Supplementary material for:
Structural phases driven by oxygen vacancies at the La0.7Sr0.3MnO3/SrTiO3 hetero-interface
M. Nord1, P.E. Vullum1,2, M. Moreau3, J.E. Boschker3, S.M. Selbach4, R. Holmestad1 and T. Tybell3, a)
1 Department of Physics, NTNU, Trondheim, Norway
2 Materials and Chemistry, SINTEF, Trondheim, Norway,
3 Department of Electronics and Telecommunications, NTNU, Trondheim, Norway
4 Department of Materials Science and Engineering, NTNU, Trondheim, Norway
a)Corresponding author: (e-mail)
The DFT (Density Functional Theory) calculations were done with the Projector Augmented Wave (PAW)1,2method as implemented in the Vienna Ab-initio Simulation Package (VASP),3-6 with the PBEsol functional7 with a GGA + U approximation.8,9 PAWpotentials treating 11 valence electrons for La (4s24p65d16s2), 10 for Sr (4s24p65s2), 15 for Mn (3s23p63d54s2) and 6 for O (2s22p4) were used. A Hubbard U correction of 3 eV was applied to the Mn 3d electrons, as this approach has previously well described a ternary manganese oxide with oxygen vacancies,10 while a Hubbard U of 10 eV was applied to the La 4f orbital to move these orbitals away from the Fermilevel.11 A cutoff energy of 550 eV was used for the plane wave basis set. A 36 atom La6Sr2Mn8O20 unit cell with a 6x6x2 gamma-centered k-point mesh for Brillouin zone integration was used for the calculations of the oxygen deficient LSMO unit cells. An initial ferromagnetic spin ordering was assumed. The unit cells for the four disordered structures are shown in Figure S1, while the three unit cells of the ordered structures are shown in Figure S2. The different structures have different ordering of the oxygen vacancies, in the ordered structures there are double vacancies in every second Mn layer, while in the disordered structures there are a single vacancy in every Mn layer. In order to take into account the strain imposed by the 001 SrTiO3 substrate the in plane lattice constants were fixed to the equilibrium lattice constant calculated for cubic SrTiO3 with the PBEsol functional, 550 eV cutoff energy, a 6x6x6gamma-centered k-mesh and Sr_sv, Ti_sv (12 valence electrons: 3s23p64s23d2) and O PAW-potentials supplied with VASP. The internal coordinates of the ions and the out of plane lattice constant was allowed to relax until the Hellmann-Feynman forces on the ions were below 0.01 eV/Å . The calculated out-of-plane lattice parameter and all atom positions are shown in Table SI.
Figure S1: The 36 atom unit cells of the disordered structures investigated. The different structures have different oxygen vacancy ordering. Dark green: La, light green: Sr, purple: Mn, red: O.
Figure S2:The 36 atom unit cells of the ordered structures investigated. The different structures have different oxygen vacancy ordering. Dark green: La, light green: Sr, purple: Mn, red: O.
Table SI: Calculated out-of-plane lattice parameter and atomic positions for the vacancy structures investigated. Empty cells correspond to the location of the vacancies.
ORDER A / ORDER B / ORDER C / DISORDER A / DISORDER B / DISORDER C / DISORDER Dc / 16,512 / 16,48 / 16,556 / 15,841 / 15,841 / 15,713 / 15,799
La (1) / (0.494,0.004,0.889) / (0.505,0.012,0.889) / (0.496,0.015,0.890) / (0.497,0.990,0.882) / (0.504,0.995,0.877) / (0.514,0.991,0.872) / (0.515,0.970,0.877)
