  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.
