Fingerprints of spin-orbital physics in cubic Mott insulators: Magnetic   exchange interactions and optical spectral weights
  The temperature dependence and anisotropy of optical spectral weights associated with different multiplet transitions is determined by the spin and orbital correlations. To provide a systematic basis to exploit this close relationship between magnetism and optical spectra, we present and analyze the spin-orbital superexchange models for a series of representative orbital-degenerate transition metal oxides with different multiplet structure. For each case we derive the magnetic exchange constants, which determine the spin wave dispersions, as well as the partial optical sum rules. The magnetic and optical properties of early transition metal oxides with degenerate $t_{2g}$ orbitals (titanates and vanadates with perovskite structure) are shown to depend only on two parameters, viz. the superexchange energy $J$ and the ratio $\eta$ of Hund's exchange to the intraorbital Coulomb interaction, and on the actual orbital state. In $e_g$ systems important corrections follow from charge transfer excitations, and we show that KCuF$_3$ can be classified as a charge transfer insulator, while LaMnO$_3$ is a Mott insulator with moderate charge transfer contributions. In some cases orbital fluctuations are quenched and decoupling of spin and orbital degrees of freedom with static orbital order gives satisfactory results for the optical weights. On the example of cubic vanadates we describe a case where the full quantum spin-orbital physics must be considered. Thus information on optical excitations, their energies, temperature dependence and anisotropy, combined with the results of magnetic neutron scattering experiments, provides an important consistency test of the spin-orbital models, and indicates whether orbital and/or spin fluctuations are important in a given compound. 
Andrzej M. Oles, Giniyat Khaliullin, Peter Horsch, Louis Felix Feiner