Strain-induced coupling of electrical polarization and structural defects in SrMnO 3 films

Transcription

1 Carsten Becher, Laura Maurel, Ulrich Aschauer, Martin Lilienblum, César Magén, Dennis Meier, Eric Langenberg, Morgan Trassin, Javier Blasco, Ingo P. Krug, Pedro A. Algarabel, Nicola A. Spaldin, José A. Pardo and Manfred Fiebig SUPPLEMENTARY INFORMATION DOI: /NNANO Strain-induced coupling of electrical polarization and structural defects in SrMnO 3 films Epitaxial growth: X-ray diffraction in all the samples grown on (001)-oriented (LaAlO 3 ) 0.3 (Sr 2 AlTaO 6 ) 0.7 (LSAT) present only the 00l reflections from the substrate and film in symmetrical θ/2θ scans, proving the epitaxial growth of the perovskite structure and the absence of impurities and secondary phases. Fig. S1a shows a θ/2θ scan around the 002 reflection in a 20-nm film on LSAT. The SrMnO 3 out-of-plane lattice parameter extracted from the film peak position is ± nm. A narrow rocking curve of the 002 reflection with 0.016º full width at half maximum (see inset in Fig. S1a) and Von-Laue oscillations demonstrate high crystal quality and structural coherence across the whole film thickness. φ-scans (not shown) and reciprocal space maps of the asymmetric 013 reflection (Fig. S1b) further prove the cube-oncube epitaxial growth and show the film to be fully strained, presenting the same in-plane lattice parameter as the substrate ( nm). Similar maps in a series of films of different thickness were used to estimate the critical thickness, above which epitaxial strain is partially relaxed, to be around 30 nm. All the epitaxial films with thickness lower than this value grow under in-plane biaxial tensile strain of 1.7% and present a tetragonally distorted perovskite cell. Occasional cracks observed in some of the films had no effect on the observations reported in our manuscript. NATURE NANOTECHNOLOGY 1

2 Fig. S1: Structural characterization of the SrMnO 3 thin films by X-ray diffraction. a, Symmetrical θ/2θ scan around the 002 reflection in a 20-nm film on (001)-oriented LSAT. Inset: Rocking curve of the film 002 reflection, showing its full width at half maximum (FWHM) value. b, Reciprocal space map around the asymmetric 013 reflection, proving that the film is fully strained. Q [010] and Q [001] are the inplane and out-of-plane components of the scattering vector Q, respectively. Local strain state: High angle annular dark field scanning transmission electron microscopy (HAADF-STEM) qualitatively shows the good crystal quality of the films, together with an atomic sharp interface with the substrate. The films appear to be fully strained. This has been confirmed by a quantitative analysis of the STEM images by geometrical phase analysis (GPA) shown in Fig. S2. Fig. S2: GPA of the HAADF image of SrMnO 3 on LSAT (001). a, HAADF image with the averaged deformation state in the substrate plane and out of plane. b, c, Colour map of the deformation state inplane and out-of-plane, respectively. 2

3 No deformation is observed in the film along the substrate-plane direction, which confirms that locally the whole SrMnO 3 film grows fully strained, with approximately a +1.7% tensile strain in the substrate plane. In contrast, GPA reveals a strong uniform out-of-plane deformation of the SrMnO 3 of (2.9 ± 0.8)% with respect to the substrate. The large error bar is related to sample instabilities along the direction perpendicular to the scan that induces artefacts in the image. Therefore, the average out-of-plane lattice parameter of SrMnO 3 is nm, which equals to a compressive strain in the out-of-plane direction of +1.1% with respect to bulk SrMnO 3. Manganese oxidation state: Electron energy loss spectroscopy (EELS) of the oxygen K edge of SrMnO 3 has been used to estimate the local oxidation state of SrMnO 3. The spectra have been acquired at 120 kv, with an energy dispersion of 0.1 ev, with a convergence angle of 22 mrad, and with a spectrometer collection angle of 35 mrad. This has been carried out following the procedure reported by Varela et al. S1 for the isoelectronic manganite series La x Ca 1-x MnO 3, which consists in the determination of the energy difference between the oxygen K main peak and the pre-peak related to the hybridization of the Mn 3d and O 2p orbitals. Fitting these peaks to two Gaussian curves, as shown in Fig. S3, an average oxidation state of +(3.9 ± 0.1) with respect to a nominal oxidation state in a fully oxygenated SrMnO 3 of +4 was obtained. The actual oxidation state is limited to the range from 4.0 to 4.1 (or δ = 0 to 0.1 in SrMnO 3-δ ) because interstitial oxygen and the loss of strontium or manganese cost too much energy according to refs. S5 and S6. Note that x-ray photoelectron spectroscopy results are in agreement with the EELS data. 3

