Observation of the strain induced magnetic phase segregation in ...
Supporting Information:
Observation of the strain induced magnetic phase segregation in manganite thin films Lorena Marín†, ‡,§,∇, Luis A. Rodríguez†, ‡,||,⊥,∇, César Magén*,†, ‡,||,#, Etienne Snoeck||,⊥, Rémi Arras||,⊥, Irene Lucas†, ‡,#, Luis Morellón†, ‡, Pedro A. Algarabel‡,§, José M. De Teresa†, ‡,§,|| and M. Ricardo Ibarra†, ‡,|| †
Laboratorio de Microscopias Avanzadas (LMA), Instituto de Nanociencia de Aragón (INA), Universidad de Zaragoza, 50018 Zaragoza, Spain. ‡Departamento de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain. §
Instituto de Ciencia de Materiales de Aragón (ICMA), Universidad de Zaragoza, 50018 Zaragoza, Spain. ||
Transpyrenean Associated Laboratory for Electron Microscopy (TALEM), CEMES-INA, CNRS-Universidad de Zaragoza, Toulouse, France. ⊥
#
CEMES-CNRS 29, rue Jeanne Marvig, B.P. 94347 F-31055, Toulouse Cedex, France.
Fundación ARAID, 50018 Zaragoza, Spain.
∇ These authors have contributed equally to this work: Lorena Marín and Luis A. Rodríguez *Author to whom the correspondence should be addressed: César Magén ([email protected]), Tel: +34 876 555369, Fax: +34 976 762776.
1.
Thin Film Growth
Epitaxial La2/3Ca1/3MnO3 (LCMO) thin films were grown on 5×5 mm2 (100)-oriented SrTiO3 (STO), (LaAlO3)0.29–(Sr0.5Al0.5TaO3)0.71 (LSAT) and LaAlO3 (LAO) substrates by Pulsed Laser Deposition (PLD) using a KrF excimer laser (λ = 248 nm), with an oxygen pressure of 400 mTorr and a substrate temperature of 820 ºC. After deposition, full oxygen pressure was used to ensure the oxygen stoichiometry of the films. Different sets of samples were deposited changing the pulse frequency (2, 10 and 20 Hz) and ablation energy. 2.
Macroscopic Characterization
θ-2θ X-ray diffraction patterns around the (002) reflection of the substrate were carried out to evaluate the crystalline quality of the films. The analysis of the Laue fringes shown in Fig. 1(a) shows that the three specimens grown at 10 Hz in LSAT, STO and LAO gives rise to calculated thickness of 32, 33 and 32 nm, respectively, comparable to the actual thickness of 43 nm. These values demonstrate that the three films have very similar crystal quality and thus it cannot be responsible for other structural and magnetic discrepancies between them. The same calculation for the sample grown on STO at 2 Hz (different batch) gives 43 nm. In addition to the information displayed in the main text, we show in Figure S1 the reciprocal space map of the LCMO film grown on STO at 10 Hz, the one presenting the NFL layer. Magnetization measurements were performed in a Superconducting Quantum Interference Device (SQUID) from Quantum Design in magnetic fields up to 5 T. In the Zero-Field and Field Cooling (ZFC and FC) experiments, the sample was cooled down at a rate of 1 K/min down to 10 K. Once the temperature is stabilized, hysteresis loops were carried out by sweeping the magnetic field between -50 to +50 kOe (saturation fields), applying it parallel to the film surface. While ZFC ramps were carried out without applying a magnetic field, in FC a fixed magnetic field was applied at room temperature, where LCMO presents a paramagnetic state, and maintained it during the cooling process.
Figure S1. Reciprocal space map of the (013) reflection of the LCMO film grown on STO at 10 Hz. Qx and Qz are the reciprocal vector components parallel to [010] and [001] directions, respectively. The lower reflection corresponds to the STO substrate and the upper one to the LCMO thin film.
3.
Transmission Electron Microscopy (TEM)
TEM was carried out in lamellas prepared by Focused Ion Beam (FIB) in an FEI Helios Nanolab. Structural and chemical nanocharacterization was performed in Scanning Transmission Electron Microscopy (STEM) mode by High Angle Annular Dark Field (HAADF) and Electron Energy-Loss Spectroscopy (EELS) in an FEI Titan 60-300 microscope operated at 300 kV and equipped with a high brightness gun (X-FEG) and probe aberration corrector from CEOS to provide a point resolution below 1Å. 3.1
Local structural and chemical characterization of LCMO on STO (100).
