The generalized equation of motion for the orbital dynamics in the presence of current

TL;DR

This paper derives a generalized equation of motion for orbital dynamics under current, revealing isotropic behavior for e_g orbitals and anisotropic for t_{2g} orbitals, with implications for orbital domain wall motion.

Contribution

It introduces a unified theoretical framework for orbital dynamics in the presence of current, extending previous models to SU(N) cases and analyzing specific orbital types.

Findings

Orbital dynamics are isotropic for e_g orbitals despite anisotropic transfer integrals.

Orbital dynamics are anisotropic for t_{2g} orbitals.

Implications for current-driven orbital domain wall motion are discussed.

Abstract

The orbital dynamics induced by the charge current is studied theoretically. The equation of motion for the isospin vector $T^A$ in the SU(N) case is derived in the presence of the current, and is applied to the cases of $e_g$ (N=2) and $t_{2g}$ (N=3) orbitals. In spite of the anisotropic transfer integrals between orbitals, the dynamics is found to be isotropic for $e_g$-orbitals similarly to the spin case, while it is anisotropic for $t_{2g}$-orbitals. The implication of this result to the current driven orbital domain wall motion is discussed.