Supplementary Information for “Epitaxial integration of ferromagnetic correlated oxide
LaCoO3 with 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 value is 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) MonkhorstPack 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 be aR = 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 nonmagnetic 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.
1.1
Ferromagnetic LCO
1.0
Energy (eV)
0.9
4.0 %
Ferromagnetic
Nonmagnetic LCO
Non-magnetic
4.0 %
0.8
0.7
0.6
3.5 %
3.1 %
3.5 %
3.1 %
2.3 %
0.5
0.4
2.3 %
0.3
0.2
7.1
7.2
7.3
7.4
7.5
7.6
7.7
c (Å)
Figure S1: c-axis optimization of LaCoO3 as a function of imposed tensile
strains for magnetic (blue) and non-magnetic (orange) solutions.
1.98
Length (Å)
1.96
by[FM]
bx[FM]
bx[NM] = by
1.94
1.92
1.90
bz[FM]
bz[NM]
Bulk Co-O bond length
1.88
1.86
2.0
2.5
3.0
3.5
Strain (%)
4.0
Figure S2: Co-O bond length in strained LaCoO3 along the a-axis (bx), b-axis
(by), and c-axis (bz) for both non-magnetic (indicated by NM) and ferromagnetic
(indicated by FM) structures. The unstrained, bulk LaCoO3 bond length is
indicated by the dashed line.
170
θxy [FM]
θxy [FM]
168
Angle (°)
166
164
162
θz [FM]
θz [NM]
160
158
156
154
2.0
Bulk Co-O-Co bond angle
2.5
3.0
3.5
Strain (%)
4.0
Figure S3: Co-O-Co bond angles in strained LaCoO3 along the a- or b- axes
(θxy), and along the c-axis (θz) for both non-magnetic (indicated by NM) and
ferromagnetic (indicated by FM) structures. The unstrained, bulk LaCoO3 bond
angle is indicated by the dashed line.
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