cubic perovskites (with n= ) suffer from Jahn-Teller (J-T) distortions, although they are much smaller and typical Mn-O-Mn angles in plane are close to 179 [Mitchell 2001]. However magnetic and electronic properties are considerably altered by the change of doping parameter. The La 1.4Sr1.6 Mn2O7 (x=0.3) compound at low temperatures is an antiferromagnet (AFM) with magnetic moments along the c axis and ferromagnetic (FM) order within the bilayer while bilayers are AFM coupled (Fig. 2.9). This type of magnetic order was also confirmed by imaging with spin-polarised scanning electron microscope [Konoto 2004]. The compounds with doping from 0.33x<0.5 are FM with moments within the ab plane. In phase diagram constructed in [Mitchell 2001]

15 Chapter 2: Properties of cubic and bilayered manganese perovskites 11 the x=0.4 compound has the same magnetic structure as the compound with x=0.35, while in [Kubota 1999, Hirota 2002] the structure is proposed to be a canted AFM. Canted AFM ordering occurs in [Mitchell 2001] in doping range 0.42x<0.5. Starting from x=0.5 A type AFM order was proposed. In this type of magnetic order, magnetic moments are within ab plane FM coupled in a single layer, but coupling between two layers is AFM. Very interesting region was found to exist in doping range 0.66x<0.74, where neutron powder diffraction showed no magnetic long range order (LRO) [Ling 2000]. Within the doping range 0.75x<0.92 the crystal structures changes to orthorhombic Immm space group. The neutron powder diffraction revealed two AF superstructures, referred as type C and type C*, in which the c is doubled [Ling 2000]. Above x=0.92 type G magnetic order was found [Mitchell 1998]. The ideal G type magnetic order, found for x=1, involves all Mn nearest neighbours coupled AF, with spins parallel to the c axis. Below x=1 spins tilt from the c axis towards ab plane [Ling 2000]. Therefore in accordance to Goodenough s theoretical predictions, when increasing Mn 4+ content (increasing number of holes in the e g orbital) one successively obtains less ferromagnetism (sheets to rods to points). Fig. 2.9 Magnetic structures of La2 2 x Sr1 + 2 xmn2o7 series of compounds at 5 K, determined by the neutron powder diffraction [Mitchell 2001]. As a result of reduced dimensionality of the compounds a highly anisotropic behaviour of the resistivity is observed. The resistivity measured within the ab plane and along the c axis differs by few orders of magnitude [Perring 1998, Matsukawa 2000] (Fig. 2.1). Reduced dimensionality of the compounds gives also rise to an enhanced magnetoresistance (MR) [Moritomo 1996]. Spin wave measurements carried out for x=0.3 to 0.4 [Perring 1998] showed that the in-plane exchange depends weakly on doping, x. The exchange between planes of the bilayer changes by factor of four with increasing x from 0.3 to 0.4 and it was concluded that with doping there is a change of the orbital character from mixed 3d d and orbital for compound with x=0.3 to 2 3z r d x y

16 Chapter 2: Properties of cubic and bilayered manganese perovskites 12 mostly d for x=0.4. A stabilization of the 3d d orbital with increasing x y doping was also proposed in another spin waves study [Hirota 2002]. Similar conclusions were derived by [Welp 2001] on the basis of magnetisation measurements on single crystals and magnetic anisotropy analysis. However there are also studies that suggest that in doping range of 0.3x0.5, occupancy of the 3d d orbital is higher than of the d orbital. In [Argyriou 2002,] z r from polarized neutron diffraction studies of the x=0.4 doped compound at 100 K, authors concluded that the 3d d orbital has higher ocupation. Similar 2 2 3z r conclusion for the compound with the same doping was made in [Akimoto 1999] basing on the Madelung potential calculation derived from the structural data. x y x y

17 Chapter 2: Properties of cubic and bilayered manganese perovskites Cubic manganese perovskites La1 Sr MnO3 x x Phase diagrams of all manganese perovskites are rich especially at low temperatures and the material magnetic and electronic properties change strongly with dopant concentration (e.g. Sr or Ca). Fig presents one of the first constructed phase diagrams of La1 xsrx MnO3 series of compounds in the region of interest. The parent compound i.e LaMnO3 is an antiferromagnet with ferromagnetic order within the plane and antiferromagnetic coupling between the planes [Wollan 1955] with Néel temperature T N 140 K and magnetic moment within the plane of µ=3.87µ B [Moussa 1996]. The spin-echo NMR 55 Mn study by Sidorenko et al. [Sidorenko 2004] revealed signal from Mn 3+ ions around 350 MHz at 10 K. The signal was vanishing fast with temperature due to fast transverse relaxation. With increasing doping the T N decreases slightly and when going out from parent compound canted antiferromagnetism (CAF) occurs. Starting from x 0.1 we have ferromagnetic spin arrangement with T C increasing with doping parameter. The compounds of interest i.e. x=0.125 and x=0.15 have T C values 205 K and 240 K respectively. Dabrowski et al. [Dabrowski 1999, Xiong 1999], have studied extensively the transport, magnetic and structural properties of La 1-x Sr x MnO 3 compounds with 0.1x0.2 and in temperature range 10T350K, the study has shown that the arrangement of spins varies from FM ordered, mainly along the b-axis (x=0.11) to FM almost Fig Phase diagram of La1 xsrx MnO3. CI, FI, FM, PI, PM, AFM denote spin canted insulating, ferromagnetic insulating, ferromagnetic metallic, paramagnetic insulating, paramagnetic metallic, antiferromagnetic [Dagotto 2001].

18 Chapter 2: Properties of cubic and bilayered manganese perovskites 14 along the c-axis (x=0.185). Up to x=0.16 compounds are insulating, both below and above the T C. Above x=0.16, below the T C compounds are still ferromagnetic, but metallic up to almost x=0.5. Unexpectedly compounds in the range 0.16<x<0.3, which are metallic at low temperatures, above the T C are insulating. In the region 0.5x0.6 the compounds are A-type AFM (see Fig. 2.9). At low temperatures starting from close to x=0.22 there is a change from orthorhombic symmetry at lower doping to rhombohedral at higher x [Paraskevopoulos 2000, Dabrowski 1999]. This structural transformation is due to an absence of coherent Jahn-Teller distortions, which are present in the orthorhombic phase. In perovskites in paramagnetic state there exist magnetic moments correlations called magnetic polarons [DeGennes 1960]. They were studied by several techniques up to now. One of first results presenting such polaronic behaviour in paramagnetic state was NMR study by Kapusta et al., [Kapusta 1999a], where authors found that such correlations existed due to the DE interaction. In La1 xsrx MnO3 system (for x=0.3 and 0.4) such polarons were experimentally found above the T C by Mannella et al., [Mannella 2004]. Formation of ferromagnetic polarons above the T C and below some certain temperature T * agrees also with theoretical calculations [Burgy 2001]. Besides magnetic polarons also orbital polarons were found in these systems. The Hartree-Fock calculations indicated that in lightly doped manganites orbital polarons in which the orbitals of Mn 3+ sites are directed towards the Mn 4+ -like site are created. Orbital polarons are stabilized by the breathing-type and Jahn-Teller-type lattice distortions and the magnetic coupling between these polarons is ferromagnetic [Mizokawa 2000]. Experimentally in lightly doped La1 xsrx MnO3, the orbital polarons were confirmed to be present below the T C down to 5 K by the inelastic light scattering [Choi 2005] Nanoparticles of La1 Sr MnO3 x In the past few years, besides single crystals, powder samples with grains of micrometric size, thin films and nanoparticle materials have also been studied [Zhu 2001, Li 2001, Bibes 2003]. They are prospective materials for biomedical applications, both for diagnostics and therapy [Mornet 2004, Gupta 2005]. For example for magnetic hyperthermia owing to their lower T C, they seem to be advantageous over commonly used magnetite or maghemite nanoparticles. Lower T C guarantees that the treated tissue is not overheated, the radiation which penetrates the tissue is only emitted if the nanoparticle is in magnetically ordered state [Pollert 2006]. Magnetic nanoparticles have already been used as a magnetic resonance imaging contrast enhancement, for tissue repair, detoxification of biological fluids, drug delivery and cell separation. The biomedical applications require that the nanoparticles have high magnetization x

19 Chapter 2: Properties of cubic and bilayered manganese perovskites 15 values, dimensions smaller than 100 nm and narrow range of the size distribution. For biomedical applications the surface of nanoparticles has to be coated, this coating has to be non-toxic, biocompatible and allow target delivery of the particle localization in the specific area. The size of the grain and in consequence different volume ratios of the atoms on the surface to the total volume, are additional parameters that highly influence electrical and magnetic properties of the perovskite manganites. It is now well established in literature that the nanoparticles consist of inner core part, which has properties similar to the bulk material and surface part, which differs in properties from the bulk material. The surface regions are spin disordered and may have some structural faults like vacancies etc. As can be expected the size of the grains has very big influence on the magnetotrasport properties (i.e. magnetoresistance) due to higher electron scattering on disordered grain surfaces at zero field and smaller scattering on ordered spins after applying the external magnetic field. From this point of view nanoparticles of manganese perovskites can in the future be used by the modern spin electronics La1 Ca MnO3 x x The phase diagram of this system is presented in Fig All manganese cubic perovskites doped with divalent alkaline earth reveal similar structural, electronic and magnetic properties at similar doping values. Therefore always similar phases occur on their phase diagrams, although at slightly different doping, which is mostly determined by the band width. The low Mn 4+ concentration region at low temperatures of the La1 xcaxmno3, similarly to the La1 xsrx MnO 3 system, transforms with doping from the AF insulator to canted AF insulator, FM insulator and to FM metal [Dagotto 2001, Biotteau 2001]. There is confusion in the literature about properties of the low doped La1 xca xmno 3 system. In [Pissas 2004] it was found that it was due to the different sample preparation processes used, namely different atmospheres during sample preparation process. The differences in the case of compound of interest, i.e. La 0.90Ca0.1MnO3 result in the fact that when prepared in helium atmosphere it has an A-type antiferromagnetic structure with an antiferromagnetic spin component along the b-axis and a ferromagnetic component along the c-axis (as was reported earlier [Biotteau 2001]) while the sample prepared in air atmosphere is ferromagnetic [Pissas 2004]. However, all our samples were prepared in air atmosphere, see for further details in sample preparation section.

20 Chapter 2: Properties of cubic and bilayered manganese perovskites 16 Fig The phase diagram the La1 xca xmno3 [Dagotto 2001], the denominations used are the same as in Fig 2.10.

21 Chapter 2: Properties of cubic and bilayered manganese perovskites Sample preparation Cubic perovskites La1 ( Sr, Ca) MnO3 The La1 x ( Sr, Ca) x MnO3 samples desribed in chapter 4 were prepared by standard ceramic procedure. First, heating in air of stoichimetric amounts of compounds containing desired elements at temperatures lower than 1000 C, grinding and pressing powder into bars and another heating at temperatures higher than 1000 C, see for example in [Algarabel 2003]. The preparation process of La 0.9 Ca 0.1 MnO 3 samples is described in more details in the chapter 4. All samples described in the chapter 5 (two with grains of nanometric and one of micrometric size) were fabricated by firing the sol-gel prepared precursors at different temperatures in order to obtain different average grain sizes. The starting compounds La 2 O 3, SrCO 3, and MnCO 3 of the actual contents of the cationic components determined by chemical analysis, were separately dissolved in nitric acid, mixed together with citric acid and ethylene glycol in the ratio of (0.75[La 3+ ]+0.25[Sr 2+ ]+[Mn 2+ ]) / 1.5[citric acid] / 2.25[ethylene glycol] and ph was adjusted to 9 by addition of NH 4 OH. Further steps included evaporation of water at o C, drying at 160 o C and calcination at 400 o C (4 hours) in air. Finally the powders were annealed at given temperatures in the range of o C in air for 3 and 15 hours and then cooled down by switching off the furnace. The size of nanoparticles was determined from broadening of X-ray diffraction lines and checked independently by the electron microscopy [Pollert 2006]. x Bilayered perovskite manganites All studied samples of bilayered perovskites were powder samples, however samples in range 0.3 x 0. 5 were prepared as single crystals with the floating zone method and were later powdered. The crystal growth was performed on sintered polycrystalline rod with use of a halogen-lamp image furnace at a rate of 12 or 14 mm/h under an atmosphere of 1 atm O 2. The preparation method of single crystals is thoroughly described in [Kimura 1998]. Higher Mn 4+ containing region (beyond x=0.5) required more complex preparation process in order to obtain stoichiometric samples, however growth of single crystals beyond x=0.5 is still unsuccessful. Polycrystalline samples of La2 2 x Sr1 + 2 xmn2o7 were prepared by high temperature, solid state reaction of La 2 O 3 (Johnson-Matthey REacton %, pre-fired at 1000 C in air for 12h), SrCO 3 (Johnson-Matthey Puratronic %, dried at 150 C in air for 12h) and MnO 2 (Johnson-Matthey Puratronic %, pre-fired at 425 C in flowing oxygen for 6h, then slow cooled at 1 C/min to room temperature). Stoichiometric quantities of the starting materials x

22 Chapter 2: Properties of cubic and bilayered manganese perovskites 18 were mixed and fired in air as powders, at 900 C for 24 h and then 1050 C for a further 24 h. Samples were then pressed into 13 mm diameter pellets at 6000 lbs and ramped at 5 C/min to 1650 C. After 18 h each compound was quenched directly from the synthesis temperature into dry ice. As is the case for Sr 3 Mn 2 O 7+δ, [Urushibara 1995] the materials are metastable below 1650 C and must be rapidly cooled to below 1000 C to prevent decomposition. The black products were subsequently annealed for 12 h at 400 C in the flowing oxygen. Materials were reground between each firing [Millburn 1999]. The Mn 4+ content of the as-made and annealed materials was determined by iodometric titration against a standardized potassium thiosulfate solution [Millburn 1999].

