Orbital Fluctuations in the Different Phases of ${\mathrm{LaVO}}_3$ and ${\mathrm{YVO}}_3$

We investigate the importance of quantum orbital fluctuations in the orthorhombic and monoclinic phases of the Mott insulators ${\mathrm{LaVO}}_3$ and ${\mathrm{YVO}}_3$. First, we construct ab initio material-specific $t_{2g}$ Hubbard models. Then, by using dynamical mean-field theory, we calculate the spectral matrix as a function of temperature. Our Hubbard bands and Mott gaps are in very good agreement with spectroscopy. We show that in orthorhombic ${\mathrm{LaVO}}_3$, quantum orbital fluctuations are strong and that they are suppressed only in the monoclinic 140 K phase. In ${\mathrm{YVO}}_3$ the suppression happens already at 300 K. We show that Jahn-Teller and ${\mathrm{GdFeO}}_3$-type distortions are both crucial in determining the type of orbital and magnetic order in the low temperature phases.

Figure 1

Temperature-dependent structural and magnetic phases of ${\mathrm{LaVO}}_3$ and ${\mathrm{YVO}}_3$. The lines show $\mathrm{LDA}+\mathrm{DMFT}$ (quantum Monte Carlo [21] ) results for the occupations, $n$, of the three $t_{2g}$ crystal-field orbitals, 1, 2, and 3 (Table ). Black lines: orthorhombic phases. Green and blue lines: monoclinic, sites 1 and 3 (see Fig. 2). For each structure we calculated the occupations down the temperature at which the orbital polarizations are essentially complete ($T\sim 200\mathrm{K}$) and then extrapolated in a standard way [21] to $T=0\mathrm{K}$.

Figure 2

Primitive cell containing four $AB{\mathrm{O}}_3$ units. $A$ ions are orange; $B$ ions are at the centers of yellow O octahedra. In terms of the primitive translation vectors, $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$ the global $\mathbf{x}$, $\mathbf{y}$, and $\mathbf{z}$ axes, directed approximately along the $B\mathrm{O}$ bonds, are $\mathbf{x}=\mathbf{a}/(2+2\alpha )+\mathbf{b}/(2+2\beta )$, $\mathbf{y}=-\mathbf{a}/(2+2\alpha )+\mathbf{b}/(2+2\beta )$, and $\mathbf{z}=(\mathbf{c}-\mathbf{c}·\mathbf{b})/(2+2\gamma )$. Here, $\alpha$, $\beta$, and $\gamma$ are small and $|\mathbf{x}|=|\mathbf{y}|=|\mathbf{z}|=3.92\AA$ (3.82 Å) for ${\mathrm{LaVO}}_3$ (${\mathrm{YVO}}_3$). The $B$-containing $bc$-plane glide mirrors [with translation $(\mathbf{b}-\mathbf{a})/2$] unit 1 in 2 and 3 in 4, and exchanges the local, $B$-centered $x$ and $y$ coordinates. In the orthorhombic $Pbnm$ structure (but not in the monoclinic $P{2}_1/a$ structure), the $A$-containing $ab$ plane mirrors unit 1 in 3 and 2 in 4. The empty crystal-field orbitals $|3{⟩}_i$ of the monoclinic phase were put on sites $i=1$, 2, 3, 4. Red (blue) indicate positive (negative) lobes.

Figure 3

$\mathrm{LDA}+\mathrm{DMFT}$ spectral matrix $A_{m,m^{\prime }}$ in the crystal-field basis. The off-diagonal terms are $\sim 5$ times smaller than in LDA. In black, the LDA DOS.