La (2) / (0.508,0.982,0.111) / (0.490,0.987,0.112) / (0.513,0.020,0.111) / (0.510,0.991,0.122) / (0.503,0.997,0.127) / (0.520,0.997,0.116) / (0.521,0.988,0.128)
La (3) / (0.997,0.480,0.890) / (0.996,0.490,0.891) / (0.011,0.491,0.892) / (0.995,0.507,0.880) / (0.005,0.492,0.866) / (0.986,0.509,0.878) / (0.978,0.473,0.872)
La (4) / (0.502,0.982,0.392) / (0.504,0.990,0.391) / (0.494,0.008,0.392) / (0.505,0.990,0.363) / (0.488,0.008,0.366) / (0.518,0.996,0.369) / (0.485,0.999,0.366)
La (5) / (0.979,0.496,0.389) / (0.995,0.512,0.389) / (0.009,0.485,0.390) / (0.011,0.504,0.371) / (0.992,0.507,0.376) / (0.982,0.504,0.381) / (0.995,0.512,0.372)
La (6) / (0.001,0.477,0.611) / (0.010,0.487,0.612) / (0.991,0.481,0.611) / (0.986,0.509,0.625) / (0.992,0.509,0.625) / (0.980,0.503,0.634) / (0.986,0.514,0.625)
Sr (1) / (0.984,0.494,0.112) / (0.997,0.506,0.114) / (0.004,0.493,0.113) / (1.000,0.509,0.125) / (0.997,0.501,0.133) / (0.988,0.514,0.120) / (0.020,0.520,0.129)
Sr (2) / (0.495,0.999,0.613) / (0.503,0.006,0.614) / (0.499,0.008,0.613) / (0.500,0.980,0.622) / (0.496,0.002,0.634) / (0.512,0.986,0.630) / (0.498,0.025,0.630)
Mn (1) / (0.439,0.535,0.249) / (0.461,0.455,0.249) / (0.547,0.554,0.249) / (0.501,0.485,0.247) / (0.493,0.500,0.251) / (0.504,0.504,0.248) / (0.507,0.492,0.249)
Mn (2) / (0.493,0.490,0.003) / (0.498,0.499,0.003) / (0.505,0.506,0.003) / (0.502,0.481,0.000) / (0.508,0.510,0.002) / (0.483,0.485,0.999) / (0.501,0.495,0.001)
Mn (3) / (0.040,0.029,0.249) / (0.965,0.047,0.250) / (0.041,0.945,0.250) / (0.001,0.007,0.249) / (0.996,0.004,0.250) / (0.015,0.007,0.248) / (0.988,0.013,0.249)
Mn (4) / (0.993,0.989,0.001) / (0.999,0.998,0.003) / (0.004,0.004,0.002) / (0.006,0.005,0.002) / (0.990,0.992,0.002) / (0.017,0.013,0.999) / (0.006,0.996,0.002)
Mn (5) / (0.524,0.540,0.749) / (0.535,0.547,0.750) / (0.463,0.555,0.750) / (0.483,0.503,0.749) / (0.496,0.498,0.751) / (0.483,0.487,0.751) / (0.486,0.505,0.750)
Mn (6) / (0.491,0.487,0.503) / (0.501,0.498,0.503) / (0.501,0.496,0.502) / (0.511,0.498,0.499) / (0.505,0.511,0.501) / (0.485,0.493,0.502) / (0.494,0.500,0.500)
Mn (7) / (0.035,0.942,0.748) / (0.039,0.955,0.749) / (0.959,0.947,0.749) / (0.008,0.003,0.750) / (0.000,0.001,0.750) / (0.017,0.015,0.751) / (0.002,1.000,0.750)
Mn (8) / (0.992,0.989,0.502) / (0.002,0.999,0.503) / (0.999,0.994,0.503) / (0.991,0.995,0.499) / (0.987,0.994,0.501) / (0.996,0.996,0.502) / (0.003,0.010,0.500)
O (1) / (0.923,0.588,0.255) / (0.786,0.724,0.263) / (0.797,0.719,0.263) / (0.771,0.740,0.234)
O (2) / (0.405,0.924,0.250) / (0.427,0.917,0.250) / (0.306,0.797,0.243) / (0.236,0.735,0.258) / (0.310,0.815,0.239) / (0.278,0.784,0.246)
O (3) / (0.460,0.445,0.865) / (0.493,0.453,0.866) / (0.492,0.468,0.867) / (0.491,0.443,0.874) / (0.451,0.461,0.874) / (0.433,0.468,0.876) / (0.420,0.505,0.878)
O (4) / (0.742,0.751,0.986) / (0.752,0.758,0.990) / (0.763,0.758,0.991) / (0.710,0.785,0.992) / (0.782,0.716,0.969) / (0.730,0.770,0.992) / (0.783,0.716,0.990)
O (5) / (0.237,0.745,0.993) / (0.243,0.756,0.985) / (0.256,0.768,1.000) / (0.228,0.713,0.996) / (0.286,0.805,0.004) / (0.234,0.727,0.007) / (0.290,0.779,0.019)
O (6) / (0.519,0.510,0.132) / (0.508,0.552,0.133) / (0.502,0.465,0.133) / (0.517,0.463,0.122) / (0.535,0.545,0.130) / (0.476,0.437,0.122) / (0.490,0.427,0.123)
O (7) / (0.085,0.403,0.253) / (0.088,0.401,0.254) / (0.200,0.289,0.245) / (0.268,0.226,0.228) / (0.222,0.270,0.270)
O (8) / (0.583,0.094,0.250) / (0.759,0.273,0.257) / (0.735,0.221,0.259)
