Damped orbital excitations in the titanates

A possible mechanism for the removal of the orbital degeneracy in $R{\mathrm{TiO}}_3$ (where $R=\mathrm{La},\mathrm{Y},\dots )$ is considered. The calculation is based on the Kugel-Khomskii Hamiltonian for electrons residing in the $t_{2g}$ orbitals of the Ti ions, and uses a self-consistent perturbation expansion in the interaction between the orbital and the spin degrees of freedom. The latter are assumed to be ordered in a Néel state, brought about by delicate interactions that are not included in the Kugel-Khomskii Hamiltonian. Within our model calculations, each of the $t_{2g}$ bands is found to acquire a finite, temperature-dependent dispersion that lifts the orbital degeneracy. The orbital excitations are found to be heavily damped over a rather wide band. Consequently, they do not participate as a separate branch of excitations in the low-temperature thermodynamics.