23 Chapter 3: Nuclear Magnetic Resonance method Nuclear magnetic resonance method 3.1. Nuclear Magnetic Resonance In this chapter the physical basis of the Nuclear Magnetic Resonance (NMR) and its application to solid state physics, with emphasis put on the magnetic properties, is described. The nuclear magnetic resonance in condensed matter was first observed independently in 1946 by two scientists, Felix Bloch and Edward M. Purcell [Bloch 1946, Purcell 1946]. They described it as a physicochemical phenomenon which was due to the magnetic properties of certain nuclei in the periodic system. They were both awarded with the Nobel Prize in Physics in Since then the NMR experiments are broadly used in many different fields of science. Nowadays various NMR techniques are applied in solid state physics (to study magnetic, electrical and structural properties), medicine (i.e. Magnetic Resonance Imaging MRI), biology, chemistry (for example structures of compounds such as polymers), biochemistry (studies of conformation and dynamics of biomolecules). Some of main advantages of the NMR are that this method is non destructive (not harmful to the sample or patient) and selective (element and even isotope selective). The NMR phenomenon relies basically on the interaction of the magnetic dipolar moment of the nucleus with the magnetic field and of the electric quadrupole moment with the electric field gradient. The information obtained from the experiment helps us to learn about the local magnetic, electrical and structural properties of the system under investigation. NMR also allows to study structure of particles, chemical reactions and bonding, crystallographic structure and, due to non invasiveness, to study living organisms and processes occurring in their bodies. For this thesis the most important is the possibility to study magnetic materials and the information resulting from such experiments, e.g. strength of magnetic interaction, magnetic moments and the magnetocrystalline anisotropy Physical basis of the NMR In 1924 Wolfgang Pauli suggested the possibility of an intrinsic nuclear spin which triggered the development of methods that would allow to prove and measure this new physical quantity. This was first done in 1933, when Otto Stern and Walther Gerlach were able to measure the effect of the nuclear spin by the deflection of a beam of hydrogen molecules. The basic description of the magnetic resonance of nuclear magnetic moments (NMR) and the electronic magnetic moments (ESR) were developed simultaneously because the basic

24 Chapter 3: Nuclear Magnetic Resonance method 20 principles are the same with the difference in results coming from different mp masses of the proton (m p ) (resp. neutron) and electron (m e ): me Quantum mechanical description The quantum mechanical description of atomic nucleus formulated by Dirac in 1930, predicted the property of spin angular momentum. This property is characterised by the spin quantum number, I. Its value is an intrinsic property of every nucleus and it is quantized it may take the half-integer or integer 1/ 2 values only. The total spin angular momentum is ( I( I + 1)). The simplest example is proton (hydrogen nucleus), with its nuclear spin I=1/2. In order to observe the nuclear magnetic resonance the nuclei have to possess non zero nuclear spin. The nuclear magnetic moment µ n is related to the spin I of the nucleus by the equation: µ n = γi, (3.1) where γ is the gyromagnetic ratio, which is isotope-specific and varies widely for different nuclei. In absence of the external magnetic field, the energy levels of nucleus are degenerated. This degeneracy is lifted by applying magnetic field and the energy, E of the nuclear magnetic moment placed in the external field, B 0 is given by the scalar product: E = µ. (3.2) n B 0 The static magnetic field, B 0 is conventionally taken to be in the ẑ direction, so that the energy is expressed as: E = B0γI z. (3.3) However, the quantization of the angular momentum restricts I z to integer and half integer values, thus: E( m) = B0γm, (3.4) where m is the eigenvalue of the operator I z and goes in integer steps from -I to +I. The applied static magnetic field causes the split of the energy into 2I+1 levels and is called the nuclear Zeeman effect. Fig 3.1 presents the diagram of energy levels and the energy difference between two spin states as a function of the external magnetic field, B 0 for the case of proton with I=1/2. The energy difference between two energy levels, E can be obtained as: E = γb 0. (3.5) If the transition occurs between two energy levels, e.g. due to absorption or emission of a photon with the energy ω0 one obtains Larmor equation: ω = γ (3.6) 0 B 0

25 Chapter 3: Nuclear Magnetic Resonance method 21 which is the most important equation in NMR spectroscopy [Kittel 1966]. Fig. 3.1 The diagram of energy levels and the energy difference between two spin states as a function of the external magnetic field, B 0 for the case of proton (I=1/2, γ>0). If the P(m) represents the population of nuclei at the m th level, then, using the Boltzman distribution function, it can be written as: E ( m) k T = E( m) β P( m) Ae A 1 for E(m)/k β T<<1, (3.7) k βt where A is a normalisation factor, T is the absolute temperature, k is the β Boltzman constant and N is the number of NMR nuclei in the sample, P ( m) = N. (3.8) m Thus, the equilibrium nuclear magnetisation of the sample at temperature T can be expressed with the formula: M Z = µ z = µ z ( m) P( m) (3.9) M X = M Y = 0 2 I( I + 1)(2 I + 1) where µ z ( m) = γm. Since m = 0 and m =, the m m 3 magnetization along the ẑ direction can be written as: 2 2 γ B) M Z = A I( I + 1)(2 I + 1), (3.10) 3k T where β N A =, so that 2 I γ B) N M Z = I( I + 1) (3.11) 3k T β [Abragam 1961]. This formula describes the nuclear magnetisation of a paramagnetic system of nuclear spins related to an uneven occupation of their energy levels in the external magnetic field.

26 Chapter 3: Nuclear Magnetic Resonance method 22 When one suddenly applies the external magnetic field, the nuclear magnetisation of the sample does not reach its equilibrium value M ( ) instantly, but the equilibrium state is gradually approached according to the formula: t = T1 M ( t) M ( ) 1 e, (3.12) T 1 is the longitudinal, or spin-lattice relaxation time. The value of T 1 depends on the material and it varies with temperature. It can range between microseconds and hours [Abragam 1961] Classical description If the nuclear magnetisation vector M is placed in a magnetic field B, it experiences a torque. The equation of motion for M can be expressed as: dm = γ M B. (3.13) dt If the magnetic field B is static and acts along the ẑ direction, B = B zˆ 0,one can write the following equations: dm dm x y = γb M, = γb M, dm z = 0 0 y 0 x dt dt dt, (3.14) and derive the solutions: M x = M cosω 0 t, M y = M sin ω 0 t, M z = M, (3.15) where M and M are the magnetization components perpendicular and parallel to the static field B 0 andω 0 is the angular frequency of the precession, ω 0 = γb0, which is the Larmor frequency [Kittel 1966]. Fig. 3.2 Precession of the magnetisation vector, M in a static magnetic field applied along the ẑ axis.

27 Chapter 3: Nuclear Magnetic Resonance method 23 In the above situation the nuclear magnetisation vector M precesses along the magnetic field direction as shown in Fig Let us now introduce a new reference frame. From the static laboratory frame (x, y, z) we can transform our system to a rotating reference frame (x, y, z ), where z is coincident with z. The field, B r seen by the magnetic moment in the frame rotating with an angular frequency ω can be written as: ω B r = B 0 zˆ'. (3.16) γ When the angular frequency fulfils the condition ω = γb0 the magnetic moment does not see the static effective magnetic field B 0 and remains at rest in the rotating frame, B = 0. r Now, with the static magnetic field B 0 applied along ẑ axis, let us consider the time varying magnetic field B 1, perpendicular to B 0 and oscillating at the angular frequency ω 0 : B t) = B ( xˆ cosω t yˆ sinω ) (3.17) 1( 1 0 0t dm y and dt dm One can write equations for x dm, z similarly to case with only B 0. dt dt Their solutions show that by applying oscillating magnetic field at angular frequency ω 0, the magnetisation simultaneously precesses around B 0 at ω 0 and around B 1 at ω 1 = γb1 Making the transformation to the same rotating frame as previously, one ω0 obtains: B r = B ˆ' ˆ 0 z + B1 x', (3.18) γ At the resonance this equation simplifies to: B r = B 1 xˆ ', which means that the nuclear magnetisation in the rotating frame precesses around xˆ axis. In NMR experiments radio frequency field is realised by placing the sample into a coil with radio frequency (rf) sinusoidal current. The linearly polarised rf field can be considered as two rotating fields with opposite helicities and two times smaller amplitudes: B = = B + B x t + y t = B t B x t x t y t + B 1 1 ) 1 ˆ cos ω 0 ( ˆ cos ω 0 ˆ sin ω 0 ) ( ˆ cos ω 0 ˆ sin ) 2 2 (3.19) 1( ω 0 +

28 Chapter 3: Nuclear Magnetic Resonance method 24 In the rotating reference frame, the angular frequency of the magnetic field B - and B + is zero and 2ω 0, respectively. Thus, the contribution of B + can be neglected.

29 Chapter 3: Nuclear Magnetic Resonance method Spin echo technique and relaxation times Nowadays, in the NMR spectroscopy, pulsed rf experiments are being used mostly. One of such techniques is the spin echo, which is described in this section. The spin echo technique uses in its simplest case two rf pulses. The nuclear magnetisation M, experiencing the external magnetic field B 0 acting along ẑ axis and the rf field B 1 acting along xˆ axis, precesses with the Larmor frequencyω 0 = γb0. The resonance can be achieved when the angular frequency ω of the rf field is close to the ω 0. Therefore, in the rotating reference frame, the magnetisation precesses around the total magnetic field experienced by the nucleus B eff, which is called the effective field, and the turning angle is given by: ϕ = γb 1 t. If the duration of one of the two rf field pulses, t 1 or t 2, corresponds to π π ϕ = or π, the pulses are called the pulse or the π pulse, respectively, as 2 2 presented schematically in Fig First pulse, the 2 π pulse turns the nuclear magnetisation M z, which was aligned along ẑ axis by the field B 0, from the z axis to the xy plane, see Figs 3.4a and 3.4.b. The magnetisation vector precesses around B zˆ 0 the xy plane and induces a signal in the receiving coil. This signal is called the free induction decay (FID), Fig Fig. 3.3 A scheme of the spin-echo pulse sequence used in NMR experiments. The free induction decay (FID) signal appears after the π/2 pulse and the spinecho signal is formed after time 2τ from the first pulse. Due to the inhomogeneity of every material, there is the distribution of the effective magnetic field at nuclei, which gives rise to different angular frequencies and a fan of nuclear moments is created (Fig. 3.4c), which is the main reason of the fast decay of the FID signal. The π pulse applied a time τ after the 2 π pulse produces a spin-echo signal appearing after a time 2τ (Fig 3.4e). The spin-echo signal can be observed if the transverse (spin-spin)

30 Chapter 3: Nuclear Magnetic Resonance method 26 relaxation time, T 2 is sufficiently long compared with the pulse separation time, τ. Fig. 3.4 Scheme of the spin-echo formation in a rotating reference frame. The pulse sequence in above picture is: (/2) x - -() y, where indices x and y denote the axes of the pulses. See the text for details. The transverse component of the nuclear magnetisation, M and, consequently, the signal induced in the coil, decrease exponentially according to the equation: d M M = (3.20) dt T 2 M τ dm 1 = dt M M T2 0 and therefore: τ T 2 (3.21) M = M e. (3.22) This equation describes (beside the recovery of the nuclear magnetization to the direction of static magnetic field) the interaction between the nuclear spins and their irreversible dephasing due to transverse relaxation which is mainly due to spin-spin relaxation processes. The possible mechanisms of the transverse relaxation are dipolar spin-spin interaction, indirect coupling between nuclear spins by means of the hyperfine interaction with conduction electrons (Ruderman-Kittel interaction) [Ruderman 1954] and Suhl-Nakamura coupling of nuclear magnetic moments with emission/absorption of electronic spin waves [Suhl 1958, Nakamura 1958].

31 Chapter 3: Nuclear Magnetic Resonance method 27 The longitudinal relaxation time (or spin-lattice relaxation time) denoted as T 1, describes the recovery of the nuclear magnetization, M z to the equilibrium state. Spin-lattice relaxation processes in magnetic materials are usually strongly related to the electron spin system. In conventional ferromagnetic metals the spin-lattice relaxation is dominated by a Korringa process in which the relaxing nuclear spin flips an electronic spin down [Weisman 1973]. Another possibility for the spin-lattice relaxation is the fluctuation of the hyperfine fields caused by migrating electron holes. One can write the following equation describing the rate of reaching the equilibrium state, M 0 : d M 0 M z M = (3.23) z dt T 1 M z t dm z 1 = dt (3.24) 0 M 0 M z T1 0 M 0 t ln = (3.25) M 0 M z T1 and therefore: t = T1 M ( ) 1 z t M 0 e. (3.26) A measurement of the spin-echo signal with the two-pulse method exploiting the spin-echo pulse sequence π/2-τ-π, with varying pulse spacing, τ allows us to determine the T 2 relaxation time by using the formula: τ T2 A( τ ) = A0e, (3.27) where A(τ) and A 0 are the spin-echo amplitudes at the time τ and τ=0, respectively. The spin-lattice relaxation time, T 1 can be determined by carrying out the measurement of the two-pulse spin-echo at a fixed, small, pulse separation, τ by varying the repetition time of the sequence. The T 1 can also be measured by the saturation-recovery method. A comb of pulses (three or more) saturates the longitudinal nuclear magnetisation, M z to a value close to zero. The subsequent recovery of M z is measured by the spin-echo produced by a two-pulse sequence as a function of its separation, t from the saturation comb. The echo intensity changes according to the formula: t = T1 A ( t) A 1 0 e. (3.28) Relaxation processes of the nuclear magnetic moments are due to a randomly varying magnetic field or a fluctuating electric field gradient at the nucleus. These fluctuating magnetic fields or electric field gradient are usually caused by molecular and electronic motions and, in the case of magnetic

32 Chapter 3: Nuclear Magnetic Resonance method 28 materials, by excitations and fluctuations of electronic moments. Measurements of the relaxation times can provide valuable information on the molecular dynamics and the dynamics of the electronic and magnetic systems [Abragam 1961, Turov 1969]. In the magnetically ordered materials the spin-lattice relaxation time, T 1 is usually a few orders of magnitude bigger than the spin-spin relaxation time, T 2. General expressions relating the relaxation rates (1/T 1 and 1/T 2 ) to the fluctuating local field, δh are following: = γ ( f ( t) cos( ωt) )dt (3.29) 1 T = + γ ( f ( t) )dt (3.30) 0 T2 2T1 where f 0 and f 1 are the correlation functions for the longitudinal and transverse field fluctuations, respectively.[moriya 1956, Turov 1969].

