Hole Dynamics in Spin and Orbital Ordered Vanadium Perovskites

A theory of doped perovskite vanadates with spin and orbital orders is presented. Mobile holes are strongly renormalized by spin excitations (magnons) in the spin $G$-type and orbital $C$-type (SG-OC) order, and orbital excitations (orbitons) in the spin $C$-type and orbital $G$-type (SC-OG) one. Hole dynamics in a staggered $t_{2g}$ orbital array is distinguished from that in the antiferromagnetic order and the $e_g$ orbital one. The fragile character of the (SG-OC) order in ${\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x{\mathrm{VO}}_3$ is attributed to the orbiton softening induced by a reduction of the spin order parameter.

Figure 1

Schematic spin and orbital structures of (a) (SG-OC) phase and (b) (SC-OG) phase. Commonly occupied $d_{xy}$ orbitals are not shown.

Figure 2

Diagrams for (a) the self-energy of electron, (b) that of magnon(orbiton), and (c) the optical conductivity. Bold lines are for the full-fermion propagators and broken lines are for the bare-magnon (orbiton) ones in the (SG-OC) [(SC-OG)] phase.

Figure 3

Contour plot of spectral function and DOS of electrons in (SG-OC) [(a) and (b)], and those in (SC-OG) [(c) and (d)] for $x=0.1$. Bold lines in (b) and (d) are for DOS and broken lines are for $A_{(0,0,\frac{\pi }{2a})}(\omega )$ multiplied by $1/5$. The origin of the vertical axis indicates the Fermi energy. The inset in (d) shows the QP weight at $\overrightarrow{k}=(0,0,\frac{\pi }{2a})$.

Figure 4

Contour plots of the spectral functions at $x=0.1$ and the DOS for orbiton (a) and (b) and those for magnon (c) and (d) in (SG-OC). White broken lines in (a) and (c) indicate dispersion relations at $x=0$. The lower branch of the orbiton in (a) corresponds to that along $(0,0,\frac{\pi }{2a})-(0,0,\frac{\pi }{a})-(\frac{\pi }{a},0,\frac{\pi }{a})$ in the Brillouin zone for the cubic perovskite unit cell.

Figure 5

(a) Reductions of the spin and orbital order parameters, $\Delta S$ and $\Delta T$, in (SG-OC). The inset shows those in (SC-OG) with $J/t=0.2$. (b) The minimum orbiton energy ${\omega }_{\mathrm{OW}}^{\mathrm{Min}}$. The filled and open symbols in (b) are for $g{Q}_E/J=1.25$ and 1, respectively.

Figure 6

Regular parts of the optical conductivity spectra for (SG-OC) (a), and those for (SC-OG) (b). The inset in (a) shows the integrated spectral weights for (SG-OC) (broken lines) and those for (SC-OG) (bold lines).