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

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.

Figures (4)

• Figure 1: (Color online) (a) Spin or orbital relaxation in the presence of a fluctuating magnetic field. $\tau_c$ and $\tau_p$ are the field correlation and spin precession times, respectively. (b) Scattering of a Bloch state with momentum ${\bf k}$ and an orbital moment ${\bf L}_{\bf k}$ towards a state ${\bf k}'$ with an orbital moment ${\bf L}_{\bf k'}$.
• Figure 2: (Color online) (a) Orbital relaxation time as a function of the momentum relaxation time for different values of the crystal field $r$. (b) Longitudinal (solid) and transverse (dashed) orbital relaxation length as a function of the mean free path.
• Figure 3: (Color online) Diffusion coefficients of the different orbital components, as indicated in the legend, as a function of the crystal field parameter $r/t$. The diffusion coefficients are normalized to the charge diffusivity.
• Figure 4: (a) Orbital relaxation rate and (b) dipole-quadrupole coupling constant a function of the momentum scattering rate for different values of $r$.