Supplementary Information for “Epitaxial integration of ferromagnetic correlated oxide LaCoO3with Si (100)”

A. Posadas, M. Berg, H. Seo, A. de Lozanne, and A.A. Demkov

Department of Physics, The University of Texas at Austin, Austin, Texas

D.J. Smith

Department of Physics, Arizona State University, Tempe, Arizona

A.P. Kirk, D. Zhernokletov, and R.M. Wallace

Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, Texas

This supplementary information provides details on the density functional calculations performed as part of the work.

For the first principles calculations of bulk and strained LaCoO3, we use density functional theory (DFT) within the local spin density approximation combined with the Hubbard U method (LSDA+U) as implemented in the VASP code (version 4.6) [S1]. Following the Dudarev approach [S2], we consider one effective Hubbard parameter Ueff = U – J of 3.8 eV to describe the Coulomb correlation effect of the Co 3d electrons. This valueis below the critical value of 4.0 eV identified by Rondinelli and Spaldin [S3] as automatically yielding a ferromagnetic state and results in a bandgap that is mid-way between reported experimental values [S4,S5]. We employ projector augmented wave (PAW) pseudopotentials [S6] to describe La, Co, and O. Valence electron configurations for the elements are 5s25p65d16s2 for La, 3d74s2 for Co, and 2s22p4 for O. A plane wave cutoff energy of 600 eV is chosen, along with a 6x6x6 (rhombohedral cell, 10 basis atoms) and a 6x6x4 (tetragonal cell, 20 basis atoms) Monkhorst-Pack special k-point grids [S7] for integration over the Brillouin zone. The rhombohedral cell is used for the unstrained bulk calculation, while the larger tetragonal cell is used for the biaxially strained calculation. The electronic total energy is converged within 10-6 eV/cell for each electronic self-consistent calculation. The ground state structure of bulk LaCoO3 has rhombohedral symmetry (space group , with a tilted CoO6 octahedral network that is expressed as (a-a-a-) in the Glazer notation [S8]. We calculate the lattice parameters of bulk LaCoO3 to beaR = 5.249 Å, α = 61.13°, and x = 0.553 where x is a parameter quantifying the tilt of the CoO6 octahedra (x = 0.5 means no tilting). These lattice parameters are in good agreement with the experimental data at T =5 K:aR = 5.345 Å, α = 61.01°, and x = 0.553 [S9]. Electronically, the system is a diamagnetic insulator with an energy gap of 0.73 eV, compared to the experimental band gap of 0.6 eV ~ 0.9 eV [S4,S5]. The valence band top mainly consists of a mixture of O 2p states and Co t2g states that are fully occupied, while the Co eg states in the conduction band bottom are un-occupied, confirming the low spin (LS) state of the LaCoO3 ground state.

For the strained calculation, we assume that tetragonal distortion is applied to the LaCoO3 film.We use a tetragonal simulation cell with four LaCoO3 formula units (see Fig. 4a in the main text) to provide more structural degrees of freedom in the calculation. This is a primary technical difference between this work and prior calculations. We impose biaxial tensile strains of 2.3% (room temperature lattice mismatch), 3.1% (mismatch at T = 10K), 3.5%,and 4.0% by adjusting the in-plane lattice constant aT of the tetragonal simulation cell. We would like to point out that the magnetic measurements are performed at low temperature, and the difference in the thermal coefficient is significant. We optimize, without any other structural constraints, the c-axis constant (Supplementary Figure S1) and the internal atomic coordinates at a given tensile strain for both non-magnetic (Co3+ ions in the low spin state) and magnetic (Co3+ ions in the intermediate spin state) solutions. The total energy as a function of strain is shown in Fig. 4b of the main text.

We identify the structural response of the system by considering change in local symmetry of CoO6 octahedra and change of the Co-O-Co bond angles, reflecting the tilting of the octahedra. The tensile strain induces tetragonal distortion on the CoO6 octahedra for the non-magnetic structure. The Co-O bond length along the c-axis (bz bond) becomes shorter while the bond length along the a or b axes (bx, by bonds) are stretched compared to the strain-free bulk Co-O bond length of 1.893 Å (see Supplementary Figure S2). The Co-O-Co bond angles θz and θxy also change under the tensile strain from the strain-free bulk value of 162.87°, with θz becoming smaller and θxy becoming larger than the bulk bond angle (see Supplementary Figure S3). Electronically, this structural distortion combined with volume the expansion induced by tensile strain reduces the band gap between the top of the t2g band and the bottom of the eg band from 0.73 eV to 0.47 eV. For the magnetic solution, all the Co-O-Co angles are larger than the non-magnetic ones, meaning the octahedral network of the magnetic structure is less tilted compared to the non-magnetic structure (Supplementary Figure S3). The bz bond length of the magnetic structure is increased from the non-magnetic case. Furthermore, the local symmetry of the Co site is further reduced from tetragonal to orthorhombic, with the bx and by bond lengths becoming different (Supplementary Figure S2). Based on the crystal field theory of an isolated CoO6 octahedron, the symmetry lowering from the tetragonal to orthorhombic reduces the energy difference between bottom eg level and top t2g level. The local orthorhombic distortion observed in our result may further contribute to the stabilization of the intermediate spin state of the Co3+ ions.

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