33 Chapter 3: Nuclear Magnetic Resonance method NMR in magnetically ordered materials The effective field at nucleus The total effective field, B eff experienced by the ion in a magnetically ordered solid can be expressed as: B = B + B + (3.33) eff HF loc B 0 where B 0 is the applied external magnetic field, B loc is the local magnetic field due to other magnetic moments in the solid, B HF is the hyperfine field resulting mainly from the spin and orbital moments of the electrons within the ion radius. The hyperfine field B HF usually dominates over other components in magnetically ordered solids. The classical local field, B loc is given by: B = B + B + B (3.34) loc D Lor dem where B dem is the demagnetising field (related to the particle shape for single domain particle or to macroscopic shape of the sample when magnetized), B Lor is the Lorenz field created by the magnetic pseudo charges at the surface of the Lorenz spherical cavity and B is the field arising from the moments within the Lorentz sphere except the central one. D B + B =0 for a spherical sample and B D =0 for atomic positions with cubic symmetry of their neighbourhood (cubic site symmetry) [Bruno 1993, Panissod 2002]. The B HF may be written as a following sum: B = B + B + B + B (3.35) HF Fermi S d orb T In the case of 3d elements the biggest is the Fermi contact term, B Fermi, which results from the contact interaction of the nuclear magnetic moment with the magnetic moments of s-like electrons, polarized mostly by the d-like electronic magnetic moments [Watson 1961]. Two next contributions come from the spin dipolar interaction between the nuclear magnetic moment and the electronic spin ( ) and from the interaction of unquenched orbital moment of BS d the electrons ( B ) [Watson 1961]. The last term is the transferred hyperfine orb field, i.e. field caused by electron spin transfer from magnetic neighbours ( B T ). The Fermi contact field, B Fermi is a result of the exchange polarization of s electrons by the unpaired electrons from not completely filled orbitals (i.e. 3d for transition metals or 4f for rare earths elements). This polarization of the s electrons produces a net spin density at nucleus, which produces the Fermi contact term of the effective magnetic field [Fermi 1933, Sternheimer 1952]. dem Lor

34 Chapter 3: Nuclear Magnetic Resonance method 30 The Fermi contact field can be written as the difference of the electron densities with spins up and down: 2 B Fermi = µ µ ( ρ ( 0) ρ ( 0) ) 0 B (3.36) 3 where: ρ ( 0), ρ ( 0) are the densities of electrons with their spins up and down at the nucleus, ρ ( 0) ρ ( 0) is the electronic spin polarization at the nucleus. In the case of the 3d transition metal elements the Fermi contact field is negative (i.e. antiparallel to electronic spin magnetic moment, µ s ) and, since B Fermi is the dominant contribution to B eff, the effective field is also negative. For the rare earth elements, the Fermi contact field is caused mainly by the electrons from the magnetic 4f shells. For manganese one can estimate the value of the core polarisation contribution ( B Fermi ) to the hyperfine field, knowing that B Fermi is proportional to the spin moment of the parent ion with the ratio 10 T/µ B [Asano 1987]. This theoretical prediction is confirmed by the electron spin resonance studies of Mn 3+ ion in TiO 2 [Geritsen 1963] and by the nuclear magnetic resonance studies [Kubo 2001]. The estimated values of the B Fermi amount to T and T respectively. The orbital hyperfine field, B orb can be expressed as: 1 B orb = 2µ 0 µ 3 L (3.37) r where: µ 0 vacuum magnetic permeability 1 - average reciprocal cube of the radius of 3d orbital 3 r µ L orbital magnetic moment in Bohr magnetons. The spin dipolar field ( BS d ) at nucleus is due to the electronic spins at individual orbitals and is given by the formula: 2 s ( ) = i r 3 s r r i 0 0 B g µ S d s B 0 5 i r s i is the spin of ith electron and 0 µ (3.38) where g s =2.0023, r is a unit vector along the leading vector, r. This field can be evaluated by multiplying the above equation * by the electron density, ρ = Ψ e Ψe and integrating over the electron coordinates of the orbital [Abragam 1970]. The results of calculations of the spin dipolar hyperfine field, BS d at nucleus produced by a single electron occupying one of the 3d e g orbitals are presented in the discussion of the results section.

35 Chapter 3: Nuclear Magnetic Resonance method 31 The anisotropic terms of the total magnetic field experienced by the nuclei are: BS d, B orb, part of the local field ( B loc ), namely the dipolar field, B D and some contributions to the transferred field, B T Enhancement of the high frequency field In NMR experiments, nuclear spins in ferromagnetic or ferrimagnetic materials are not excited directly by the rf field B 1, but they experience oscillations of the hyperfine fields resulting from the electronic magnetic moment response to the B 1. Even small oscillations with the magnitude ϕ can produce an oscillating transverse component of the effective field at nucleus, B (Fig. 3.5). As a result, the rf field with small amplitude can produce the eff field B with much larger amplitude given by the equation: eff B eff = ( η + 1) B (3.39) 1 where (for spherical single domain particle): Beff η (3.40) Bext + BAniz B Aniz is the magnetocrystalline anisotropy field, B ext is the external field (if present) and η is called the NMR enhancement factor. It describes the induced reinforcement of B eff by adding an oscillating transverse component that is directly responsible for the nuclear transitions. The enhancement factor is proportional to the magnetic AC susceptibility of the electronic system at the NMR frequency. Relative values of enhancement factors corresponding to magnetically different regions can be derived from measurements carried out at the optimal rf field amplitude, B opt rf, corresponding to the first maximum of the spin echo, using the formula: 1 γ opt η = 2t B rf (3.41) 2π where t is the pulse length [Savosta 2004]. The enhancement factor may also depend on the macroscopic demagnetisation field and, consequently, on the shape of the particles in the sample. In ferromagnetic or ferrimagnetic materials the enhancement factor is usually bigger for nuclei in domain walls than in domain interiors. For nuclei in domain interiors typical value of η is the range , while for nuclei in domain walls it can amount to and its value varies throughout the domain wall. In antiferromagnetic materials the enhancement factor is close to unity. For the elements (ions) which exhibit anisotropy of the hyperfine field, the signals from domains and domain walls (domain wall edges and domain wall centres) can be resolved, as they appear at different frequencies. They can also

36 Chapter 3: Nuclear Magnetic Resonance method 32 be distinguished due to their different values of η, or by applying external magnetic field (domain walls disappear at high enough field) and also due to different relaxation times in domains and in domain walls. Signals from domain walls exhibit a faster nuclear spin relaxation than signals from domains [Davis 1976, Leung 1977, Weisman 1973]. Fig. 3.5 A scheme of the NMR enhancement effect in magnetically ordered materials, M el stands for electronic magnetisation, the rest of symbols is explained in the text Owing to the enhancement effect, the pulse power required in the NMR experiments on magnetically ordered materials is η 2 times smaller than in dia- or paramagnetic materials and the echo amplitude is η times larger.

37 Chapter 3: Nuclear Magnetic Resonance method NMR spectrometers and magnetometers In this section a description of the equipment used for experiments is presented, including two NMR spectrometers and two magnetometers i.e. the Vibrating Sample Magnetometer (VSM) and the SQUID (superconducting quantum interference device) magnetometer. Since a detailed description of one of the spectrometers can be found in [Riedi 1994, Lord 1995], in view of similarities of the design of both spectrometers used, only the second (Bruker) NMR spectrometer is described in more details in this thesis. The spectrometer used for the most experiments carried out in this thesis is a home made spectrometer designed to work over the frequency range MHz, with particular application to NMR measurements of magnetically ordered materials. However, both spectrometers consist of: the pulse generator, with the splitters and the power amplifier in the transmitter section, the receiver section, with the signal amplifiers, the protection diodes and mixers, the digital section, with the averaging oscilloscope and the computer. A stable frequency is provided by a synthesized oscillator whose sinusoidal output is divided into a reference signal and a to sample excitation signal. The spin-echo signal, phase sensitive detected in two orthogonal channels, is averaged in the digital oscilloscope and stored in the computer. The spin-echo signal can be separated from the FID and spurious signals (including receiver recovery effects) following the /2-- - sequence by phase switching and, additionally, by an electronic transmit/receive switch, [Riedi 1994, Lord 1995]. The recovery time of the spectrometer is of 4-6 µs, depending on the frequency range. The spectrometer used in the NMR laboratory in Prague for NMR/NQR spectroscopy is a system based on a commercial BRUKER AVANCE highresolution console. The original apparatus was adapted in order to cover broad frequency range needed e.g. for experiments carried out on magnetic materials. The present setup covers the frequency range of MHz. The spectrometer performs coherent summation (averaging) of NMR signals in the time domain for required number of scans, which guarantees a high sensitivity and possibility to detect signals which have very low intensity. The minimal time delay between a radiofrequency pulse end and the start of data acquisition (detection) is about 5 µs, which allows us to measure samples with correspondingly short spin-spin relaxation time T 2. A wobbler unit allowing carrying out tuned measurements is also integrated in the spectrometer system.

38 Chapter 3: Nuclear Magnetic Resonance method 34 Main parts of the spectrometer are shown in the block diagram in Fig The transmitter line consists of two synthesizers - Signal Generation Units (SGU units),. The phase, amplitude and frequency are generated by the Direct Digital Synthesis (DDS). SGU provide phase resolution better than 0.05 and the frequency resolution better than 0.05 Hz. The low level high frequency pulses from the SGU unit are amplified in the power amplifier. Two linear power amplifiers (transmitters) are implemented in the spectrometer: BLAX 500 (500 W) works in frequency range of MHz, and BLAH 300 (300 W) in frequency range of MHz. Blanking pulses are used to block the amplifier in time intervals when no rf pulses are transmitted. The rf pulses of appropriate power are transmitted from the power amplifier via transmit/receive (T/R) switch (integrated in multilink HPPR/2 unit) to the probe coil. The switch protects the receiver input during excitation pulses and disconnects the transmitter line during data acquisition in order to eliminate possible noises and leakages from the transmitter line. In the usual experimental setup the same coil acts as the excitation and the pick-up coil. The SGU generates also the Local Oscillator (LO) frequency for mixing procedure in the receiver line. The NMR signal induced in the coil (can be of few V only) is processed in the receiver line. The signal proceeds to the multilink HPPR/2 unit and to a low noise HP-preamplifier. Next, the signal is mixed with Local Oscillator (LO) frequency (LO is by the value of the intermediate frequency IF of 720 MHz higher from the excitation frequency). The output signal converted to the Intermediate Frequency (IF) 720 MHz, is filtered by the IF filter and amplified with adjustable gain. The amplified signal (of order of Volts) is then registered with quadrature detection. The digital quadrature detection (DQD) using Slow A/D Converter SADC and oversampling option is limited to 25 khz band. Therefore, the analogue quadrature detection mode is commonly used for broad spectral lines, by means of the fast digitizer (FADC, 12 bit digitizer, 10 MHz sampling rate). Before digitizing the signals from two quadrature detection channels I, Q, the analogue bandwidth is reduced with a low pass filter system ('aliasing' filter, amendable bandwidth 4 MHz MHz). The digitized data (after coherent summation) are transferred to the NMR PC workstation and stored there. The acquisition computer of the spectrometer includes a complete acquisition computer system (Communication Control Unit - CCU) and the spectrometer specific function boards, TCU (Timing Control Unit), FCU (Frequency Control Unit) and Receiver Control Unit (RCU). The Timing Control Unit (TCU) is a pulse programmer which provides exact timing and flexibility in the data acquisition with 12.5 ns timing resolution, controlled by a fast RISC processor. The TCU generates the most of the realtime clock pulses for the spectrometer. Basing on this clock, the synchronization of the transmitter system (TCU, FCU) and the receiver system

39 Chapter 3: Nuclear Magnetic Resonance method 35 (RCU) is maintained. The Communication Control Unit (CCU) with a high speed RISC processor, 16 MByte memory, dedicated Fast Ethernet and RS-232 connection ports creates the communication link to the NMR PC workstation. Pulse sequence programs, as well as the acquisition and processing parameters are set by the PC operator using either the original XWINNMR Bruker software display, or by means of the special software, developed for frequency swept spectra only. Fig.3.6: The block diagram of Bruker AVANCE spectrometer used for NMR measurements. For details and explanation of abbreviations see the text. Magnetization measurements were carried out with the vibrating sample magnetometer (VSM) and the Superconducting Quantum Interference Device (SQUID) magnetometer. The measurements of bilayered perovskites with doping range 0.5 x 1 presented in this thesis were carried out with the Lakeshore VSM magnetometer. In this magnetometer magnetisation is measured owing to the Faraday law: dφ ξ = B (3.42) SEM dt where ξ SEM is the electromotive force (EMF) and Φ B is the magnetic flux. Variable magnetic flux in the VSM is created due to the harmonic motion of the magnetic sample inside the pick-up coils in the magnetometer (Fig. 3.7). Changes of the magnetic flux induce the electromotive force, ξ SEM in the pick-up coils, which is proportional to the sample magnetisation. This signal is measured by a selective nanovoltometer assembly, which is a part of the magnetometer

