Multipolar orbital relaxation of the $t_{2g}$ states

TL;DR

This paper analytically investigates the relaxation dynamics of orbital dipolar and quadrupolar moments in t2g states, revealing how disorder and crystal fields influence relaxation times and the coupling of orbital moments.

Contribution

It provides a nonperturbative analytical framework for understanding orbital relaxation in t2g states considering disorder and crystal field effects.

Findings

Orbital relaxation time scales with momentum scattering in weak disorder.

Strong disorder averages out crystal field effects, inversely affecting relaxation time.

Dipolar and quadrupolar moments are coupled, leading to complex orbital dynamics.

Abstract

Using a nonperturbative approach, the relaxation rate of orbital dipolar and quadrupolar moments is computed analytically for the t2g states. In the presence of short-range impurities and in the absence of spin-orbit coupling, the orbital relaxation emerges from the competition between momentum scattering and the effect of the crystal field. In the case of weak disorder, the orbital relaxation time is proportional to the momentum scattering time: each scattering event contributes to destroying the orbital moment. In the case of strong disorder, the effect of the crystal field is averaged out, and the orbital relaxation time is inversely proportional to the momentum scattering. We finally find that the dipolar and quadrupolar orbital moments are coupled by the crystal field, resulting in a complex dynamical behavior upon orbital injection.