STEM-EELS characterization was carried out to certify that there is no significant local variation of the structural and chemical properties that might be responsible for the formation of a NFL in strained LCMO. To illustrate this point, a complete analysis performed in LCMO grown on STO (100) with and without NFL.
HAADF-STEM imaging was carried out with a convergence angle of 25 mrad that provides a probe size below 1 Å. HAADF detector inner angle was 58 mrad. Figure S2(a) shows the HAADF image of a LCMO layer grown on STO (100) at a laser frequency of 10 Hz, presenting a NFL in the top surface. Geometrical Phase Analysis (GPA)1 has been applied to determine the variation of the lattice parameters of the LCMO film with respect to the STO substrate in order to identify possible strain relaxations responsible for the appearance of the NFL. Figure S2(b) shows the variation of the in-plane lattice parameter of the films (εxx) with respect to the substrate, which confirms that the film is fully strained all over the sample thickness. The out of plane lattice parameter is also uniform along the film. As can be observed in Fig. S3, the value of the tetragonality εxx = (c-a)/a = -1.6 ± 0.2 is comparable and a bit inferior to the one determined by x-rays diffraction. The discrepancy could be associated to a slightly different sample drift when the beam irradiates the film (conductor) and the substrate (an insulator).
Figure S2. a) HAADF-STEM image of LCMO//STO (100) grown at 10 Hz presenting NFL. b) In-plane (εxx) and c) out-of-plane (εzz) deformation state of the LCMO film with respect to the STO substrate determined by GPA.
STEM-EELS spectrum lines were acquired to explore the chemical composition of LCMO films with NFL and the local Mn oxidation states in order to discard possible chemical inhomogeneities or difference in the chemical composition of the FM layer and the NFL. All these experiments were carried out in the probe corrected Titan described above, which is also equipped with a Gatan Energy Filter Tridiem 866 ERS for spectroscopy and image filtering.
Figure S3. Line profiles of εxx and εzz from Figure S1 showing the homogeneity of the strain state both in-plane and out-of-plane through the whole sample thickness. Signal to noise ratio has been improved by horizontal integration of 500 pixels.
Line profiles to determine the chemical composition were carried out in with an energy dispersion of 0.5 eV, an acquisition time of 0.1 s, a collection angle of 60 mrads, and a beam current of ~350 pA. Figure S4 depicts a profile of relative compositions of La, Ca, Mn and O obtained along a direction perpendicular to the substrate/film interface. The analysis was carried out in the same specimen used for electron holography to allow a direct comparison. Edge signal integration was calculated following the standard procedures of background subtraction and intensity integration implemented in the DigitalMicrographTM software package. Within the experimental accuracy of the technique, there is no significant change of composition along the film thickness. It is noteworthy that the anomaly observed in the last 4 nm at the surface of the LCMO film, much smaller than the extent of the NFL, is likely to be a artifact related to FIB specimen preparation due to beam damage and protective Pt re-deposition during milling which perturbs the chemical quantification at the very surface of the film.
Figure S4. Profile of relative chemical composition determined from a STEM-EELS spectrum line of the sample LCMO//STO (100) at 10 Hz.
Mn oxidation state was determined in spectrum lines at a dispersion of 0.1 eV, acquisition time of 1 s, a collection angle of 47 mrad and a beam current of ~250 pA. We followed the procedure developed by Varela et al.2 for the LaxCa1-xMnO3 based on the energy difference between the main peak of the O K edge and the prepeak related to the hybridization of Mn and O orbitals. A change in the Mn oxidation state would be the signature of lack of stoichiometry of the sample, either by the presence of oxygen vacancies or off-stoichiometry of the cations. Figure S5 shows a comparison of the estimated Mn oxidation state with the relative composition of Mn and O extracted from the O K and the Mn L2,3 edges from the same spectrum line. Again, the oxidation state is very uniform all along the layer. Furthermore, the coincidence of the estimated oxidation state and the nominal one is remarkably good, +3.34 ± 0.01, where the error bar is the standard deviation upon integration of the value along the whole layer. Similarly to the chemical quantification in Fig. S4, the profile of the Mn oxidation state presents an anomaly in the last 2 nm at the surface of the LCMO film, which can be easily attributed to surface beam damage during FIB preparation. Thus, this is further indication that not only the chemical composition is uniform along the layer, but also
the whole stoichiometry is close to nominal. This confirms that the discrepancy in the quantification obtained from STEM-EELS profiles are due to artifacts related to specimen thickness.