40 Chapter 3: Nuclear Magnetic Resonance method 36 set-up, which also contains a controller of sample vibrations. Sample probe is placed inside the cryostat in order to carry out measurements at variable temperatures. More detailed discussion about the VSM magnetometer used can be found in [Tokarz 2001]. Fig. 3.7 A Scheme illustrating the physical principle of the vibrating sample magnetometer (VSM) operation. The Quantum Design SQUID magnetometer was used for magnetisation measurements of La1 xsrx MnO3 nanoparticles. The superconducting quantum interference device (SQUID) consists of two superconductors separated by thin insulating layers to form two parallel Josephson junctions. The device may be configured as a magnetometer to detect very small magnetic fields. Similarly to the VSM magnetometer, the measurement in the SQUID magnetometer is performed by moving a sample through the superconducting detection coils, which, as shown in Fig. 3.8, are located at the centre of the magnet. The sample moves along the symmetry axis of the detection coil and magnet. As the sample moves through the coils the magnetic dipole moment of the sample induces an EMF and the corresponding electric current in the detection coils. This is due to the fact that detection coils, connecting wires and the SQUID input coil form a superconducting loop and any change of the magnetic flux in detection coils produces a change in the persistent current in the detection circuit, which is proportional to the change of the magnetic flux. The thin film SQUID device located below the magnet and inside the superconducting shield essentially functions as a very sensitive current-to-

41 Chapter 3: Nuclear Magnetic Resonance method 37 voltage converter, so that variations in the current in the detection coil circuit produce corresponding variations in the SQUID output voltage, which is proportional to the magnetic moment of the sample. In a fully calibrated system, measurements of the voltage variations from the SQUID detector as a sample is moved through detection coils provide highly accurate measurement of the magnetic moment of sample. Under ideal conditions, the magnetic moment of the sample does not change during movement through the detection coil [McElfresh]. Fig. 3.8 Geometrical configuration of the magnet, detection coils and the sample chamber in the SQUID magnetometer.

42 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO Cubic perovskites La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Sr 0.1 MnO La Sr MnO 3 and La 0.85 Sr 0.15 MnO 3 55 Mn and 139 La NMR results and discussion La Sr MnO 3-55 Mn NMR In this section results and discussion of the 55 Mn NMR spin echo measurements of the La Sr MnO 3 compound are presented. In Fig. 4.1 the 55 Mn frequency swept spectra measured at various temperatures ranging from 4.2 K to 225 K are shown. In all the presented NMR results at no applied magnetic field the measured signal comes mostly from domain walls owing to their larger enhancement factor. The dependences of the spin echo signal on the pulse length were measured at the maximum pulse amplitude for most of the resonance lines observed in the frequency swept spectra, starting from short pulses (mostly 0.1 µs) to 1-2 µs in order to find the first maximum of the echo signal, i.e. to determine the optimal excitation conditions. Unless stated differently, the presented frequency swept spectra are measured for excitation conditions which are optimal for the double exchange line. Usually, the enhancement factor of the Mn 4+ line was found to be slightly larger and for the Mn 3+ resonances - slightly smaller than for the DE line. A correction of the frequency response of the spectrometer was provided by inserting a 6 db attenuator at the top of the probehead, which was found to reduce substantially the standing waves arising from a lack of impedance matching of the untuned coil. As the exact frequency response of the spectrometer and the frequency dependence of the enhancement factor were not known, the spectra are presented with no frequency correction. At 4.2 K we observe several lines, namely Mn 4+ line (at 327 MHz), the DE line (around 400 MHz) and two Mn 3+ lines (ranging from MHz). The appearance of several lines in the 55 Mn spectra suggests the occurrence of phase separation in the compound studied, in agreement with results of [Allodi 1997, Papavassiliou 1999, 2000, Renard 1999, Kapusta 2000a, 2000b, Novak (2004)] as was described in the Introduction. The origin of the Mn 4+ and Mn 3+ lines are the Mn cations, which are in ferromagnetic insulating (FMI) regions, while the DE line is associated with Mn cations of intermediate valence, which is related to a fast, DE driven, 3d e g electron hopping between the Mn 3+ and Mn 4+ ions leading to ferromagnetism and metallicity (FMM) of these regions [Matsumoto 1970]. The ground state of the La Sr MnO 3 compound in the literature [Dabrowski 1999] is reported to be FMI, however, at low temperatures we observe signals not only from FMI, but also from FMM regions. This indicates that there exists a phase separation into FMM and FMI regions in the compound studied. As was mentioned in the Introduction, the phase separation problem in lightly doped perovskite manganites has recently been studied by many researchers with means of many different techniques.

43 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 39 Normalized spin echo intensity [arb. units] 225K 212K 182K La Sr MnO 3 170K 160K T C =180K T CO =160K 136K 121K 97K 77K 4.2K Frequency [MHz] Fig The 55 Mn frequency swept spectra of La Sr MnO 3 at various temperatures. T CO and T C are the charge ordering temperature and Curie temperature respectively, reported in the literature [Dagotto 2001]. In [Mostovshchikova 2004] the amount of the FMM phase was obtained by analysing the temperature dependence of the light absorption and dc conductivity in lightly Sr and Ca doped La 1-x (Sr,Ca) x MnO 3 compounds. In the case of La 0.9 Sr 0.1 MnO 3 compound they evaluated the volume of the FMM phase at 100 K at 0.1% only. The size of the metallic-like regions in lightly doped manganites reported in the literature varies from 10 Å to 100 Å [Hennion 1998]. As can be seen in Fig. 4.1, the DE line exists well above the bulk magnetic ordering temperature, T C of 180 K [Dagotto 2001, Hennion 2006] and the signal was measured even at 225 K. This fact is attributed to long lived FMM regions (FM polarons [Salafranca 2006]). The fast diminishing of the Mn 3+ signal with increasing temperature is due to a fast decrease of the spin-spin relaxation time, T 2 and at 77 K very weak Mn 3+ signals are observed at 420 MHz and at 500 MHz. A fast decrease of the Mn 3+ signal from FMI regions with increasing temperature was also observed in lightly Ca doped cubic manganese perovskite, La 0.9 Ca 0.1 MnO 3 [Algarabel 2003]. The FMI Mn 4+ line is observed up to 160 K, which is reported to be the temperature of transition to the charge ordered state [Dagotto 2001]. One can also

44 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 40 notice that the resonant frequencies of the Mn 4+, DE and Mn 3+ lines decrease as the temperature is increased, which is due to a decrease of the manganese magnetic moment, <S z >, with temperature. 40 DE line Mn 4+ line Effective field [T] Temperature [K] Fig Temperature dependence of the effective field, B eff of the FMI Mn 4+ and DE lines of the La Sr MnO 3 compound. Solid lines are guides for eyes only. 1,00 1,00 Normalized effective field - B eff 0,95 0,90 0,85 0,80 DE B eff Mn 4+ B eff 0,95 0,90 0,85 0,80 0,75 0, Temperature [K] Fig.4.3. Normalised effective field, B eff versus temperature (for the FMI Mn 4+ line and Mn ions in the DE regions of the La Sr MnO 3 compound). Lines are guides for eyes only.

45 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 41 The temperature dependences of the effective field at nucleus, B eff of the Mn 4+ and Mn cations in the DE regions are shown in Fig Points on the plot are central frequencies of Gaussian curves fits to the experimental data. At 4.2 K the B eff at the Mn 4+ nuclei in the FMI regions amounts to T and at the Mn nuclei in FMM regions (averaged Mn 4+ and Mn 3+ valence state) it is higher and amounts to 37.9 T (400 MHz). The value of the B eff for the DE line decreases merely by 17% between 4.2 K and 212 K. Since the B eff is approximately proportional to the average spin magnetic moment, this indicates almost fully saturated Mn magnetisation in the FMM regions in this temperature range. The existence of the FMM regions above the T C was observed by NMR also in other manganese perovskites [Kapusta 1999]. The respective change of the Mn 4+ B eff is larger and amounts to 18%, between 4.2 K and 154 K, compared to 10.7% for the DE line at this temperature range. This indicates a weaker magnetic coupling in the FMI than in the FMM regions. A similar effect was found in the lightly Ca doped manganite system [Kapusta 2000]. τ = 300µs Normalised spin echo intensity [arb.units] τ = 200µs τ = 150µs τ = 75µs τ = 10µs Frequency (MHz) Fig Mn NMR spin echo spectra of the La Sr MnO 3 compound at 4.2 K and different values of pulse spacing, τ. Lines are guides for eyes only. Signals from the Mn 3+ ions at 4.2 K in the FMI regions range from 425 MHz (40.28 T) to 550 MHz (52.12 T). Such a broad distribution is due to the large anisotropy of the Mn 3+ hyperfine field. Mn 3+ is a Jahn-Teller ion and thus a

46 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 42 different occupation of the e g orbitals can be expected. Additionally, in the case of Mn 3+ ion the orbital moment is not quenched and can be of µ B (4-6% of the spin magnetic moment) in the lightly Sr doped cubic manganese perovskites [Koide 2001]. In order to identify the origin of the Mn 3+ lines at 440 MHz and at 530 MHz at 4.2 K, measurements with various pulse spacing, τ were carried out. Their results for τ ranging from 10 µs to 300 µs are presented in Fig As τ increases, the intensity of the DE line decreases and the Mn 4+ and Mn 3+ lines at 325 MHz and 530 MHz, respectively, remain dominant. The Mn 3+ line at 530 MHz persists for higher pulse spacing, indicating that nuclei contributing to this signal have a longer spin-spin relaxation time T 2 compared with nuclei contributing to the Mn 3+ line at 440 MHz. Nuclear moments corresponding to shorter T 2 relax out before the appearance of the second pulse and they do not contribute to the spin echo signal. The line with shorter T 2 (at lower frequency) is attributed to the domain wall centre and the line which has a longer T 2 (at higher frequency) is attributed to the domain wall edge, where the ionic magnetic moments are within or close to the easy magnetisation direction (EMD) [Weisman 1973, Davis 1976, Leung 1977]. The signal from domain wall centre corresponds to the ions with magnetic moments along (or close to) the hard magnetisation direction(s) (HMD). However, according to this line attribution, the line at 440 MHz attributed to domain wall centre should Normalized spin echo intensity [arb. units] Frequency [MHz] 0T 3T 0T magn. at 3T Figure Mn NMR spin echo spectra of the La Sr MnO 3 compound at 3.2 K at no applied field (black line), at 3 T (blue line) and at 0 T after switching the field off (red line).

47 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 43 have different enhancement factor, which is not the case. The enhancement factor of the line at 440 MHz is almost the same as for the line at 530 MHz, the optimal pulse length (first maximum on the dependence of the spin echo signal on the pulse length) was 1.2 µs and 1 µs for the line at 440 MHz and 530 MHz respectively. Additionally, measurement at 3 T and at 3.2 K was carried out to verify the attribution of Mn 3+ lines described above (see Fig. 4.5). As it can be seen at 3 T the FMI Mn 4+ and FMM DE lines shift towards lower frequencies, as the Mn 3+ line at 530 MHz also does. However, the Mn 3+ line at 440 MHz does not shift, but only decreases in intensity compared with other lines. The shift towards lower frequencies confirms that the observed signals, from the Mn 4+ ions and from regions where the DE interaction is effective, come from ferromagnetically ordered regions. The hyperfine field, B HF which is the dominant component of the effective field, is negative (antiparallel to the electronic spin moment, µ s and to the applied field, B 0 ). Therefore with increasing applied field the effective field and the corresponding resonant frequency decrease (see Fig. 4.6). Resonant frequencies decrease from 327 to 299 MHz (28 MHz) and from 393 to 375 MHz (18 MHz) for the Mn 4+ line and the DE line, respectively. A smaller change in the case of the DE line is probably due to a higher demagnetising field and/or magnetocrystalline anisotropy in the DE regions. Fig. 4.6 Scheme illustrating decrease of the effective field, B eff as the external magnetic field, B 0 is applied (bottom). In the case of Mn 3+ lines, the line at 530 MHz, which has longer spin-spin relaxation time, shifts towards lower frequencies at 3 T while the line at 440 MHz remains at the same frequency and only decreases in intensity. Assuming that observed signals come from domain walls, which is usual in NMR experiments due to higher enhancement factor of nuclei in domain walls than within domains, the shift of the line at 530 MHz means that magnetic moments of ions contributing to this line are parallel to the applied field. This means that they may be located in domain wall edges. In the domain wall centres magnetic moments are perpendicular to the applied field. Since the effective field is much larger than the applied field (42 T comparing to 3 T) no shift of the line at 440 MHz is observed at 3 T. The strong decrease of the intensity of this line can be due to domain walls removal at the applied field.