4 Fig. S3: EELS of the O K edge of SrMnO 3 grown on LSAT (001). Gaussian curves have been used to fit the spectrum, extracting peak positions as described in ref. S1. Evaluation of second harmonic light polarisation dependence: In the non-polar centrosymmetric phase, the point symmetry of the strained tetragonal SrMnO 3 films is 4/mmm. Here, leading-order second harmonic generation (SHG) (2 ) ( ), ( ) ( ) is symmetry-forbidden, i.e. ( ) = 0. In contrast, the polar phase with an in-plane polarisation P S leads to the polar point group symmetry 4mm or mm2 for a polar axis either oriented along an in-plane principal axis or along an in-plane diagonal, respectively. Both of these point groups permit the tensor components,,,, to be non-zero tensor. Here, the z direction corresponds to the respective direction of the polar axis for the two symmetries S2. For fitting the measured angular dependence of the SHG signal we apply the following criteria: 1. We assume the presence of two orthogonal polar axes P 1 and P 2 along which the spontaneous polarisation can be oriented along the up or down direction. In total, this leads to the four possible polar states P 1± and P 2±, which we assume to be mixed in the sample. 2. We introduce r = P 1 /P 2, the ratio of the areas taken by the P 1 and P 2 domains, as free fit parameter 4

5 3. We further introduce the angle δ between the polar axes and the crystal axes (sketched in Fig. S4) as free fit parameter. δ = 0 and δ = 45 correspond to a polar axes along ([100], [010]) and ([110], [110]) respectively. 4. We disregard the susceptibilities, because the light is incident along the [001] direction parallel to the y axis, implying ( ) =0 5. We account for the complex values of the remaining components,, by introducing phase factors ( ), ( ), and ( ). The reference phase is arbitrary so that we choose φ as zero. 6. The SHG signal is then given as (2 ) ( ), ( ) ( ) with,,, Fig S4: Sketch of the SHG process for a multidomain sample with a mixture of polarisation domains P 1± and P 2±. Light is incident along the [001]-direction so that ( ) =0. The polar axes P 1 and P 2 are assumed to be orthogonal to each other and the angle δ is the angle between the [100] axis and the polar z axes. Fig S5: Set of SHG polarisation measurements with the according fits (grey lines) based on the parameters from table T1. The angles ϕ ω and ϕ 2ω denote the polarisation of the incident fundamental and the emitted SHG light, respectively, with the [100] axis as reference axis (ϕ = 0). Panel a shows 5

6 an anisotropy measurement in which ϕ ω and ϕ 2ω are rotated simultaneously. Panel b shows a polarizer measurement in which ϕ ω is tuned and ϕ 2ω is kept constant. Panel c shows an analyzer measurement in which ϕ ω is kept constant and ϕ 2ω is tuned. Fig. S5 shows a complete set of SHG polarisation dependences with for a 20-nm SrMnO 3 film grown on LSAT. Based on our model, we find excellent agreement between all SHG polarisation dependences and their fits (grey lines), by using the fit parameters of table T1. Parameter Value Error (ϕ zzz ) 10.1 (0) - (ϕ xxz ) -3.2 (1.57) 0.2 (0.10) (ϕ zxx ) -3.9 (1.05) 0.2 (0.15) r = P 1 /P δ T1: Fit parameters for the SHG polarisation measurements in Fig. S5 for a 20-nm SrMnO 3 /LSAT film. Note that the fit of the angle δ reveals a value around 45, while a fit with a fixed value δ = 0 fails. This shows that the polar axes are oriented along the cyrstallographic in-plane <110> directions of the SrMnO 3 as predicted by DFT S3. Furthermore, independent of the SrMnO 3 /LSAT sample we investigated, all SHG polarisation measurements can be fitted with exactly the same fit parameters for the complex SHG susceptibilities as in table T1. Only the domain population ratio r = P 1 /P 2 needs to be adopted and the angle δ needs to be fine-tuned around 45. The small deviation from 45, which is also apparent in table T1, is caused by a slight misorientation of the sample on the sample mount. Electrostatic force microscopy as probe of local conductance: In electrostatic force microscopy (EFM), an AFM is used in non-contact mode and an AC voltage is applied to a conducting tip. Following the deviations from ref. S4, an AC voltage sin( ) leads to the electrostatic driving force F EL = sin( ) 1 4 cos(2 ). Here q and q i denote the charge on the sample surface and its image charge on the tip, respectively. C is the total capacitance of the tip-sample system and z is the tip-sample 6