Figure S5. Line profile of Mn oxidation state estimated from the O K edge acquired from STEM-EELS spectrum line of the sample LCMO//STO (100) at 10 Hz.
4.
Off-axis Electron Holography (EH).
EH was performed in an image-corrected FEI Titan Cube 60-300 microscope equipped with a Lorentz lens for imaging in field-free conditions, which is integrated in the image corrector from CEOS. Since LCMO is paramagnetic at room temperature (with a Curie temperature TC~160 K), EH experiments were carried out at 100 K using a TEM cryoholder cooled with liquid nitrogen to ensure the ferromagnetic state of the LCMO film. 4.1
Introduction to EH. EH is a TEM-based technique that allows extracting the
phase shift of the electron wave when it passes through the sample3-8. The electron phase shift is related to important physical parameters of the sample, such as the electrostatic potential, the magnetic induction or strain fields5,6. Therefore, EH provides local quantitative information of the magnetic fields created by magnetic specimens with a high spatial resolution, in the case of magnetic fields down to few nm.
In the case of a ferromagnetic material, the phase shift of the electron wave that can be expressed as8: ϕ ( x, y) = C E ∫ V ( x, y, z )dz −
e B⊥ ( x, y, z )dxdydz =ϕ E ( x, y ) + ϕ M ( x, y ) ! ∫∫
(1)
where z is the direction of the electron beam trajectory (optical axis), and perpendicular to x and y directions, CE is an interaction constant (CE = 6.53 × 106 rads V-1 m-1 for 300 kV), e is the electron charge, ħ is the reduced Planck constant, V is the electrostatic potential and B⊥ is the magnetic induction component orthogonal to x,y unitary vector. From Eq. 1, it is clear that the phase shift can be expressed as a sum of two phase shift contributions where the first term is related with the electrostatic potential (ϕE), and the second one with the magnetic potential (ϕM). A qualitative description can be easily made if we calculate the gradient of the phase shift, considering that V(x,y,z) is constant for each material. Thus:
∇ϕ ( x, y ) = ∇ϕ E ( x, y ) + ∇ϕ M ( x, y ) = C EVmip t ( x, y ) −
e B⊥ ( x, y )t ( x, y ) !
(2)
where Vmip is the mean inner potential of each materials and t(x,y) is the sample thickness. The sketch shown in Figure S6 illustrates how would be the behavior of ϕE and ϕM for the case of the cross sectional TEM specimen of a ferromagnetic LCMO thin film where its magnetization is aligned parallel to the interface with the substrate. We have assumed that the specimen has a uniform thickness variation perpendicular to the interfaces. A phase profile shows that the magnetic phase shift follows an increasing linear variation with the distance (y) only inside the ferromagnetic layer. Non-magnetic layers or the substrate will show a flat dependence. In Equation 2 we can see how this linear variation is proportional to the perpendicular magnetic component of the in-plane induction (Bx). On the other hand, the electrostatic phase shift will always exhibit a nonzero slope, with different slope values for each layer. The variations of the electrostatic phase shift are proportional to Vmip·t.
z Magnetic layer
Resine or Pt
Substrate
Coordinate axis y x t
j j
M
∂ φM ∝ Bx ∂y Vmip·t
E
t y
Figure S6. Schematic illustration of EH profiles for electrostatic (ϕE) and magnetic (ϕM) phase shifts in our system.
In our case, LCMO is paramagnetic at room temperature, so the electrostatic phase shift related to the mean inner potential was extracted from holograms collected at room temperature. Then, this contribution was subtracted from the phase shifts obtained from holograms collected at 100 K, below TC, which contains both electrostatic and magnetic phase shifts. 5.
Theoretical Methods
First principle calculations were carried out based on the density functional theory + U (DFT+U) method. We used the full-potential linearized augmented plane waves code Wien2K9 with the GGA-PBE approximation10. The fully-localized and rotationally invariant Ueff-dependent (Ueff = U – J) correction11,12 was applied on the 3d orbitals of Mn atoms and 4f orbitals of La atoms, with the respective values of Ueff(Mn, 3d) = 2 eV and Ueff(La, 4f) = 7 eV. We used a 2√2×2√2×2 supercell containing 16 formula units of La0.375Ca0.625MnO3. We chose a distribution of La and Ca cations leading to the space group 6-Pm (according to the Bilbao crystallographic server13). We fixed the in-plane lattice parameters to 3.8 or 3.9 Å, these values are respectively close to the experimental lattice parameters of LaAlO3 (3.791 Å) and SrTiO3 (3.905 Å), and performed different calculations for different out-of-plane parameters. 4 magnetic orderings have been envisaged: FM, and AX-type, AZ-type, or C-type AFM. In each case, we performed a full relaxation of internal atomic coordinates. The irreducible part of the first Brillouin zone was sampled with 8 k-points. Ax and C-type AFM orderings correspond to inplane AFM orderings, respectively along the [100] and [110] directions; Az-type AFM is oriented along the out-of-plane [001] direction.
