Mott Transition and Suppression of Orbital Fluctuations in Orthorhombic $3d^1$ Perovskites

Using $t_{2g}$ Wannier functions, a low-energy Hamiltonian is derived for orthorhombic $3d^1$ transition-metal oxides. Electronic correlations are treated with a new implementation of dynamical mean-field theory for noncubic systems. Good agreement with photoemission data is obtained. The interplay of correlation effects and cation covalency (${\mathrm{GdFeO}}_3$-type distortions) is found to suppress orbital fluctuations in ${\mathrm{LaTiO}}_3$ and even more in ${\mathrm{YTiO}}_3$, and to favor the transition to the insulating state.

Figure 1

$Pbnm$ primitive cells (right panels), subcells 1 (left panels), and the occupied $t_{2g}$ orbitals for ${\mathrm{LaTiO}}_3$ (top panels) and ${\mathrm{YTiO}}_3$ (bottom panels) according to the $\mathrm{LDA}+\mathrm{DMFT}$ calculation. The oxygens are violet, the octahedra yellow, and the cations orange. In the global, cubic $xyz$ system directed approximately along the Ti-O bonds, the orthorhombic translations are $\mathbf{a}\mathrm{=}(1,-1,0)(1+\alpha )$, $\mathbf{b}\mathrm{=}(1,1,0)(1+\beta )$, and $\mathbf{c}\mathrm{=}(0,0,2)(1+\gamma )$, with $\alpha$, $\beta$, and $\gamma$ small. The Ti sites 1 to 4 are $\mathbf{a}/2$, $\mathbf{b}/2$, $(\mathbf{a}+\mathbf{c})/2$, and $(\mathbf{b}+\mathbf{c})/2$. The La(Y) $ab$ plane is a mirror $(z\leftrightarrow -z)$ and so is the Ti $bc$ plane $(x\leftrightarrow y)$ when combined with the translation $(\mathbf{b}-\mathbf{a})/2$.

Figure 2

$t_{2g}$ LDA DOS matrix (states$/$eV$/$spin$/$band) in the Wannier representation. On-site-1 elements: $N_{xz,xz}$ (red) $N_{yz,yz}$ (green), and $N_{xy,xy}$ (blue). Insets: $N_{yz,xz}$ (red), $N_{xz,xy}$ (green), and $N_{xy,yz}$ (blue). ${\epsilon }_F\equiv 0$.

Figure 3

DMFT spectral function at $T=770\mathrm{K}$ (thick line) and LDA DOS (thin line). $\mu \equiv 0$.