Orbital Wave and its Observation in Orbital Ordered Titanates and Vanadates

TL;DR

This paper develops a theoretical framework for orbital waves in perovskite titanates and vanadates, analyzing their dispersion relations and proposing methods for their experimental observation through scattering techniques.

Contribution

It introduces a theory of orbital waves in $t_{2g}$ orbital systems and predicts their unique scattering signatures distinct from $e_g$ systems.

Findings

Orbital wave dispersion relations are calculated for LaVO$_3$, YVO$_3$, and YTiO$_3$.

Distinct scattering spectra are predicted for titanates and vanadates.

Observation methods for orbital waves are qualitatively different from those in $e_g$ systems.

Abstract

We present a theory of the collective orbital excitation termed orbital wave in perovskite titanates and vanadates with the triply degenerate $t_{2g}$ orbitals. The dispersion relations of the orbital waves for the orbital ordered LaVO$_3$, YVO$_3$ and YTiO$_3$ are examined in the effective spin-orbital coupled Hamiltonians associated with the Jahn-Teller type couplings. We propose possible scattering processes for the Raman and inelastic neutron scatterings from the orbital wave and calculate the scattering spectra for titanates and vanadates. It is found that both the excitation spectra and the observation methods of the orbital wave are distinct qualitatively from those for the $e_g$ orbital ordered systems.