7 distance. While the first two terms are frequency independent, the electrostatic interaction between tip and sample causes the cantilever to oscillate at Ω and 2Ω. The tip oscillation at Ω is induced by the static surface charge q. The tip oscillation at 2Ω is induced by the build-up of mirror charges given by the spatial derivative of the capacitance, which in particular contains the local conductance. For separating the simultaneously measured electrostatic response at Ω and 2Ω, we record the x-channel outputs of two lock-in amplifiers (SRS 830, Stanford Research). Fig. S6 shows the corresponding measurement scheme. Fig. S6: a, Contrast mechanisms for the Ω and 2Ω response of the EFM. b, Measurement scheme for EFM. The electrostatically induced tip oscillations at Ω and 2Ω are detected by two lock-in amplifiers that provide the information about fixed and mobile charges, respectively. For EFM calibration, we used a gold-sputtered glass substrate as reference sample. Figure S7 shows a calibration scan across the edge of the gold-sputtered region. To generate contrast in the static charges readout, we biased the gold with a positive voltage and adjusted the lock-in settings for maximum contrast with positive charge and high conductance corresponding to high brightness in Ω and 2Ω, respectively. 7

8 Fig S7: EFM calibration sample with glass (top) and gold surface (bottom). a, The Ω readout channel shows pronounced contrast as soon as the gold is biased by a DC voltage of V while the 2Ω channel probing the conductance (see b) remains unaffected. This proves that there is no crosstalk between the Ω and 2Ω readout channel. High brightness corresponds to positive charge and high conductance at Ω and 2Ω, respectively. All EFM experiments were carried out with a commercial scanning force microscope NTEGRA from NT-MDT with the scan parameters given in table T2: Tip Diamond-coated DCP 11 (tip radius ~ 50 nm) Ω ~ 34 khz U 0 ~ 7 V Tip-sample distance control: Magnitude setpoint (1-5)% of free magnitude Ω Res ~ 300 khz T2: Experimental parameters for non-contact EFM on the SrMnO 3 films. 8

9 Annealing experiments performed in different oxygen environments: In a series of annealing experiments we scrutinized our proposed relation between the presence of oxygen vacancies and the formation of the insulating polar domain walls. At first, we estimated the relation between the concentration of oxygen vacancies and the annealing conditions. Figure S8 shows the equilibrium concentration δ as a function of the oxygen partial pressure during annealing. We derived this relation by DFT, assuming an annealing temperature of 650 K and a tensile strain of 4% in the SrMnO 3-δ films. Because of the errors in the parameters entering the calculation and our neglect of oxygen exchange with the substrate we refrain from giving absolute values for δ but the qualitative dependence shown in Fig. S8 is independent of these effects. We find the δ is always nonzero and positive because, as mentioned earlier, both interstitial oxygen and the loss of strontium or manganese are energetically too costly so that δ = 0 poses an asymptotic lower threshold S5,S6. Oxygen vacancy concentration δ SrMnO 3-δ +4% strain 650 K Oxygen partial pressure (bar) Fig S8: Equilibrium concentration δ of oxygen vacancies in SrMnO 3-δ films for annealing cycles in different oxygen environments according to DFT. Calculations were done for an annealing temperature of 650 K and 4% tensile strain. Absolute values for δ are omitted as discussed above. In the next step, we annealed our samples at 620 K with different oxygen partial pressures. As in Fig. 2b the c-afm response reflects the local conductance of the film within its domains. Its increase can be directly associated with an increase in the density of oxygen vacancies as discussed, e.g., in ref