O (9) / (0.974,0.044,0.862) / (0.966,0.058,0.862) / (0.040,0.047,0.862) / (0.006,0.027,0.873) / (0.047,0.052,0.882) / (0.067,0.032,0.874) / (0.077,0.017,0.876)
O (10) / (0.248,0.222,0.008) / (0.248,0.238,0.004) / (0.245,0.252,0.003)
O (11) / (0.756,0.242,1.000) / (0.754,0.241,0.010) / (0.755,0.243,0.994) / (0.784,0.284,0.996) / (0.709,0.207,0.002) / (0.757,0.266,0.988) / (0.719,0.220,0.982)
O (12) / (0.944,0.960,0.135) / (0.037,0.955,0.136) / (0.961,0.024,0.135) / (0.967,0.002,0.127) / (0.958,0.965,0.122) / (0.011,0.050,0.124) / (0.987,0.065,0.125)
O (13) / (0.906,0.580,0.750) / (0.917,0.594,0.750) / (0.583,0.912,0.755) / (0.799,0.712,0.755) / (0.770,0.730,0.758) / (0.774,0.724,0.768)
O (14) / (0.411,0.895,0.754) / (0.412,0.901,0.754) / (0.076,0.583,0.749) / (0.317,0.821,0.752) / (0.275,0.769,0.756) / (0.266,0.773,0.743)
O (15) / (0.532,0.502,0.366) / (0.534,0.558,0.362) / (0.467,0.453,0.362) / (0.471,0.448,0.377) / (0.453,0.454,0.374) / (0.424,0.457,0.374) / (0.542,0.543,0.377)
O (16) / (0.748,0.743,0.510) / (0.746,0.741,0.510) / (0.745,0.739,0.491) / (0.688,0.808,0.488) / (0.714,0.783,0.468) / (0.703,0.781,0.487)
O (17) / (0.234,0.742,0.496) / (0.252,0.738,0.504) / (0.251,0.735,0.500) / (0.208,0.688,0.505) / (0.204,0.714,0.502) / (0.190,0.685,0.511) / (0.194,0.693,0.496)
O (18) / (0.450,0.457,0.633) / (0.463,0.455,0.636) / (0.541,0.476,0.635) / (0.517,0.456,0.623) / (0.541,0.537,0.629) / (0.489,0.450,0.626) / (0.522,0.556,0.623)
O (19) / (0.164,0.317,0.747) / (0.216,0.280,0.728) / (0.211,0.285,0.731)
O (20) / (0.725,0.235,0.758) / (0.743,0.234,0.762) / (0.715,0.223,0.766)
O (21) / (0.939,0.950,0.362) / (0.007,0.953,0.366) / (0.010,0.031,0.367) / (0.041,0.022,0.374) / (0.047,0.049,0.381) / (0.076,0.043,0.376) / (0.937,0.976,0.375)
O (22) / (0.235,0.232,0.484) / (0.257,0.256,0.485) / (0.258,0.250,0.503) / (0.317,0.186,0.493)
O (23) / (0.754,0.239,0.497) / (0.748,0.258,0.490) / (0.748,0.255,0.494) / (0.811,0.312,0.495) / (0.799,0.289,0.503) / (0.765,0.279,0.491) / (0.804,0.320,0.502)
O (24) / (0.992,0.041,0.634) / (0.992,0.052,0.633) / (0.001,0.036,0.633) / (0.979,0.013,0.627) / (0.961,0.962,0.622) / (0.024,0.063,0.628) / (0.962,0.962,0.625)
Geometrical phase analyses (GPA)13of STEM-HAADF data was used to map the strain state of the system, using a probe corrected FEI TITAN 80-300 on "year 0" (Fig. 1, 2 and 3 in article) and a double corrected JEM-ARM 200F on "year 1.5" (Fig. 4 in article). The STEM data was acquired with the fast scan direction parallel to the direction we wanted to analyze the strain. For example, for the out-of-plane strain analyses the fast scan direction was parallel to the out-of-plane direction (001). This to avoid scan distortions in the slow scan direction introducing artifacts in the GPA. No drift correction was used, since the sample had little drift in the acquisition period. The GPA was done with the software "GPA for DigitalMicrograph"14, using the SrTiO3(STO) substrate as a reference. The average strain, as shown in Fig. 3c in the article, was found by taking the mean in the in-plane direction of the strain map. In the substrate, far away from the interface, we have standard STO bulk lattice parameter. To calculate the uncertainty of the average strain, the standard deviation of the average strain in this region is used. Which gives an uncertainty of 0.17%.
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