48 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 44 Fig. 4.7 Schematic view of the structure with two manganese positions (Mn1 and Mn2), blue arrows indicate magnetic moments. Mn1 and Mn2 sites have different angles between magnetic moment direction and directions of Mn-O bonds. The situation is in fact more complicated, because in the compound studied there are two non equivalent Mn sites. Taking into account only crystallographic structure there is only one Mn lattice site, but introducing magnetic order related to distortions and tilting of manganese-oxygen octahedra results in two non equivalent Mn sites. For these two sites angles between direction of the magnetic moment and main directions in the octahedron are different (see Fig. 4.7). Presence of two non equivalent Mn sites can be the reason of the asymmetric line shape of the Mn 4+ FMI line at 330 MHz (see Fig. 4.4). However, the Mn 3+ lines observed (at 440 and 530 MHz) cannot be due to two non equivalent Mn sites, because they both should shift towards lower frequencies at the applied field, which is not observed for the line at 440 MHz. An alternative explanation for the lack of the shift in the applied field could be its assignment to antiferromagnetically coupled moments. However, as was mentioned the enhancement factor, η is similar for both lines while it should be much smaller in the case of the signal from antiferromagnetically coupled moments than for ferromagnetically coupled [Turov 1970]. In Fig. 4.5 also the measurement at no applied field, but after magnetising sample at 3 T is presented. The frequency swept spectrum looks almost the same as in the measurement with the non magnetized sample. This indicates that no metamagnetic transition was induced by the field of 3 T in contrast to e.g. another manganite Pr 0.67 Ca 0.33 MnO 3 in which a field of 7 T resulted in a transition from antiferromagnetic state to the ferromagnetic metallic state and the dominant DE line was observed in the remanent state [Oates 2005].

49 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 45 We have also carried out measurements of the spin-spin relaxation time, T 2 for nuclei contributing to each line, for the FMI Mn 4+ at 337 MHz, for the DE line at 382 MHz and for the two Mn 3+ lines at 442 and 532 MHz (Fig. 4.8a) at various temperatures. In the fitting procedure a single exponential decay of the spin echo was assumed and it provided a good agreement of the fit with the experimental data. The following formula was used: 2τ A( τ ) = A + n Aτ = 0 exp (4.1) T2 where A (τ ) and A τ = 0 are the spin-echo amplitudes at the time τ, and τ=0 (see also chapter: Introduction to NMR). The magnitude of the A n parameter corresponds to the noise level, so a possible contribution from large T 2 processes can be discarded within the error margin. a) Spin echo intensity [arb. units] Mn 4+ line DE line 442 MHz 532 MHz T 2 [µs] b) DE line Mn 4+ line 432MHz 532MHz Pulse spacing [µs] Temperature [K] Fig. 4.8 a) Spin echo decay curves (in linear scale) of the La Sr MnO 3 compound for resonant frequencies of the Mn 4+ line, the DE line and Mn 3+ lines at 442 and 532 MHz at 4.2 K. Red lines are fits to the experimental data (points); b) temperature dependence of the T 2. At 4.2 K the shortest T 2 is observed for the DE line indicating that manganese nuclei in FMM regions relax faster than the Mn 3+ and Mn 4+ nuclei in FMI regions, which have longer spin-spin relaxation time. At higher temperatures T 2 values of Mn 4+ and DE lines are obtained only. The signals from Mn 3+ nuclei are not observed at higher temperatures due to fast decrease of the T 2 with increasing temperature (at 77 K T 2 of Mn 3+ nuclei is the shortest measured, Fig.

50 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO b). Above 100 K the T 2 values of nuclei contributing to the DE line and Mn 4+ line do not change much and remain in the range 5-10 µs (Fig. 4.8b) La 0.85 Sr 0.15 MnO 3-55 Mn NMR With increasing content of Sr (hole doping) the average ionic radius of the perovskite A-site cations increases (the ionic radius of Sr 2+ is larger than La 3+ ). This is called the chemical pressure effect [Xu 2003], which results in the increase of the Mn-O-Mn bond angle and a decrease of the distortions [Xiong 1999]. Therefore, one might expect a higher effectiveness of the DE interaction (effectiveness of the DE interaction increases with increase of the Mn-O-Mn bond angle, see chapter 2). The FMM phase content should also increase with increasing Sr doping, thus it should be higher in the x=0.15 Sr doped compound than in the compound with x= As expected, we observe this kind of behaviour in the NMR spectra. τ = 300µs τ = 150µs τ = 9µs Normalised spin echo intensity [arb.u.] Frequency (MHz) Fig Mn NMR spin echo spectra of the La 0.85 Sr 0.15 MnO 3 compound at 4.2 K with three different values of the pulse spacing, τ. The 55 Mn NMR frequency swept spectra at different pulse spacing, τ at 4.2 and 77 K, of the La 0.85 Sr 0.15 MnO 3 compound are presented in Figures 4.9 and Similarly to La Sr MnO 3, the spectra of La 0.85 Sr 0.15 MnO 3 at 4.2 K reveal the co-existence of ferromagnetic insulating regions and ferromagnetic metallic regions. The line at 334 MHz is due to Mn 4+ ions and signals ranging from 410 to

51 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO MHz are due to Mn 3+ ions in the FMI regions while the line at 396 MHz is due to FMM regions Normalised spin echo intensity [arb.u.] τ = 100µs τ = 8µs Frequency (MHz) Fig Mn NMR spin echo spectra of the La 0.85 Sr 0.15 MnO 3 compound at 77 K obtained with two different values of the pulse spacing, τ. One can also notice that the DE line at 4.2 K is not symmetrical (Fig. 4.9). Similar behaviour was also observed in the case of compound with x=0.16 and it was suggested that there are two DE lines present at low temperatures [Savosta 2003]. According to [Savosta 2003] these two lines originate from hole-rich and hole-poor Mn sites due to charge density wave, possibly accompanied by a partial orbital ordering. The difference between hyperfine fields of manganese ions on those two sites was found to be of 2.3 T (24.3 MHz) at 22 K. However, we propose that the asymmetric line shape is due to the anisotropy of the hyperfine field. A similar observation was made for La 0.75 Sr 0.25 MnO 3 (see chapter 5) and bilayered manganites La 1.2 Sr 1.8 Mn 2 O 7 and LaSr 2 Mn 2 O 7 (see chapter 6). At 77 K resonant frequencies of the FMI Mn 4+ and the DE lines are lower than at 4.2 K due to a decrease of the magnetic moment with temperature. The DE line shifts towards lower frequencies by 17 MHz (1.6 T) to 382 MHz. The shift of the FMI Mn 4+ is harder to estimate because the intensity of this line decreases strongly with increasing temperature. The Mn 3+ line is not observed at 77 K due to a fast increase of the nuclear relaxation rate of Mn 3+ in the charge localised FMI regions with increasing temperature. In Figures 4.9 and 4.10 it is clearly visible that a dip in the centre of the DE line appears with increasing pulse spacing. The effect can be explained by the Suhl-Nakamura interaction [Suhl 1958, Nakamura 1958, Davis 1974] between nuclear spins of neighbouring Mn ions. The nuclear spin, which sees the electronic

52 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 48 spin of its own ion through the hyperfine coupling, excites a spin wave through this coupling, and another nuclear spin absorbs it through its hyperfine coupling [Suhl 1958]. The observed dependence of the spectra on the pulse spacing means that nuclear spins, which precess at or near the central frequency, reveal a faster spin-spin relaxation than spins contributing to the wings of the resonance line. As the centre of the DE resonance line originates mainly from the spins inside the DE regions, a minimum at the line centre denotes that the neighbouring manganese ions are magnetically equivalent, which makes the Suhl-Nakamura (SN) interaction effective. This is much less effective at the boundaries of DE regions where manganese neighbours differ in terms of magnetic moments and/or their directions, which prevents the exchange of virtual spin waves and results in a slower spin-spin relaxation. An indication of the Suhl-Nakamura interaction is the frequency dependence of the spin-spin relaxation time, T 2 which should have a minimum at the centre of the DE line. Such minimum is observed in the case of La 0.85 Sr 0.15 MnO 3, but not for La Sr MnO 3 (see Fig. 4.11). Values of the spinsin relaxation time presented in Fig were calculated using frequency swept spectra measured with different pulse spacing, τ (Figures. 4.4 and 4.9) T 2 [µs] 70 DE x= x= Frequency [MHz] Fig Frequency dependence of the spin-spin relaxation time, T 2 for x=0.125 and x=0.15 compounds. The DE mark denotes the resonant frequency. Lines are guides for eyes only. For the La Sr MnO 3 compound the DE line vanishes with increasing pulse spacing and no dip at the line centre appears (Fig. 4.4) in contrast to the La 0.85 Sr 0.15 MnO 3 compound (see figures 4.9 and 4.10). The Suhl-Nakamura interaction was also observed in other ferromagnetic metallic manganites [Savosta 2001, Rybicki 2004]. On this basis we conclude that the Suhl-Nakamura interaction is effective only in the x=0.15 doped compound and that the regions, where DE interaction is dominant are much larger in size in the x=0.15 than in the

53 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 49 x=0.125 doped compound. For the sample with x=0.15 the dip at the centre of the DE line is also observed at 77 K. This is a clear evidence that DE regions are large enough to ensure the Suhl-Nakamura interaction between neighbouring nuclear spins to be effective at this temperature. The earlier NMR results by Savosta et al. [Savosta 2001], which revealed that the Suhl-Nakamura interaction is effective in manganites at higher temperatures were obtained for ferromagnetic metallic La 0.7 Sr 0.3 MnO 3, while our results concern lower Sr doped ferromagnetic insulating compound, where the amount of DE regions is expected to be smaller. The ferromagnetic metallic clusters of the size of 10 nm were also found in the x=0.15 compound by the small angle neutron scattering (SANS) technique [Ibarra, unpublished]. Spin-spin relaxation times obtained from pulse spacing measurements carried out for La 0.85 Sr 0.15 MnO 3 at 4.2 K and 77 K are presented in the table 4.1. Similarly to x=0.125 compound the shortest value of T 2 is obtained for manganese nuclei in FMM regions and the longest - for Mn 3+ nuclei in FMI insulating regions (signals above 400 MHz). All values of the T 2 obtained for La 0.85 Sr 0.15 MnO 3 are smaller than those obtained for La Sr MnO 3 compound and the biggest difference is found for the T 2 of nuclei contributing to the DE line. This difference amounts to 9 µs (24%) and can be attributed to the Suhl-Nakamura interaction, which is less effective in the La Sr MnO 3 compound. One can also notice that for La 0.85 Sr 0.15 MnO 3 the T 2 of nuclei contributing to the DE line does not decrease so dramatically with increasing temperature as in La Sr MnO 3. At 77 K it amounts to 15 µs versus 6 µs for the higher and the lower Sr doped compounds, respectively (see table 1 and Fig. 4.8b). At 4.2 K At 77 K Freq. [MHz] T T 2 [µs] 2 Freq. [µs] [MHz] T T 2 [µs] 2 [µs] Table 4.1 Spin-spin relaxation times, T 2 and their uncertainties, for nuclear magnetic moments of manganese ions obtained using equation (4.1) for La 0.85 Sr 0.15 MnO 3 at 4.2 K and 77 K La Sr MnO 3 and La 0.85 Sr 0.15 MnO La In manganese perovskites, besides 55 Mn NMR also signals from 139 La nuclei have been measured in many compounds doped with calcium [Allodi 1997, Papavassiliou 1997, 2001] or with sodium [Savosta 1999]. Lanthanum nucleus (nuclear spin I=7/2) is subjected to the transferred hyperfine field (from manganese neighbours) and dipolar interactions with electronic moments as well

54 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 50 as to the quadrupolar coupling with the electric field gradient. However, satellite lines which would indicate the presence of quadrupolar interactions have never been observed experimentally in manganese perovskites. The NMR signal of 139 La originates indirectly from the overlap of the Mn 3d> with oxygen 2p> wave functions, in conjunction with σ bonding of the oxygen with sp 3 > hybrid states of the La 3+ cation [Papavassiliou 1997]. The frequency swept spectra of 139 La NMR are presented in Fig For both compounds with different Sr doping two lines are observed, however with different relative intensities. Resonant frequencies are obtained by fitting Gaussian curves to the data and they amount to 17,64±0.09 MHz and 32,80±0.11 MHz for x=0.125 Sr doped compound. For x=0.15 Sr doped one resonant frequencies amount to 18.57±0.04 MHz and 32.92±0.14 MHz. The corresponding values of the effective field, B eff at the 139 La nuclei amount to 2.94 T and 5.46 T for the x=0.125 compound and 3.09 T and 5.48 T for the x=0.15 one. The difference between effective fields of those two lines for both compounds is close to 2.5 T and it cannot be explained by the anisotropy of the dipolar field, B D which is of order of a few tenths of Tesla. The transferred hyperfine field on gallium ion at the site of manganese in Pr 0.5 Ca 0.5 Mn 0.97 Ga 0.03 O 3 compound, amounting to 5.3 T was obtained previously by the NMR [Oates 2005]. This value is similar to the value obtained by us for 139 La (the upper line). The 139 La signal at frequency 20 MHz and a tail at higher frequencies (up to 35 MHz) were observed also for La Ca MnO 3 compound [Papavassiliou 2001]. The authors suggested that the higher frequency signal is due to the formation of Mn octant cells with enhanced Mn-O wave functions overlap resulting in a higher effective field on 139 La nuclei. The signal at higher frequency is not observed for the FMM manganese perovskites doped both with Sr (see the spectrum for x=0.3 Sr doped compound, Fig 4.12a, and for x=0.25, chapter 5) and with Ca [Papavassiliou 1998], where a single line at the lower frequency is observed only. Therefore, one can assume that the line at lower frequency is due to 139 La ions in FMM regions and the higher frequency line is due to 139 La in charge localised (CL) FMI regions. This assumption can be supported by the fact that the relative intensity of the CL line is higher for x=0.125 doped compound, thus meaning that the amount of the FMI phase is higher for this compound than for the x=0.15 one.