10 2 μm As-grown 200 bar O 2 1 bar O 2 0 bar O Film destroyed Fig S9: c-afm scans of the same region of a sample subjected to successive thermal annealing cycles. Annealing was done for 2 hours at 620 K. Note the oxygen partial pressure applied during annealing and the resulting change in the relative c-afm conductance (grey scales) measured as in Fig. 2b. Figure S9 shows the same region of a SrMnO 3 film before and after successive annealing cycles in oxygen partial pressures of 200 bar (pure O 2 ), 1 bar (pure O 2 ) and 0 bar (pure Ar at 1 bar). Compared to the as-grown film, annealing at 200 bar already increases the c-afm response and, hence, the related oxygen vacancy concentration. According to Fig. S8 this points to a rather low vacancy concentration in the as-grown film. Note, however, that even with a concentration as low as δ = 0.005, the number of oxygen vacancies in a domain of ~1 μm lateral extension is still sufficient to, in principle, place a vacancy in each unit cell of a polar domain wall of a few monolayers thickness. We can thus assume that in all our experiments the domain walls are saturated with vacancies Annealing in 1 bar O 2 increases the c-afm response/vacancy concentration further. Annealing at 0 bar O 2 destroys the film which manifests as drastic reconstruction in an AFM scan and a loss of the characteristic SHG signal indicating the polar state. According to Fig. S8 the equilibrium vacancy concentration increases steeply towards 0 bar and is thus in agreement with the observed disintegration of the film. Note that the rate of oxygen passing through the surface of the film depends logarithmically on the inverse temperature S6. Because of this, the films cannot adapt their oxygen vacancy concentration to the (lower) roomtemperature equilibrium value after the annealing. (NB: Since diffusion within the film and through the film surface are parameterized by different values they set in at different temperatures S6.) Figure S9 nicely shows the increase in the density of polar domain walls with increasing concentration of oxygen vacancies until the sample is destroyed by the oxygen depletion. If, for double-checking, the annealing is done such that the c-afm response/vacancy 10

11 concentration does not change further, the density of domain walls does not change either and the domains reappear at the same position as prior to this annealing cycle. It shows that, even though above T C the vacancies migrate away from the former domain walls according to Fig. 3b, some sort of memory effect prevails. It is possible that structural inhomogeneities like defects drive modulations in the oxygen vacancy distribution so that the two effects together promote the nucleation of domain walls which, once they have formed, attract more oxygen vacancies until they are saturated. Note that an increased density of oxygen vacancies in Fig. S9 always leads to additional domain walls but never to the deletion of previously existing walls which supports this coupled nucleation mechanism. References: [S1] Varela, M., Oxley, M. P., Luo, W., Tao, J., Watanabe, M., Lupini, A. R., Pantelides, S. T. & Pennycook, S. J. Atomic-resolution imaging of oxidation states in manganites, Phys. Rev. B 79, (2009) [S2] Birss, R. R., Symmetry and Magnetism. (North Holland, 1966). [S3] Lee, J. H. & Rabe, M. K. Epitaxial-Strain-Induced Multiferroicity in SrMnO 3 from First Principles, Phys. Rev. Lett. 104, (2010) [S4] Johann, F., Hoffmann, A. & Soergel, E. Impact of electrostatic forces in contact-mode scanning force microscopy, Phys. Rev. B 81, (2010) [S5] Merkle, R. How is oxygen incorporated into oxides? A comprehensive kinetic study of a simple solid state reaction with SrTiO 3 as a model material, Angew. Chem. Int. Ed. 47, (2008). [S6] Mizusaki, J., Mori, N., Takai, H., Yonemura, Y., Minamiue, H., Tagawa, H., Dokiya, M. & Inaba, H. Oxygen nonstoichiometry and defect equilibrium in the perovskite-type oxides La 1-x Sr x MnO 3+d, Solid State Ionics 129, (2000). [S7] De Souza, R. A. Oxygen transport in La 1-x Sr x Mn 1-y Co y O 3±δ perovskites. Part II. Oxygen surface exchange. Solid State Ionics 126, (1999). 11