5.1
DFT+U calculations on LAO substrate.
In addition to the results shown in the main manuscript, DFT+U calculations have also been carried out for a = 3.8 Å, equivalent to the in-plane compressive strain induced by LAO with the corresponding increase of c. The same procedure as in the case of a = 3.9 Å (STO substrate) has been followed. These results are summarized in Figure S7. For a tetragonality as high as 0.125 the FM ordering remains the most stable. Above τ = 0.075, the total energy difference between the FM and the Ax-AFM ordering is lower than 11.6 meV/f.u., which also suggests that both phase can also coexist. Our results also confirm that such tendencies are accompanied by a change in the egbands occupation due to the tetragonal distortion, favoring the occupation of the dx2-y2 bands for c/a < 1, with an increase by 12.5% of the d-eg orbitals averaged occupation to the detriment of the d3z2-r2 bands (for τ = 0.1), and the reverse for c/a > 1.
Figure S7. Energy variation of LCMO determined from first-principles calculations for different magnetic orderings as a function of the tetragonality and for a fixed in-plane lattice parameter equal to that of the LAO substrate.
It is worth noting that, for a lattice parameter ratio c/a > 1, the transition is generally considered in the literature to occur between FM and the C-type AFM ordering, whereas our calculations suggests that the Ax-AFM ordering is the most stable. This is however in agreement with the results of Colizzi et al.14, who also found a strong competition between these three orderings in LSMO. A direct comparison with previous works on other manganites is however complicated for several reasons. The different magnetic transitions certainly depend closely on atomic structure distortions (i.e. oxygen octahedral tilts) which can be affected by the nature and the distribution of the
cations on the A position of the perovskites. The calculation parameters for the use of GGA+U methods can also result in some slight quantitative differences comparing to the experimental measurements15. Supposing that the suitable c/a ratio can be stabilized, our calculations however demonstrates clearly that, due to very similar energy stability, the coexistence of FM and AFM phases is plausible for sufficiently high tetragonality for both c/a < 1 or > 1 and may be observed experimentally for both a = 3.8 and 3.9 Å. The tetragonality at which one of these transitions will happen can be non-universal and would also certainly depend on the lattice mismatch with the substrate.
References 1.
Hÿtch, M. J.; Snoeck, E.; Kilaas, R. Ultramicroscopy 1998, 74, 131.
2.
Varela, M. et al. Phys. Rev. B 2009, 79, 085117.
3.
Midgley, P. Micron 2001, 32, 167.
4.
Shindo, D.; Murakami, Y. J. Phys. D. Appl. Phys. 2008, 41, 183002.
5.
McCartney, M. R.; Smith, D. J. Annu. Rev. Mater. Res. 2007, 37, 729.
6.
Lichte, H.; Lehmann, M. Reports Prog. Phys. 2008, 71, 016102.
7.
Dunin-Borkowski, R. E. et al. Microsc. Res. Tech. 2004, 64, 390.
8.
Tonomura A. Am. Phys. Soc. 1987, 59, 639.
9.
Blaha P.; Schwarz K.; Madsen G. K. H.; Kvasnicka D.; Luitz J. WIEN2k, An Augmented Plane Wave + Local Orbitals program for calculating crystal properties, 2001 Karlheinz Schwarz, Techn. Universität Wien, Austria.
10.
Perdew, J. P.; Burke K.; Ernzerhof M. Phys. Rev. Lett. 1997, 78, 1396.
11.
Anisimov, V. I.; Solovyev, I. V; Korotin, M. A.; Czyżyk, M. T.; Sawatzky, G. A. Phys. Rev. B 1993 48, 16929.
12.
Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J. Phys. Rev. B 1995, 52, R5467.
13.
Aroyo, M. I.; Kirov, A.; Capillas, C.; Perez-Mato, J. M.; Wondratschek, H. Acta Crystallogr. A. 2006, 62, 115.
14.
Colizzi, G.; Filippetti, A.; Cossu, F.; Fiorentini, V. Phys. Rev. B 2008, 78, 235122 (2008).
15.
Chen, H.; Ismail-Beigi, S. Phys. Rev. B 2012, 86, 24433.