55 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 51 a) Normalised spin echo intensity [arb. units] x=0.3 x=0.15 x= Frequency (MHz) b) Normalized echo intensity [arb. units] x= /0.4 µs 1.5/3 µs x= /0.4 µs 1.5/3 µs Frequency [MHz] Fig a) 139 La NMR frequency swept spectra at 4.2 K, for x=0.125, x=0.15 Sr doped compounds and for x=0.3 for a comparison; b) the spectra measured with shorter exciting pulses for both compounds (red lines). The solid curves are Gaussian fits to the experimental data. As can be seen in Fig. 4.12b the line at lower frequency requires a smaller rf pulse amplitude or pulse length, whereas the line at higher frequency is not observed for a small pulse length (0.2 µs). This indicates that the enhancement factor, η of nuclei contributing to the signal at lower frequency is bigger. A possibility that one of observed lines could be due to some remaining antiferromagnetic phase (the AF FM phase boundary occurs for 10% of Sr doping) can be excluded, since the 139 La signal from AF phase can only be observed at high applied fields. Such a signal was observed at 7 T in the antiferromagnetic La 0.5 Ca 0.5 MnO 3 [Allodi 1998] and at similar fields in La 0.95 Sr 0.05 MnO 3 [Kumagai 1999] and (La 0.25 Pr 0.75 ) 0.7 Ca 0.3 Mn 18 O 3 [Yakubowskii 2000]. Even if 139 La signal from the AF phase could be observed at 0 Tesla, it should correspond to much lower frequencies than the signal from the FM phase. Since the hyperfine transferred field from AF ordered manganese neighbours of lanthanum would be smaller than from FM ordered manganese ions. So this hypothetical La signal from AF phase at lower frequencies should, according to previous studies [Allodi 1998, Kumagai 1999, Yakubowskii 2000], have a smaller enhancement factor and shorter relaxation times, which is not the case (see Fig. 4.12b and table 4.2).

56 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 52 Spin-spin relaxation times, T 2 for 139 La nuclei are longer than for nuclei of 55 Mn (see table 4.2), both for the CL FMI regions and for the FMM regions. In the case of La Sr MnO 3 and La 0.85 Sr 0.15 MnO 3 the T 2 of 139 La nuclei in FMM regions are considerably longer (more than two times) than those in FMI regions. x=0.125 x=0.15 Freq. [MHz] T 2 [µs] T 2 [µs] Table 4.2 Spin-spin relaxation times, T 2 and their uncertainties, for 139 La obtained using equation (4.1) for La Sr MnO 3 and La 0.85 Sr 0.15 MnO 3 compounds at 4.2 K. As was previously discussed for the frequency swept spectra, there is no indication of the electric quadrupolar interaction, however, such an indication was reported earlier in measurements of the spin-lattice relaxation time with the recovery of the spin echo method [Allodi 1998, Savosta 2003]. Therefore, for 139 La also the spin-lattice relaxation time, T 1 has been measured. In principle, as the separation time between the saturating comb of pulses and the probing two-pulse sequence (π/2 and π pulses) increases, the spin echo recovers according to the equation: t = T1 M ( t) M t = 1 e (4.2), where M t= is the nuclear magnetisation for time t=. If the nuclear magnetisation is not saturated to zero at time t=0 (M t=0 0), above equation changes to: t = + T1 M ( t) M t= 0 M t= 1 e (4.3) It is assumed that the signal is a sum of two contributions with different enhancement factors and saturation is reached for one contribution only. If the not saturated component has much longer T 1, the M t=0 means the long-relaxing component. As was found by Allodi et al., in manganese perovskites the recovery of the spin echo is not single exponential. They attributed it to the quadrupole interaction [Allodi 1998]. The spin lattice relaxation of a I=7/2 nucleus with quadrupole splitting of the nuclear Zeeman levels is governed by the master equations which predict a multiexponential behaviour [Gordon 1978]. Assuming that the spinlattice relaxation mechanism is predominantly of magnetic origin and only the central -1/2 1/2 transition is saturated, the nuclear magnetisation in the spinlattice relaxation time measurement recovers according to the equation:

57 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO Wt 2 12Wt 20 30Wt Wt M ( t) = M t= 1 e e e e (4.4) where the transition probability 2W =. T1 As can be seen in Fig. 4.13a, the recovery of the spin echo can be relatively well fitted with the single exponential function (equation 4.3). In contrast, fitting with the equation 4.4 does not give satisfactory results unless one adds the parameter M t=0, corresponding to unsaturated nuclear magnetisation, similarly to the recovery described by the single exponential function (equation 4.3). However, in this case the obtained spin-lattice relaxation times are more than one order of magnitude bigger than those derived from single exponential fits (see table 4.3). For a comparison also the literature results for the La 0.8 Na 0.2 MnO 3 compound at 77 K are presented in Fig. 13b, after [Savosta 2003]. As can be seen in Fig. 13b, discrepancies between single exponential fit and experimental data occur at larger t (the time between the saturating comb of pulses and probing pulse sequence of π/2 and π pulses) values, while our measurements were carried out up to t value of 5 ms (Fig. 12a). A "misfit" of the equation 4.4 (with M t=0 parameter included) and 4.3 at small values of t reveals an additional contribution with short T 1, which denotes the presence of two different spin-lattice relaxation processes. a) 0,40 Pulses: 0.2 µs 0.4 µs Pulse-Spacing: 12 µs Frequency: +17 MHz M (t) [arb. units] 0,35 0,30 0,25 single exponential multiexponential multiexponential with M t= t [µs] Fig a) Recovery of the longitudinal component of the 139 La nuclear magnetization, M for La Sr MnO 3 measured at 17 MHz (FMM line) using single exponential function, equation 4.3 (black line), multiexponential function equation 4.4 without (blue line) and with (red lines) parameter M t=0. Black and red lines coincide. b) Literature results [Savosta 2003], see text for details.

58 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 54 Freq. T T [MHz] 1 [ms] T 1 [ms] 1me T 1 me [ms] [ms] x= x= Table 4.3 Spin-lattice relaxation times, T 1 and their uncertainties, for 139 La obtained using equation (4.3) for La Sr MnO 3 and La 0.85 Sr 0.15 MnO 3 compounds at 4.2 K. T 1me are spin lattice relaxation times with obtained by fitting multiexponential function.

59 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO La 0.9 Ca 0.1 MnO 3-55 Mn NMR results In this section NMR results obtained on four samples (three powder samples and a single crystal) of La 0.9 Ca 0.1 MnO 3 are presented. As was mentioned, all powder samples were calcined in air atmosphere, later milled and then sintered either air (Zaragoza and SB#2 samples) [Algarabel 2003, Ghivelder 1998] or in oxygen atmosphere (FCB11 sample) [Ghivelder 1998]. However, the Zaragoza sample was sintered in air at 1250 C and at 1400 C for 12 hours with intermediate grinding while the SB#2 sample was sintered at 1400 C only for 5 hours. The single crystal was also prepared in air atmosphere. Fig The phase diagram of La 1-x Ca x MnO 3 for a) the air atmosphere (AP) prepared samples, solid circles denote the paramagnetic ferromagnetic transition, open circles correspond to the onset temperature T B of the jump in the ZFC dc magnetization curves; and b) for R (He atmosphere annealed) samples, solid circles denote the transition from the paramagnetic to the canted antiferromagnetic or ferromagnetic state. Taken from [Pissas 2004]. As was found recently, the atmosphere in which sintering process is carried out is crucial not only for stoichiometry, but also for crystallographic and magnetic structure of the compound [Hory 2004, Pissas 2004]. In the case of low doped

60 Chapter 4: Cubic perovskites: La Sr MnO 3, La 0.85 Sr 0.15 MnO 3 and La 0.9 Ca 0.1 MnO 3 56 La 1-x Ca x MnO 3 series of compounds new phase diagrams were established, depending on the preparation process, see Fig [Pissas 2004]. Properties of the compound of interest, i.e. La 0.9 Ca0 0.1 MnO 3, depend on the oxygen partial pressure during preparation, which influences the Mn 4+ content and in order to prepare stoichiometric samples a low oxygen partial pressure is needed [Pissas 2004]. Samples prepared in atmospheric conditions for x<0.16 were found to be cation deficient in such a way that the Mn 4+ concentration remains constant regardless of x. Moreover, as can be seen from Fig samples prepared in atmospheric conditions at low temperatures are not canted antiferromagnets, as reported for samples prepared in helium, [Pissas 2004] or argon atmosphere [Terashita 2005], but they exhibit ferromagnetism [Pissas 2004]. For the Zaragoza sample neutron diffraction showed no evidence of antiferromagnetic domains [Algarabel 2003]. The values of T C and temperature denoted as T B agree well with those derived from AC susceptibility measurements for our samples. For single crystal and SB#2 samples T B was found to be of 110 K and T C amounts to 158 K and 165 K respectively [Yates 2003]. Basing on this as well as on the magnetic and other measurements presented in [Ghivelder 1998, Yates 2003, Algarabel 2003] we conclude that the ground state of the samples studied by us is not a canted antiferromagnet but ferromagnet. Fig Mn NMR spin echo spectra of the SB#2 sample at 4.2 K and different pulse spacing, τ. Lines are guides for eyes only. Fig Mn NMR spin echo spectra of the single crystal sample at 4.2 K and different pulse spacing, τ. Lines are guides for eyes only.

61 Chapter 4: La Sr MnO 3 and La 0.85 Sr 0.15 MnO 3 - NMR results 57 Fig Mn NMR spin echo spectra of the FCB11 sample at 4.2 K with different values of pulse spacing, τ. Lines are guides for eyes only. Fig Mn NMR spin echo spectra of the Zaragoza sample at 4.2 K with different values of pulse spacing, τ. Lines are guides for eyes only. After this explanation we present the 55 Mn NMR results carried out at 4.2 K. Figures present the frequency swept spectra carried out at various pulse spacing, τ. The interpretation of the frequency swept spectra for all the samples of La 0.9 Ca0 0.1 MnO 3 is analogous to La Sr MnO 3. Starting from the low frequency side there is a sharp peak at around 320 MHz, due to Mn 4+ in ferromagnetic insulating regions. The line around 380 MHz is attributed to the ferromagnetic metallic regions where the DE driven fast hopping of carriers between the adjacent Mn 4+ and Mn 3+ sites takes place [Matsumoto 1970, Kapusta 2000]. The higher frequency lines appearing in the range from 400 to 550 MHz are attributed to Mn 3+ ions in the ferromagnetic insulating regions. One can notice that there are three distinct lines in this region, which are denoted in Fig as line I, II, III, in contrast to the frequency swept spectra for La Sr MnO 3 compound where two Mn 3+ lines were observed. Similar NMR frequency swept spectra of all samples of La 0.9 Ca0 0.1 MnO 3 compound to La Sr MnO 3 also suggest that their ground state is similar, i.e. the ground state of La 0.9 Ca0 0.1 MnO 3 is a ferromagnet rather than a canted antiferromagnet. For one of the samples (i.e. Zaragoza sample) also measurements at the applied field (up to 6 T) were carried out [Algarabel 2003]. Their results are

62 Chapter 4: La Sr MnO 3 and La 0.85 Sr 0.15 MnO 3 - NMR results 58 similar to those obtained for La Sr MnO 3 presented earlier in this chapter. Again the lines: FMI Mn 4+, the DE and the Mn 3+ line at 530 MHz shift towards lower frequencies in the applied field and the Mn 3+ line at 450 MHz does not shift even at 6 T and only decreases in intensity [Algarabel 2003]. This suggests that, as in the case of La Sr MnO 3, the Mn 3+ line at 450 MHz is due to magnetic moments directed perpendicular to the applied field direction. It is worth noting that in the samples FCB11 and Zaragoza at the longest pulse spacing the Mn 3+ line at 530 MHz remains, similarly to the La Sr MnO 3 compound (see Fig. 4.4). The signal which stays at the longest pulse spacing (longest relaxation times) can be attributed to ions located in domain wall edge, where the magnetic moments are within or close to the easy magnetisation direction (EMD) [Weisman 1973, Davis 1976, Leung 1977]. The spin-spin relaxation time, T 2 of the Mn 3+ lines is the longest for the line above 500 MHz (see table 4.4). However, for the SB#2 and the single crystal samples the Mn 3+ line at 400 MHz remains at longest pulse spacing. This may be due to a smaller anisotropy field in the SB#2 and the single crystal samples and, correspondingly, to a different easy magnetisation direction. It is worth noting that the 55 Mn NMR spectra of the Zarogaza sample (sintered in air atmosphere) are similar to those of the FCB11 sample, which was sintered in oxygen atmosphere, rather than to the NMR spectra of other samples prepared in air atmosphere (SB#2 and single crystal samples). This can be explained by a much longer time of sintering process of the Zaragoza sample and, possibly, to an excess of oxygen in the FCB11 and Zaragoza samples. The problem of oxygen nonstoichiometry and its effects on the properties of manganese perovskites have been studied by many researchers, see for example [Wołcyrz 2003, Hory 2003]. The effect of oxygen nonstoichiometry on 55 Mn NMR spectra can be very significant, see for example in [Kapusta 1999]. Freq. [MHz] SB#2 Single crystal Zaragoza FCB11 T 2 T 2 Freq. T 2 T 2 Freq. T 2 T 2 Freq. T 2 [µs] [µs] [MHz] [µs] [µs] [MHz] [µs] [µs] [MHz] [µs] T 2 [µs] Table 4.4 Spin-spin relaxation times, T 2 and their uncertainties, for 55 Mn resonance lines, fitted with the equation (4.1) for all the studied samples of La 0.9 Ca 0.1 MnO 3 at 4.2 K. Similarly to both compounds doped with Sr, described previously, the spin-spin relaxation time, T 2 is the shortest for the DE line. However, for the

63 Chapter 4: La Sr MnO 3 and La 0.85 Sr 0.15 MnO 3 - NMR results 59 La 0.9 Ca 0.1 MnO 3 samples the values of T 2 are much larger than for the Sr doped compounds (see table 4.4, table 4.1 and Fig. 8b). Publication related to problems raised in this chapter: Rybicki D., et al., Acta Physica Polonica 105, 183 (2004)

64 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, Nanoparticles of La 0.75 Sr 0.25 MnO Mn NMR results of La 0.75 Sr 0.25 MnO 3 nanoparticles This chapter presents results and discussion of magnetisation measurements carried out on the SQUID magnetometer and 55 Mn NMR spin echo measurements at 4.2 K and at 77 K of three samples of La 0.75 Sr 0.25 MnO 3 compound carried out on the spectrometer in Kraków. Sample with grains of micrometric size (SM) and two samples with average grains size 114 nm (S114) and 33 nm (S33) were measured. The results of magnetization measurements are presented in Fig As it was found earlier by other groups, for manganese perovskite compounds with grains of nanoparticle size, the saturation magnetization, M S decreases with decreasing average grain size [Balcells 1998, Bibes 2003, Savosta 2004]. The effect is related to the presence of non-ferromagnetic (non-collinear, antiferromagnetic or nonmagnetic) outer layers of the grains. A higher relative volume contribution of this layer to the total volume in smaller grains corresponds to a smaller value of M S. The thickness (l) of this layer can be estimated using following expression [Balcells 1998]: M S ( φ) l 1 2 M S ( bulk) 1 3 φ (5.1) where φ is the average grain diameter. The derived values of l amount to 1.7 nm and 1.54 nm for the sample S33 and S114 respectively. M [emu/g] M [emu/g] T [K] S33 S114 SM ,5-0,4-0,3-0,2-0,1 0,0 0,1 0,2 0,3 0,4 0,5 µ 0 H [T] Fig. 5.1 Magnetisation plots versus applied field (M vs H) for samples S33 (red), S114 (black) and SM (blue) of La 0.75 Sr 0.25 MnO 3 at 4.2 K. Inset presents the temperature dependence of the magnetisation, M.

