Phase diagram of ${\text{LaVO}}_3$ under epitaxial strain: Implications for thin films grown on ${\text{SrTiO}}_3$ and ${\text{LaAlO}}_3$ substrates

Various exotic phenomena have been observed in epitaxially grown films and superlattices of transition-metal oxides. In these systems, not only the interface properties but also the strain-induced modification in the bulk properties play important roles. With the recent experimental activities [Y. Hotta, T. Susaki, and H. Y. Hwang, Phys. Rev. Lett. 99, 236805 (2007)] in mind, we have studied the epitaxial strain effects on the electronic structure of Mott insulator ${\text{LaVO}}_3$. The present work is based on the calculations using density-functional theory supplemented by adding local Coulomb repulsion $U$ for $\text{V}d$ orbitals. The range of strain studied here extends from $c/a=0.98$ (bulk ${\text{LaVO}}_3$ case) to $c/a=1.107$ (${\text{LaAlO}}_3$ substrate case). In this range of the strain, we have found the following three different antiferromagnetic spin-ordering (SO) phases. For $0.98<c/a<1.005$, the combination of $C$-type SO and $G$-type orbital ordering (OO) is the most stable. The bulk ${\text{LaVO}}_3$ belongs to this range. For $1.005<c/a<1.095$, the ground state has $A$-type SO and $G$-type OO. ${\text{LaVO}}_3$ epitaxially grown on ${\text{SrTiO}}_3$ is in this range. When $c/a>1.095$, $G$-type SO with ferromagnetic OO becomes the ground state. This range includes the case of ${\text{LaAlO}}_3$ substrate. The implications of these results with regard to the experimental data for thin films of ${\text{LaVO}}_3$ on ${\text{SrTiO}}_3$ and ${\text{LaAlO}}_3$ substrates will be described. Detailed discussion is given on the mechanisms of stabilizing particular combination of SO and OO in each of three phases.

Figure 1

(Color online) The total energies of ${\text{LaVO}}_3$ with FM-, $A$-, $C$-, and $G\text{-AF}$ SO under different epitaxial strain (measured by $c/a$ value). $A^{\prime }\text{-SO}$ and $C^{\prime }\text{-SO}$ denote $A$-type and $C$-type SOs, respectively, with the principal axis lying in the $x$ direction (Fig. 6). The zero-energy point has been shifted to the total energy of $C\text{-SO}$ in ${\text{LaVO}}_3$ with $c/a=0.98$. Note that the results are obtained with an assumption that the volume of ${\text{LaVO}}_3$ is conserved. See comments in Ref. 24.

Figure 2

(Color online) The partial density of states of $t_{2g}$ orbitals for V ions in ${\text{LaVO}}_3$ with $c/a=0.98$ with $C\text{-SO}$ and $G\text{-OO}$. Fermi level is set at 0.0 eV.

Figure 3

(Color online) Schematic energy diagram of $d^2$ $t_{2g}$ orbitals from the Hubbard model with the rotationally invariant form of the local Coulomb interaction. This diagram corresponds to the p-DOS at V1 and V4 sites in Fig. 2. Here $U$ is the intraorbital Coulomb interaction and $J_{\text{H}}$ is Hund’s coupling. The vertical single arrow indicates the increasing of energy. Its left side is for the spin-up channel and the right side is for the spin down. The horizontal dashed line marks the Fermi level. The energy level separations are shown by vertical double arrows.

Figure 4

(Color online) Schematic pictures of magnetic coupling between V1 and V2 ions along $x$ direction ordered in (a) FM and (b) AF configurations. Those between V1 and V3 along $z$ direction ordered in (c) FM and (d) AF configurations are also shown. The virtual hopping paths bringing energy gain in each case are indicated by solid arrows. The dashed arrows in (d) are the paths which can make only negligible contribution to the magnetic coupling.

Figure 5

(Color online) The CFOs and their splittings in (a) t-LVO (b) LVO/STO, and (c) LVO/LAO listed in Table . The main component of each CFOs is indicated in the parentheses. Here only V1 site is shown for each case. In each of three cases (a), (b), and (c), the position of CFO mostly composed of $d_{xy}$ orbital is the same for all V sites [the lowest for (a) and the highest for (b) and (c)], while those of $d_{zx}$ and $d_{yz}$ are altered from site to site as shown in Table . $t_{ab}$ is the averaged hopping integrals between CFOs in the $ab$ layer and $t_c$ is that in the $c$ direction from Table . $U$ is taken as 3.0 eV and all other energies are in millielectron volt.

Figure 6

(Color online) (Upper) The charge density of occupied $t_{2g}$ orbitals in (a) FM, (b) $A$-, (c) $C$-, and (d) $G\text{-AF}$ LVO/STO. Isovalue for plotting is $\pm 0.05e/\text{a}\text{.u}{\text{.}}^3$ (Lower) The partial density of states of $t_{2g}$ orbitals for selected V ions in FM, $A$-, $C$-, and $G\text{-AF}$ LVO/STO. Four V sites are labeled as V1, V2, V3, and V4, respectively. The local axes $x$, $y$, and $z$ at V sites are defined as the [110], [110], and [001] directions of the unit cell.

Figure 7

(Color online) The CF orbitals and splittings (in meV) of ${\text{LaVO}}_3$ with octahedral rotation and tilting by $12°$ and that under compressive and tensile strain.