Observation of the strain induced magnetic phase segregation in manganite thin films Lorena Marín†, ‡,§,∇, Luis A. Rodríguez†, ‡,||,⊥,∇, César Magén*,†, ‡,||,#, Etienne Snoeck||,⊥, Rémi Arras||,⊥, Irene Lucas†, ‡,#, Luis Morellón†, ‡, Pedro A. Algarabel‡,§, José M. De Teresa†, ‡,§,|| and M. Ricardo Ibarra†, ‡,|| †
Laboratorio de Microscopias Avanzadas (LMA), Instituto de Nanociencia de Aragón (INA), Universidad de Zaragoza, 50018 Zaragoza, Spain. ‡Departamento de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain. §
Instituto de Ciencia de Materiales de Aragón (ICMA), Universidad de Zaragoza, 50018 Zaragoza, Spain. ||
Transpyrenean Associated Laboratory for Electron Microscopy (TALEM), CEMES-INA, CNRS-Universidad de Zaragoza, Toulouse, France. ⊥
#
CEMES-CNRS 29, rue Jeanne Marvig, B.P. 94347 F-31055, Toulouse Cedex, France.
Fundación ARAID, 50018 Zaragoza, Spain.
∇ These authors have contributed equally to this work: Lorena Marín and Luis A. Rodríguez *Author to whom the correspondence should be addressed: César Magén ([email protected]), Tel: +34 876 555369, Fax: +34 976 762776.
1.
Thin Film Growth
Epitaxial La2/3Ca1/3MnO3 (LCMO) thin films were grown on 5×5 mm2 (100)-oriented SrTiO3 (STO), (LaAlO3)0.29–(Sr0.5Al0.5TaO3)0.71 (LSAT) and LaAlO3 (LAO) substrates by Pulsed Laser Deposition (PLD) using a KrF excimer laser (λ = 248 nm), with an oxygen pressure of 400 mTorr and a substrate temperature of 820 ºC. After deposition, full oxygen pressure was used to ensure the oxygen stoichiometry of the films. Different sets of samples were deposited changing the pulse frequency (2, 10 and 20 Hz) and ablation energy. 2.
Macroscopic Characterization
θ-2θ X-ray diffraction patterns around the (002) reflection of the substrate were carried out to evaluate the crystalline quality of the films. The analysis of the Laue fringes shown in Fig. 1(a) shows that the three specimens grown at 10 Hz in LSAT, STO and LAO gives rise to calculated thickness of 32, 33 and 32 nm, respectively, comparable to the actual thickness of 43 nm. These values demonstrate that the three films have very similar crystal quality and thus it cannot be responsible for other structural and magnetic discrepancies between them. The same calculation for the sample grown on STO at 2 Hz (different batch) gives 43 nm. In addition to the information displayed in the main text, we show in Figure S1 the reciprocal space map of the LCMO film grown on STO at 10 Hz, the one presenting the NFL layer. Magnetization measurements were performed in a Superconducting Quantum Interference Device (SQUID) from Quantum Design in magnetic fields up to 5 T. In the Zero-Field and Field Cooling (ZFC and FC) experiments, the sample was cooled down at a rate of 1 K/min down to 10 K. Once the temperature is stabilized, hysteresis loops were carried out by sweeping the magnetic field between -50 to +50 kOe (saturation fields), applying it parallel to the film surface. While ZFC ramps were carried out without applying a magnetic field, in FC a fixed magnetic field was applied at room temperature, where LCMO presents a paramagnetic state, and maintained it during the cooling process.
Figure S1. Reciprocal space map of the (013) reflection of the LCMO film grown on STO at 10 Hz. Qx and Qz are the reciprocal vector components parallel to [010] and [001] directions, respectively. The lower reflection corresponds to the STO substrate and the upper one to the LCMO thin film.
3.
Transmission Electron Microscopy (TEM)
TEM was carried out in lamellas prepared by Focused Ion Beam (FIB) in an FEI Helios Nanolab. Structural and chemical nanocharacterization was performed in Scanning Transmission Electron Microscopy (STEM) mode by High Angle Annular Dark Field (HAADF) and Electron Energy-Loss Spectroscopy (EELS) in an FEI Titan 60-300 microscope operated at 300 kV and equipped with a high brightness gun (X-FEG) and probe aberration corrector from CEOS to provide a point resolution below 1Å. 3.1
Local structural and chemical characterization of LCMO on STO (100).
