Spin, Orbital, and Charge Order at the Interface between Correlated Oxides

The collective behavior of correlated electrons in the ${\mathrm{VO}}_2$ interface layer of the ${\mathrm{LaVO}}_3/{\mathrm{SrTiO}}_3$ heterostructure is studied within a quarter-filled $t_{2g}$-orbital Hubbard model on a square lattice. We argue that the ground state is ferromagnetic, driven by the double-exchange mechanism, and is orbitally and charge ordered due to a confined geometry and electron correlations. The orbital and charge density waves open gaps on the entire Fermi surfaces of all orbitals. The theory explains the observed insulating behavior of the $p$-type interface between ${\mathrm{LaVO}}_3$ and ${\mathrm{SrTiO}}_3$.

Figure 1

(a) The hopping amplitudes of $t_{2g}$ electrons on a square lattice. (b) The Fermi surfaces for $d_{yz}$ (horizontal lines), $d_{xz}$ (vertical lines), and $d_{xy}$ (square) electrons in the ferromagnetic state. (c) A sketch of the orbital and charge-ordered state for $U>V\gg t$. In a symmetry broken state, the system is insulating at any values of $U$ and $V$.

Figure 2

Order parameters of the orbital (${\tau }_{1,2,3}$ for $d_{yz,xz,xy}$ bands, respectively) and charge ($\delta$) density waves vs nearest-neighbor repulsion $V$ at large $U$.

Figure 3

Band gaps (left) and kinetic energy per site $K$ (right) vs nearest-neighbor repulsion $V$.

Figure 4

Order parameters of the orbital (${\tau }_{1,2,3}$) and charge ($\delta$) density waves vs $U$. The dashed line marks a first-order phase transition (see text for details).

Figure 5

(a) ${\mathrm{V}}^{3.5+}{\mathrm{O}}_2$ bilayer formed by replacement of a LaO (001) layer of ${\mathrm{LaVO}}_3$ by SrO. (b) Spin structure of the ${\mathrm{V}}^{3.5+}{\mathrm{O}}_2$ bilayer. Large (small) circles and spins indicate sites where ${\mathrm{V}}^{3+}{d}_{xy\uparrow }{d}_{yz\uparrow }$ (${\mathrm{V}}^{4+}{d}_{zx\uparrow }$) configuration is favored. The layers are coupled ferromagnetically via the DE between $S=1$ and $S=1/2$ states. (c) Periodic sequence of ${\mathrm{V}}^{3.5+}{\mathrm{O}}_2$ bilayers. Spin coupling through the intermediate ${\mathrm{V}}^{3+}S=1$ ions of ${\mathrm{VO}}_2$ layer is antiferromagnetic (as shown here) if the charge-ordering patterns of different bilayers are in-phase.