Defect-Induced Orbital Polarization and Collapse of Orbital Order in Doped Vanadium Perovskites

We explore mechanisms of orbital-order decay in the doped Mott insulators $R_{1-x}(\mathrm{Sr},\mathrm{Ca}{)}_x{\mathrm{VO}}_3$ ($R=\mathrm{Pr},\mathrm{Y},\mathrm{La}$) caused by charged (Sr,Ca) defects. Our unrestricted Hartree-Fock analysis focuses on the combined effect of random charged impurities and associated doped holes up to $x=0.5$. The study is based on a generalized multiband Hubbard model for the relevant vanadium $t_{2g}$ electrons and includes the long-range (i) Coulomb potentials of defects and (ii) electron-electron interactions. We show that the rotation of $t_{2g}$ orbitals, induced by the electric field of defects, is a very efficient perturbation that largely controls the suppression of orbital order in these compounds. We investigate the inverse participation number spectra and find that electron states remain localized on few sites even in the regime where orbital order is collapsed. From the change of kinetic and superexchange energy, we can conclude that the motion of doped holes, which is the dominant effect for the reduction of magnetic order in high-$T_c$ compounds, is of secondary importance here.

Figure 1

Schematic view of occupied and unoccupied (grayed out) $t_{2g}$ V orbitals for (a) $G$-AO order in undoped $R{\mathrm{VO}}_3$ with $C$-AFM spin order marked by red and blue arrows, and (b) a defect cube around a ${\mathrm{Ca}}^{2+}$ defect (red sphere) in $R_{1-x}{\mathrm{Ca}}_x{\mathrm{VO}}_3$, with $\{a^{\prime },b^{\prime },c^{\prime }\}$ orbitals in the large $\mathcal{D}$ limit. Finite $\mathcal{D}$ modifies the standard $t_{2g}$ basis $\{a,b,c\}$ at each V site to $\{a^{\prime },b^{\prime },c^{\prime }\}$; the lowest orbitals $\{c^{\prime },b^{\prime }\}$ are occupied at all but the hole ($h$) site. (c) $t_{2g}$ orbital energies at a V ion for $\mathcal{D}\sim {\mathrm{\Delta }}_c/2$, with the $\{a^{\prime },b^{\prime }\}$ doublet split by $2\mathcal{D}$.

Figure 2

Average electron density (per V ion) vs orbital-polarization parameter $\mathcal{D}$ (2) for doping $x\in [0.0,0.5]$ [legend in (a)] for (a) $c$ orbitals, $n_c$; (b) $\{a,b\}$ orbital doublet, $n_{a+b}$. Parameters: $U=4.5$, $J_H=0.5$, $t=0.2$, $V_D=2.0$ (all in eV).

Figure 3

Orbital-order parameter $m_{a+b}^o$ (3) (a) for increasing orbital polarization $\mathcal{D}$ at different doping [same legend as in Fig. 2], and (b) for increasing doping $x\in [0,0.5]$ at representative values of $\mathcal{D}$ (see legend). Parameters are as in Fig. 2.

Figure 4

IPN spectrum $P_{n,s}^{-1}$ vs ${\omega }_{n,s}$ and average $P^{-1}(\omega )$ for different $\mathcal{D}$’s (see legend) at $x=0.3125$. Black lines show $N(\omega )$ with LHB and UHB for $\mathcal{D}=0$. The $\mathcal{D}$ dependence of HS $d^2\to d^3$ transitions on defect cubes at $\omega \in (2.7,3.5)\mathrm{eV}$ reflects the melting of OO (see shading). Parameters are as in Fig. 2.

Figure 5

(Top panels) Kinetic energies per site vs orbital-polarization strength $\mathcal{D}$ for different dopings $x\in [0,0.5]$ [for the color convention, see the legend in (c)]: (a) total energy $K$, and (b) the kinetic energy on active bonds $K_{\mathrm{AB}}$. (Bottom panels) Energies per defect (4): (c) change of total kinetic energy $\delta k$ (relative to $x=0$), and (d) the kinetic energy on an active bond $k_{\mathrm{AB}}$. Parameters are as in Fig. 2.