STEM-EELS characterization was carried out to certify that there is no significant local variation of the structural and chemical properties that might be responsible for the formation of a NFL in strained LCMO. To illustrate this point, a complete analysis performed in LCMO grown on STO (100) with and without NFL.
HAADF-STEM imaging was carried out with a convergence angle of 25 mrad that provides a probe size below 1 Å. HAADF detector inner angle was 58 mrad. Figure S2(a) shows the HAADF image of a LCMO layer grown on STO (100) at a laser frequency of 10 Hz, presenting a NFL in the top surface. Geometrical Phase Analysis (GPA)1 has been applied to determine the variation of the lattice parameters of the LCMO film with respect to the STO substrate in order to identify possible strain relaxations responsible for the appearance of the NFL. Figure S2(b) shows the variation of the in-plane lattice parameter of the films (εxx) with respect to the substrate, which confirms that the film is fully strained all over the sample thickness. The out of plane lattice parameter is also uniform along the film. As can be observed in Fig. S3, the value of the tetragonality εxx = (c-a)/a = -1.6 ± 0.2 is comparable and a bit inferior to the one determined by x-rays diffraction. The discrepancy could be associated to a slightly different sample drift when the beam irradiates the film (conductor) and the substrate (an insulator).
Figure S2. a) HAADF-STEM image of LCMO//STO (100) grown at 10 Hz presenting NFL. b) In-plane (εxx) and c) out-of-plane (εzz) deformation state of the LCMO film with respect to the STO substrate determined by GPA.
STEM-EELS spectrum lines were acquired to explore the chemical composition of LCMO films with NFL and the local Mn oxidation states in order to discard possible chemical inhomogeneities or difference in the chemical composition of the FM layer and the NFL. All these experiments were carried out in the probe corrected Titan described above, which is also equipped with a Gatan Energy Filter Tridiem 866 ERS for spectroscopy and image filtering.
Figure S3. Line profiles of εxx and εzz from Figure S1 showing the homogeneity of the strain state both in-plane and out-of-plane through the whole sample thickness. Signal to noise ratio has been improved by horizontal integration of 500 pixels.
Line profiles to determine the chemical composition were carried out in with an energy dispersion of 0.5 eV, an acquisition time of 0.1 s, a collection angle of 60 mrads, and a beam current of ~350 pA. Figure S4 depicts a profile of relative compositions of La, Ca, Mn and O obtained along a direction perpendicular to the substrate/film interface. The analysis was carried out in the same specimen used for electron holography to allow a direct comparison. Edge signal integration was calculated following the standard procedures of background subtraction and intensity integration implemented in the DigitalMicrographTM software package. Within the experimental accuracy of the technique, there is no significant change of composition along the film thickness. It is noteworthy that the anomaly observed in the last 4 nm at the surface of the LCMO film, much smaller than the extent of the NFL, is likely to be a artifact related to FIB specimen preparation due to beam damage and protective Pt re-deposition during milling which perturbs the chemical quantification at the very surface of the film.
Figure S4. Profile of relative chemical composition determined from a STEM-EELS spectrum line of the sample LCMO//STO (100) at 10 Hz.
Mn oxidation state was determined in spectrum lines at a dispersion of 0.1 eV, acquisition time of 1 s, a collection angle of 47 mrad and a beam current of ~250 pA. We followed the procedure developed by Varela et al.2 for the LaxCa1-xMnO3 based on the energy difference between the main peak of the O K edge and the prepeak related to the hybridization of Mn and O orbitals. A change in the Mn oxidation state would be the signature of lack of stoichiometry of the sample, either by the presence of oxygen vacancies or off-stoichiometry of the cations. Figure S5 shows a comparison of the estimated Mn oxidation state with the relative composition of Mn and O extracted from the O K and the Mn L2,3 edges from the same spectrum line. Again, the oxidation state is very uniform all along the layer. Furthermore, the coincidence of the estimated oxidation state and the nominal one is remarkably good, +3.34 ± 0.01, where the error bar is the standard deviation upon integration of the value along the whole layer. Similarly to the chemical quantification in Fig. S4, the profile of the Mn oxidation state presents an anomaly in the last 2 nm at the surface of the LCMO film, which can be easily attributed to surface beam damage during FIB preparation. Thus, this is further indication that not only the chemical composition is uniform along the layer, but also
the whole stoichiometry is close to nominal. This confirms that the discrepancy in the quantification obtained from STEM-EELS profiles are due to artifacts related to specimen thickness.
Figure S5. Line profile of Mn oxidation state estimated from the O K edge acquired from STEM-EELS spectrum line of the sample LCMO//STO (100) at 10 Hz.
