Theory of optical spectral weights in Mott insulators with orbital degrees of freedom

Introducing partial sum rules for the optical multiplet transitions, we outline a unified approach to magnetic and optical properties of strongly correlated transition metal oxides. On the example of ${\mathrm{LaVO}}_3$ we demonstrate how the temperature and polarization dependences of different components of the optical multiplet are determined by the underlying spin and orbital correlations dictated by the low-energy superexchange Hamiltonian. Thereby the optical data provide deep insight into the complex spin-orbital physics and the role played by orbital fluctuations.

Figure 1

(Color online) (a) Kinetic energy $K_1^{\left(c\right)}$ for the high-spin excitations within classical and quantum models. Solid (dashed) line with (without) joint spin-orbital fluctuations. (b) Intersite correlations along the $c$ axis: spin $s_c={⟨{\vec{S}}_i\bullet {\vec{S}}_j⟩}_c$, orbital ${⟨{\vec{\tau }}_i\bullet {\vec{\tau }}_j⟩}_c$, and spin orbital $f_{ij}$. Orbital order parameter $\tau$ is also shown. Dotted line (filled circles) for $-f_{ij}$ obtained from high-temperature expansion (17) (by exact diagonalization). Parameters: $\eta =0.12,V_c=0.9J,V_{ab}=0.2J$.

Figure 2

(Color online) Kinetic energy $K_n^{\left(\gamma \right)}$ (solid lines) and total $K^{\left(\gamma \right)}$ (dashed lines) in units of $2J$ for (a) the $c$ axis and (b) $ab$-plane polarization. Parameters are as in Fig. 1. Filled squares in panel (a) represent the effective carrier number $N_{\mathrm{eff}}^{\left(c\right)}$ in ${\mathrm{LaVO}}_3$ which includes the sum of the peaks 1 and 2 below 3 eV in Fig. 3 of Ref. 7. The experimental data follows well the calculated intensity of the high-spin transition, $n=1$.

Figure 3

(Color online) Exchange constants as functions of $T$ along $c(a∕b)$ axis: (a) orbital $J_{\gamma }^{\tau }$ (11), and (b) spin $J_{\gamma }^s$ (9). Parameters: $\eta =0.12,V_c=0.9J,V_{ab}=0.2J$.