65 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, 61 This is in a good agreement with results obtained for nanoparticles of La 2/3 Sr 1/3 MnO 3, approx. 1.2 nm for the sample with 20nm grains [Balcells 1998]. The Curie temperature increases with the average particle size, from 335 K to 352 K in the case of average grain size of 33 nm and 120 nm respectively [Pollert 2006]. The coercive field, H C increases with decreasing particle size, which can be attributed to a higher anisotropy field, B A in smaller grains and a possible influence of domain walls in bigger particles. Also the character of domain walls is likely to change with decreasing grain size and approaching the single domain limit. This result is consistent with a change of the NMR enhancement factor () for samples with different grain sizes and it is discussed later on. Values of the T C derived from Arrot plots decrease with decreasing average grain size, from 360 K for sample with grains of micrometric size (SM sample) to 353 K and 344 K for S114 and S33 samples [Pollert 2006] Mn NMR spin echo spectra at 4.2 K and 77 K Figure 5.2 presents 55 Mn NMR spin echo spectra at zero field, at 0.2 T and at 0.5 T for samples SM, S114 and S33. The dominant main line centred close to 380 MHz corresponds to a fast hopping of the electron (hole) among the Mn sites in ferromagnetic metallic (FMM) regions, at a rate faster than the NMR (Larmor) frequency due to the double-exchange (DE) interaction. A weak signal at lower frequencies ( MHz), is ascribed to Mn 4+ ions in ferromagnetic insulating (FMI) regions located in the outer layers of the grains [Matsumoto 1970, Kapusta 2000]. Our observation of two resonant lines is similar to that in the NMR 55 Mn study of La 0.66 Ca 0.33 MnO 3 nanoparticle materials [Bibes 2003, Savosta 2004] and in epitaxial thin films of La 0.67 Sr 0.33 MnO 3 [Sidorenko 2006]. Similarly to the results presented in [Bibes 2003, Savosta 2004] the intensity of this signal per unit mass decreases with increase of the average grain size (Fig. 5.2). The relative amount of the FMI phase estimated from the line intensities of the spectra at zero field is of 3% and 1% for the samples S33 and S114, respectively (see inset in Fig 5.3). The values of the resonant frequencies of the DE line obtained from Gaussian curve fits to the spectra for samples S114, S33 and SM at zero field are MHz, MHz and MHz respectively (Fig. 5.4). Since the magnitude of the hyperfine field, B HF is approximately proportional to the electronic spin moment (<S>), = Aˆ S, where  is the hyperfine coupling tensor and S is a average electronic spin moment, therefore different values of the B HF for all samples could be attributed to a slightly different Mn 3+ /Mn 4+ ratio in all studied samples. This may be due to a possibly different oxygen stoichiometry in different samples resulting in non stoichiometric B HF

66 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, at 4.2K at 0T at 0.2T at 0.5T SM at 77K at 0T at 0.2T at 0.5T SM Echo intensity [arb. units] S114 S Frequency [MHz] Echo intensity [arb. units] Frequency [MHz] S114 S33 Fig. 5.2 Normalized NMR 55 Mn spin echo spectra of La 0.75 Sr 0.25 MnO 3 with grains of micrometric size (SM), with 114nm (S114) and 33nm (S33) grains at 4.2 K and 77 K, at 0 T (black lines), 0.2 T (blue lines) and 0.5 T (red lines). S33 S114 SM Normalised echo itensity Frequency [MHz] Fig. 5.3 Normalized 55 Mn spin echo spectra of bulk (blue line) La 0.75 Sr 0.25 MnO 3 and samples with 114 nm (red line) and 33 nm grains (black line) at 4.2 K and at no applied field. Zoomed view of low frequency region is presented in the inset.

67 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, 63 Mn 3+ /Mn 4+ ratio and/or an influence of the related negative pressure in small grains, which would decrease the value of B HF [Kapusta 2001]. The DE line shifts towards lower frequencies with increasing applied field as expected for the hyperfine field antiparallel to the Mn magnetic moment. For the sample S114 at 0.5T, the B eff is reduced to T from T at no applied field, for the sample S33 it decreases from T to T and for the microcrystalline sample from T to T (see also Fig. 5.4). One can conclude that the demagnetizing field, B dem is smaller than 0.2 T and that even at the smallest applied magnetic field our samples are the most likely in a single domain state ,0 0,1 0,2 0,3 0,4 0,5 Resonant frequency [MHz] S33 at 4.2K S33 at 77K S114 at 4.2K S114 at 77K SM at 4.2K SM at 77K 0,0 0,1 0,2 0,3 0,4 0,5 External field [T] Fig. 5.4 Resonant frequencies obtained from Gaussian curve fits to the DE lines for the NMR 55 Mn spin echo spectra, at fields 0 T, 0.2 T, 0.5 T and at temperatures 4.2 K (solid lines) and 77 K (dashed lines), for samples SM (black lines), S33 (blue lines) and S114 (red lines). However, the spin-spin relaxation time (T 2 ) for all studied samples reveals a non-exponential behaviour at 0 T, whereas T 2 decreases with a single exponential character at 0.5 T (Fig. 5.5). This indicates the presence of some domain wall-like magnetic inhomogeneities in all studied samples at 0 T, which disappear after applying magnetic field of 0.5 T, similar behaviour was also observed by Savosta et al. [Savosta 2004]. On this basis we assume that the DE line originates from Mn ions located both in domains and domain-wall like inhomogeneities (i.e. close to surface regions, where magnetic moments change their orientation similarly to the behaviour of magnetic moments in domain walls). The existence of typical domain

68 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, 64 walls is put in question due to very small size of grains in the samples S33 and S114. A similar assumption was also made in [Savosta 2004] a) at 0.5T Echo intensity [arb. units] b) at 0T SM S114 S Pulse spacing [µs] Fig. 5.5 Spin echo decay curves for resonant frequencies of the DE lines at 4.2 K for all studied samples of the La 0.75 Sr 0.25 MnO 3 ; a) at 0.5 T and b) at 0 T. Note the logarithmic scale of the echo intensity. 0,0 0,1 0,2 0,3 0,4 0,5 Full width at half maximum [MHz] ,0 0,1 0,2 0,3 0,4 0,5 External field [T] S33 S114 SM Fig. 5.6 The DE line widths (given as full widths at half maximum) obtained from Gaussian curve fits to the NMR 55 Mn spin echo spectra, at fields 0 T, 0.2 T, 0.5 T and at the temperature 4.2 K, for samples SM (black line), S33 (blue line) and S114 (red line) of the La 0.75 Sr 0.25 MnO 3.

69 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, 65 The width of the DE line at 4.2 K decreases with the increasing average grain size. This effect can be attributed to a narrowing of the distribution of the hyperfine field values due to less amount of defects for samples with higher average particle size and, possibly due to the more pronounced anisotropy of the hyperfine field in samples with smaller particles and also due to the differences in distributions of demagnetizing fields. The line width also decreases with application of the field for all the samples studied (see Fig. 5.6) and this decrease is the most dramatic (by 25%) for the sample with grains of micrometric size, while the relative decrease for S114 and S33 amounts to 18% and 8% respectively. This can be explained by the effect of the domain wall (or domain wall like regions) rearrangement and their partial removal induced by applying magnetic field. In the sample SM the amount of domain walls is the biggest so the effect of the field is the largest. Accounting for the shift of the DE line with the applied field, the line narrowing on application of 0.2 T and 0.5 T occurs at the expense of the high frequency part of the line, which suggests that the signal from domain walls or domain wall like regions corresponds to that part of the spectrum (see Fig. 5.2) The spin-spin and spin-lattice relaxations at 4.2 K and 77 K There are two possible methods of obtaining values of the spin-spin relaxation times, T 2. The first one is to measure the decay of the spin-echo signal as a function of the pulse spacing, τ (as in Fig. 5.5). The second is to make several frequency swept spectra with different pulse spacing (Figures 5.6 and 5.7) and using values of the spin echo signal for given frequency from all spectra, calculate the spin-spin relaxation time, T 2. The measurements of the T 2 at 0 T (at 4.2 K and 77 K) for all samples were carried out by measuring the decay of the spin-echo signal as a function of the pulse spacing, τ. As was mentioned above in this chapter, the decay of the spinecho signal at 0 T in not a single exponential function, but two exponents have to be used in order to fit the data. This is due to presence of signals both from D DW domains ( T 2 ) and from domain walls (or domain wall like regions) ( T 2 ), since in a ferromagnetic materials signals from nuclei in domains and nuclei in domain walls can be detected. The nuclei in domain walls have shorter spin-spin relaxation time than nuclei in domain interiors [Weisman 1973, Davies 1976, Leung 1977]. The experimental data were fitted with the following curve: = D 2τ + DW 2τ A( τ ) A exp A exp τ = 0 D τ = 0 DW (5.2) T T 2 2 D DW where A(τ ) and A, τ = 0 are the spin-echo amplitudes at the time τ, and τ=0 (for

70 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, 66 domains and domain walls (or domain wall like regions), respectively. The obtained values of the spin-spin relaxation times for nuclear magnetic moments, D DW and T 2 for all the samples at 0 T, at 4.2 K and 77 K are presented in table 5.1. T 2 Sample DW T 2 [µs] 4.2K 77K D T 2 [µs] DW T 2 [µs] D T 2 [µs] SM 4.3 ± ± ± ± 0.6 S ± ± ± ± 4.7 S ± ± ± ± 6.6 Table 5.1. Spin-spin relaxation times for nuclear magnetic moments in domains D DW ( T 2 ) and in domain walls (or in domain wall like regions) ( T 2 ), obtained using equation 5.2 for all studied samples of La 0.75 Sr 0.25 MnO 3 at 0 T, 4.2 K and 77 K measured at the resonant frequency of line maximum for each sample. S114 sample 4.2K, 0T S114 sample 4.2K, 0.5T Normalised echo intensity τ=100µs τ=50µs τ=20µs τ=10µs Frequency [MHz] Fig. 5.7a Normalized 55 Mn spin echo spectra of La 0.75 Sr 0.25 MnO 3 S114 sample at 4.2 K, at 0 T with various pulse spacing,. Normalised echo intensity τ=300µs τ=150µs τ=100µs τ=50µs τ=20µs τ=10µs Frequency [MHz] Fig. 5.7b Normalized 55 Mn spin echo spectra of La 0.75 Sr 0.25 MnO 3 S114 sample at 4.2 K, at 0.5 T with various pulse spacing,.