4.
Off-axis Electron Holography (EH).
EH was performed in an image-corrected FEI Titan Cube 60-300 microscope equipped with a Lorentz lens for imaging in field-free conditions, which is integrated in the image corrector from CEOS. Since LCMO is paramagnetic at room temperature (with a Curie temperature TC~160 K), EH experiments were carried out at 100 K using a TEM cryoholder cooled with liquid nitrogen to ensure the ferromagnetic state of the LCMO film. 4.1
Introduction to EH. EH is a TEM-based technique that allows extracting the
phase shift of the electron wave when it passes through the sample3-8. The electron phase shift is related to important physical parameters of the sample, such as the electrostatic potential, the magnetic induction or strain fields5,6. Therefore, EH provides local quantitative information of the magnetic fields created by magnetic specimens with a high spatial resolution, in the case of magnetic fields down to few nm.
In the case of a ferromagnetic material, the phase shift of the electron wave that can be expressed as8: ϕ ( x, y) = C E ∫ V ( x, y, z )dz −
e B⊥ ( x, y, z )dxdydz =ϕ E ( x, y ) + ϕ M ( x, y ) ! ∫∫
(1)
where z is the direction of the electron beam trajectory (optical axis), and perpendicular to x and y directions, CE is an interaction constant (CE = 6.53 × 106 rads V-1 m-1 for 300 kV), e is the electron charge, ħ is the reduced Planck constant, V is the electrostatic potential and B⊥ is the magnetic induction component orthogonal to x,y unitary vector. From Eq. 1, it is clear that the phase shift can be expressed as a sum of two phase shift contributions where the first term is related with the electrostatic potential (ϕE), and the second one with the magnetic potential (ϕM). A qualitative description can be easily made if we calculate the gradient of the phase shift, considering that V(x,y,z) is constant for each material. Thus:
∇ϕ ( x, y ) = ∇ϕ E ( x, y ) + ∇ϕ M ( x, y ) = C EVmip t ( x, y ) −
e B⊥ ( x, y )t ( x, y ) !
(2)
where Vmip is the mean inner potential of each materials and t(x,y) is the sample thickness. The sketch shown in Figure S6 illustrates how would be the behavior of ϕE and ϕM for the case of the cross sectional TEM specimen of a ferromagnetic LCMO thin film where its magnetization is aligned parallel to the interface with the substrate. We have assumed that the specimen has a uniform thickness variation perpendicular to the interfaces. A phase profile shows that the magnetic phase shift follows an increasing linear variation with the distance (y) only inside the ferromagnetic layer. Non-magnetic layers or the substrate will show a flat dependence. In Equation 2 we can see how this linear variation is proportional to the perpendicular magnetic component of the in-plane induction (Bx). On the other hand, the electrostatic phase shift will always exhibit a nonzero slope, with different slope values for each layer. The variations of the electrostatic phase shift are proportional to Vmip·t.
z Magnetic layer
Resine or Pt
Substrate
Coordinate axis y x t
j j
M
∂ φM ∝ Bx ∂y Vmip·t
E
t y
Figure S6. Schematic illustration of EH profiles for electrostatic (ϕE) and magnetic (ϕM) phase shifts in our system.
In our case, LCMO is paramagnetic at room temperature, so the electrostatic phase shift related to the mean inner potential was extracted from holograms collected at room temperature. Then, this contribution was subtracted from the phase shifts obtained from holograms collected at 100 K, below TC, which contains both electrostatic and magnetic phase shifts. 5.
Theoretical Methods
First principle calculations were carried out based on the density functional theory + U (DFT+U) method. We used the full-potential linearized augmented plane waves code Wien2K9 with the GGA-PBE approximation10. The fully-localized and rotationally invariant Ueff-dependent (Ueff = U – J) correction11,12 was applied on the 3d orbitals of Mn atoms and 4f orbitals of La atoms, with the respective values of Ueff(Mn, 3d) = 2 eV and Ueff(La, 4f) = 7 eV. We used a 2√2×2√2×2 supercell containing 16 formula units of La0.375Ca0.625MnO3. We chose a distribution of La and Ca cations leading to the space group 6-Pm (according to the Bilbao crystallographic server13). We fixed the in-plane lattice parameters to 3.8 or 3.9 Å, these values are respectively close to the experimental lattice parameters of LaAlO3 (3.791 Å) and SrTiO3 (3.905 Å), and performed different calculations for different out-of-plane parameters. 4 magnetic orderings have been envisaged: FM, and AX-type, AZ-type, or C-type AFM. In each case, we performed a full relaxation of internal atomic coordinates. The irreducible part of the first Brillouin zone was sampled with 8 k-points. Ax and C-type AFM orderings correspond to inplane AFM orderings, respectively along the [100] and [110] directions; Az-type AFM is oriented along the out-of-plane [001] direction.
5.1
DFT+U calculations on LAO substrate.
In addition to the results shown in the main manuscript, DFT+U calculations have also been carried out for a = 3.8 Å, equivalent to the in-plane compressive strain induced by LAO with the corresponding increase of c. The same procedure as in the case of a = 3.9 Å (STO substrate) has been followed. These results are summarized in Figure S7. For a tetragonality as high as 0.125 the FM ordering remains the most stable. Above τ = 0.075, the total energy difference between the FM and the Ax-AFM ordering is lower than 11.6 meV/f.u., which also suggests that both phase can also coexist. Our results also confirm that such tendencies are accompanied by a change in the egbands occupation due to the tetragonal distortion, favoring the occupation of the dx2-y2 bands for c/a < 1, with an increase by 12.5% of the d-eg orbitals averaged occupation to the detriment of the d3z2-r2 bands (for τ = 0.1), and the reverse for c/a > 1.
Figure S7. Energy variation of LCMO determined from first-principles calculations for different magnetic orderings as a function of the tetragonality and for a fixed in-plane lattice parameter equal to that of the LAO substrate.
It is worth noting that, for a lattice parameter ratio c/a > 1, the transition is generally considered in the literature to occur between FM and the C-type AFM ordering, whereas our calculations suggests that the Ax-AFM ordering is the most stable. This is however in agreement with the results of Colizzi et al.14, who also found a strong competition between these three orderings in LSMO. A direct comparison with previous works on other manganites is however complicated for several reasons. The different magnetic transitions certainly depend closely on atomic structure distortions (i.e. oxygen octahedral tilts) which can be affected by the nature and the distribution of the
cations on the A position of the perovskites. The calculation parameters for the use of GGA+U methods can also result in some slight quantitative differences comparing to the experimental measurements15. Supposing that the suitable c/a ratio can be stabilized, our calculations however demonstrates clearly that, due to very similar energy stability, the coexistence of FM and AFM phases is plausible for sufficiently high tetragonality for both c/a < 1 or > 1 and may be observed experimentally for both a = 3.8 and 3.9 Å. The tetragonality at which one of these transitions will happen can be non-universal and would also certainly depend on the lattice mismatch with the substrate.
References 1.
Hÿtch, M. J.; Snoeck, E.; Kilaas, R. Ultramicroscopy 1998, 74, 131.
2.
Varela, M. et al. Phys. Rev. B 2009, 79, 085117.
3.
Midgley, P. Micron 2001, 32, 167.
4.
Shindo, D.; Murakami, Y. J. Phys. D. Appl. Phys. 2008, 41, 183002.
5.
McCartney, M. R.; Smith, D. J. Annu. Rev. Mater. Res. 2007, 37, 729.
6.
Lichte, H.; Lehmann, M. Reports Prog. Phys. 2008, 71, 016102.
7.
Dunin-Borkowski, R. E. et al. Microsc. Res. Tech. 2004, 64, 390.
8.
Tonomura A. Am. Phys. Soc. 1987, 59, 639.
9.
Blaha P.; Schwarz K.; Madsen G. K. H.; Kvasnicka D.; Luitz J. WIEN2k, An Augmented Plane Wave + Local Orbitals program for calculating crystal properties, 2001 Karlheinz Schwarz, Techn. Universität Wien, Austria.
10.
Perdew, J. P.; Burke K.; Ernzerhof M. Phys. Rev. Lett. 1997, 78, 1396.
11.
Anisimov, V. I.; Solovyev, I. V; Korotin, M. A.; Czyżyk, M. T.; Sawatzky, G. A. Phys. Rev. B 1993 48, 16929.
12.
Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J. Phys. Rev. B 1995, 52, R5467.
13.
Aroyo, M. I.; Kirov, A.; Capillas, C.; Perez-Mato, J. M.; Wondratschek, H. Acta Crystallogr. A. 2006, 62, 115.
14.
Colizzi, G.; Filippetti, A.; Cossu, F.; Fiorentini, V. Phys. Rev. B 2008, 78, 235122 (2008).
15.
Chen, H.; Ismail-Beigi, S. Phys. Rev. B 2012, 86, 24433.