71 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, 67 In order to study the spin-spin relaxation more systematically, the spectra of all samples at 0 T and at 0.5 T for various pulse spacing, were measured at 4.2 K. Figures 5.7a and 5.7.b present measurements for sample S114 at 0 T and 0.5 T. Similar measurements for other two samples were also carried out, but the results look almost the same and, therefore, their spectra in dependence on are not presented here in details. It is clearly visible that with increasing pulse spacing a dip in the centre of the DE line appears similarly to La 0.85 Sr 0.15 MnO 3 [see chapter 4]. The effect can be explained by the Suhl-Nakamura interaction [Suhl 1958, Davis 1974] between nuclear spins of neighbouring Mn ions at 4.2K at 0.5T S33 S114 SM T 2 [µs] Frequency [MHz] Fig. 5.8 Frequency dependence of the spin-spin relaxation time, T 2 for samples S33, S114 and SM of La 0.75 Sr 0.25 MnO 3 at 4.2 K and at 0.5 T with error bars marked. The presence of the Suhl-Nakamura interaction can be shown in the other way in the frequency dependence of the spin-spin relaxation time, T 2 which should have a minimum at the resonant frequency. Fig. 5.8 presents such a dependence for all the studied samples at 4.2 K and at 0.5 T. The values of the T 2 were calculated from all measured frequency swept spectra with different pulse spacing used. They were obtained assuming a single exponential decay of the spin-echo signal (see Fig 5.5a) i.e. a single domain state of the sample at 0.5 T. Similar behaviour of the frequency dependence of T 2 is observed in the case of measurements at 0 T. However, a weakening of the spin-echo signal with increasing pulse spacing and a two exponential behaviour of T 2 (signals from nuclei in domains and in domain walls)

72 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, 68 result in larger uncertainty of the fitting. The Suhl-Nakamura interaction for 55 Mn ion in bulk metallic La 0.7 Ca 0.3 MnO 3 compound has the effective range of 35 at 140 K [Savosta 2001]. As can be seen in Fig. 5.8, samples S114 and SM have similar values of the T 2, for a given frequency, while T 2 of the S33 sample is significantly smaller. This means that the relaxation of nuclear spins is faster, which can be attributed to less effective coupling mechanisms between nuclear spins in the S33 sample due to a smaller size of grains. In metallic-like perovskite manganites there are two main mechanisms responsible for the spin-spin relaxation of nuclear magnetic moments [Savosta 2004]. The first one are fluctuations of the hyperfine fields caused by hopping of electron holes, T ( hop ) 2. The second mechanism is the spin-spin relaxation due to the Suhl- Nakamura interaction, T 2 ( SN), which is not effective at the sides of the resonant line, where only mechanism due to electron (hole) hopping has to be considered. Therefore, both relaxation processes can be separated using the formula [Savosta 2004]: T = T ( hop) + T ( SN) (5.3) 1 where T 2 is the value for given frequency, taken from Fig From this formula the contribution of the Suhl-Nakamura interaction to the relaxation rate is derived. The values of the relaxation rates, T 1 ( SN) 2 amount to 6.97 ms -1, 6.61 ms -1 and 7.63 ms -1 for S33, S114, SM samples respectively for the DE line and one can conclude that in all the samples studied the effective range of the Suhl-Nakamura interaction is comparable or smaller than the size of DE regions. Nanosized samples exhibit smaller Suhl-Nakamura contribution to the relaxation rate than sample with grains of micrometric size. This can be explained knowing that the effectiveness of the Suhl-Nakamura interaction depends on the number of nuclear spins, which precess at or near the resonance frequency and this number can be smaller in samples with nanometric grains. The obtained results of the DE line widths (given as full widths at half maximum) from the Gaussian curve fits support this finding (see Fig. 6). The DE line of the S33 sample is the broadest (the broader the resonance line - the less nuclear spins, which precess at or near the resonance frequency). Similar observation was made for the nanoparticles of La 0.7 Sr 0.3 MnO 3 [Savosta 2004]. The T 1 ( hop) 2 is larger for S33, i.e. for sample with smallest grains ( T 1 ( hop) 2 1/100 µs -1 ) than for samples S114 and SM ( T 1 ( hop) 2 1/260 µs -1 ). This implies, that in the sample with the smallest grains electrons and 1 holes are moving slower, since T ~ τ [Savosta 2004], where τ hop is the correlation 2 hop time of electron (hole) hopping [Savosta 1999]. Values of the spin-spin relaxation times, T 2 at 0 T could not be derived in a

73 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, 69 similar way to those at 0.5 T, because the signal to noise ratio in the measurements at 0 T with increasing pulse spacing was decreasing much faster than in the case of measurements carried out at 0.5 T (compare Fig. 5.6 and 5.7 for the same value of pulse spacing, τ). Due to this fact frequency swept spectra within shorter range of pulse spacing values could be measured only before signal was lost in noise, and additionally at 0 T the spin-spin relaxation is two exponential; therefore a reasonable fit to these data is not possible. One can also notice that spin-spin relaxation times, T 2 of nuclear magnetic moments measured at 0.5 T are considerably longer that those obtained at 0 T. The T 2 at 0 T lies in the range µs for all samples (table 2) while at 0.5 T it amounts to 62 µs, 93 µs and 86 µs for S33, S114 and SM samples respectively. This fact is a result of the two factors. First, the contribution to the spin-spin relaxation time from nuclei within domain walls (or domain wall like regions) decreases and is later eliminated as domain walls (domain wall like regions) are removed by the applied field [Leung 1977]. As was shown the spin-spin relaxation time is shorter for nuclei within domain walls than for nuclei in domains. The second factor is the fact that the Suhl-Nakamura interaction depends on the external field, so that the spin-spin relaxation, T 2 increases as the external field increases [Hone 1969, Davis 1974]. This effect was observed in the manganese ferrite [Davis 1976] and in La 0.69 Pb 0.31 MnO 3 [Leung 1977]. The spin-lattice relaxation times, T 1 for all the samples measured at 4.2 K and at 77 K at 0 T are presented in Fig The recovery of the nuclear magnetisation is not a single exponential function and it fits very well to two exponents: M ( t) t 1 exp T1 + A t 1 exp T1 = A a b T a T b 1 1 (5.4) The results of the fits with above formula are presented in table 5.2. Necessity of using two exponents in the fitting curve in order to obtain good fit means that spinlattice relaxation contains the contribution from domains and domain walls (or domain wall like regions), similarly to the spin-spin relaxation. Also the spin-lattice relaxation times are shorter for samples with grains of nanometric size and decrease with the particle size, which can be attributed to additional T 1 relaxation present in nanometric particles, but absent in a bulk material. This additional relaxation is due non-ferromagnetic atoms on the particle surface layer, such observation was also made for nanometric particles of ferromagnetic cobalt in [Kaplan 1968], where the authors concluded that additional T 1 relaxation observed in nanometric particles is due to paramagnetic like atoms in the surface layer of particles and nuclear spin diffusion

74 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, 70 to paramagnetic like regions [Kaplan 1968]. Arb. units a) c) Arb. units b) Recovery time [µs] Arb. units Recovery time [µs] Fig. 5.9 Measurements of the spin-lattice relaxation times, T 1 at 4.2 K and 77 K at 0 T for all the samples of La 0.75 Sr 0.25 MnO 3 studied; a) for sample SM (blue squares); b) for samples S33 (red squares) and S114 (green squares); c) at 77 K for all three samples with the same colours as in a) and b). Lines are fits to the experimental data using equation 5.3. The plots are arbitrary off-set for clarity. Sample a T 1 [µs] 4.2K 77K b T 1 [µs] SM 2923 ± ± ± 8 83 ± 3 S ± 5 36 ± ± ± 3 S ± 7 22 ± ± ± 4 a b Table 5.2. Spin-lattice relaxation times, T 1 and T 1 obtained using equation 5.4 for all of La 0.75 Sr 0.25 MnO 3 samples studied, at 4.2 K and 77 K and at 0 T. a T 1 [µs] b T 1 [µs] The enhancement factor of 55 Mn at 4.2 K and 77 K In order to analyse the NMR enhancement factor, which is related to the susceptibility of the electronic system at the NMR frequency, χ RF the optimal pulse lengths corresponding to the maximum of the spin echo for the resonant frequency of the DE lines have been compared for all the samples studied. For measurements at 4.2 K they are presented in table 3 and for measurements at 77 K only the relative

75 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, 71 changes of the optimal pulse lengths are given (see table 5.4). The enhancement factor, is inversely proportional to the optimal pulse length, t [Turov 1972] (see equation 3.41 in chapter 3): η 1 χ (5.4) RF t therefore at 0 T is the largest for sample SM with grains of micrometric size and the smallest for S33 sample with the smallest grains. at 0T at 0.2T at 0.5T S33 0.8µs 1.1µs 1.6µs S µs 1µs 1.5µs SM 0.2µs (+4dB) 1.9µs 3.7µs Table 5.3 Optimal lengths of the first exciting pulse (second pulse is always kept two times longer) used for all the samples studied at 4.2 K for resonant frequency of the DE lines. For SM sample at 0 T additional pulse attenuation was used in order to observe maximum in the dependence of the spin echo signal intensity on the pulse length. Table 5.4 presents ratios of the enhancement factors, e.g. at 0.5 T to at 0 T for all studied samples at 4.2 K and at 77 K, calculated as inverse ratios of the optimal pulse lengths (equation 5.4). For all the samples at both temperatures enhancement factors decrease after applying magnetic field, which is due to rearrangement and/or removal of the domain walls (domain wall like regions), nuclei of atoms in domain walls or in domain wall like regions have larger enhancement factor than those in domain interiors. However, the biggest change of the enhancement factor is observed for sample SM with the largest grains: at 4.2 K after applying 0.5 T decreases nearly 17 times. Such a big decrease compared to that of 114 and 33 is attributed to the presence of domain walls in the microcrystalline sample, which are removed by the applied field, whereas in the samples S33 and S114 there are much less domain walls or domain wall like regions. η33(0.5t ) η114(0.5t ) ηbulk (0.5T ) η (0T ) η (0T ) η (0T ) bulk 4.2K K Table 5.4. Ratios of enhancement factors at 0.5 T and at 0 T for all studied samples at 4.2 K and at 77 K.

76 Chapter 5: Nanoparticles of La 0.75 Sr 0125 MnO 3, La signal at 4.2 K and at no applied field The 139 La signal was measured at 4.2 K and the results are presented in Fig Unlike in the case of lower Sr doped compounds (see chapter 4), the frequency swept spectra of La 0.75 Sr 0.25 MnO 3, both with micrometric and nanometric grains, consist of a single resonance line. The resonance line of the S114 sample is centred at 26 MHz (6 MHz higher than for the SM sample) and is much broader. It is worth noting that the manganese resonant line of the S114 sample is also larger than that of the SM sample (see Fig. 5.6). The reason for a much larger line width is the bigger distribution of the transferred hyperfine fields at the La site due to smaller grain sizes and, correspondingly, to a higher influence of inhomogeneities in smaller grains. The signal from the sample with the smallest grains (S33 sample) was too weak to enable its observation in a reasonable time. Normalized echo intensity [arb. units] S114 sample SM sample Frequency [MHz] Fig Normalized NMR 139 La spin echo spectra of La 0.75 Sr 0.25 MnO 3 with grains of micrometric size (SM sample) and with 114nm grains (s114 sample) at 4.2K and at no applied field. Some of the results shown in this chapter are presented in: Rybicki D., et al., Physica Status Solidi C 3, 155 (2006)

77 Chapter 6: Bilayered manganese perovskites, La 2-2x Sr 1+2x Mn 2 O Bilayered manganese perovskites, La 2-2x Sr 1+2x Mn 2 O Mn NMR of bilayered manganese perovskites, La 2-2x Sr 1+2x Mn 2 O 7 In this chapter 55 Mn and 139 La NMR results and discussion on bilayered manganese perovskites, La 2-2x Sr 1+2x Mn 2 O 7 with 0.3 x 1 are presented together with magnetisation measurements carried out with the VSM magnetometer (for compounds 0.5 x 1). Before presenting the NMR results a closer look is given at the contribution to the hyperfine field, B HF called spin-dipolar field, BS d. As was mentioned in the subchapter dedicated to hyperfine fields in magnetically ordered materials, it is due to spins of electrons at individual orbitals and is given by the formula: 2 s i i = r 3 B g µ S d s B 0 5 i r ( s r ) r0 0 µ (6.1) where g s =2.0023, s i is the spin of ith electron and 0 leading vector, r. This field can be computed by multiplying the above equation r is a unit vector along the * by the electron density, ρ = Ψ e Ψe and integrating over the electron coordinates [Abragam 1970]. Calculation of the BS d field for 3d orbitals is essential for the explanation of observed 55 Mn NMR frequency swept spectra (see paragraph 6.2.2). The wave function describing the electron consists of the radial part and the angular part. For 3d the radial part of the wave function, R 3d is given by the equation: 3 ρ 1 2 2Zr 2 2 R3 d = ρ Z e, where ρ = (6.2) 9 30 n r is the radius in atomic units, in our case n=3 and Z is the effective nuclear charge. The value of the effective nuclear charge, Z eff used for calculation amounted to [Clementi 1963, Clementi 1967], which is the value for the 3d orbital for Mn ion including screening effect by the inner electrons. The angular parts of the electronic wave function are different for electrons on different 3d orbitals. These orbitals are usually denoted as xy, xz, yz, x 2- y 2, 3z 2 -r 2 and the angular parts, Y 3d of the respective orbitals are given by equations: 60 xy 1 Y3 d ( xy ) = 2 4 r 4π (6.3) 60 xz 1 Y3 d ( xz ) = 2 4 r 4π (6.4) 60 yz 1 Y3 d ( yz ) = 2 4 r 4π (6.5)

78 Chapter 6: Bilayered manganese perovskites, La 2-2x Sr 1+2x Mn 2 O ( x y ) 1 Y 2 2 = 3d ( x y ) 2 4 r 4π (6.6) (2z x y ) 1 Y 2 2 = 3d (3z r ) 2 4 r 4π (6.7) 2 where r = x + y + z. The graphical representations of these angular wave functions are presented in Fig Fig Graphical representations of angular wave functions for five 3d orbitals, t 2g orbitals are off axes and e g orbitals lie along coordination axes. In the compounds studied the Mn 3+ ion has four electrons in the 3d band in a high spin state, e.g. 3 electrons with spin up on t 2g orbitals and one electron with spin up on one of the two e g orbitals (see also chapter 2). Calculations of the spin-dipolar field, BS d at nucleus produced by a single electron occupying one of the 3d e g orbitals were carried out in the Mathematica program using numerical integration and method called Multidimensional, which is as an adaptive Genz-Malik algorithm [Genz 1991]. The results of calculations are presented in table 6.1. In order to test the results, other methods available in Mathematica for numerical integration were used The quasi Monte Carlo method (non-adaptive Halton-Hammersley-Wozniakowski algorithm) gave the result 0.2% bigger and the non adaptive Monte Carlo method gave result 7% smaller than the method Multidimensional. Due to the symmetry of the three t 2g orbitals the BS d field produced by the three electrons occupying t 2g orbitals is zero and one obtains a nonzero value of the BS d produced by the electron occupying one of the two e g orbitals. If magnetic moments lie along one of the axes x, y or z, the corresponding spin dipolar field also has its component only along one of these axes.