Disorder induced time-reversal-odd nonlinear spin and orbital Hall effects

TL;DR

This paper develops a comprehensive theory for disorder-induced, time-reversal-odd nonlinear spin and orbital Hall effects, highlighting the roles of Berry curvature dipoles and various scattering mechanisms.

Contribution

It introduces a unified framework for understanding disorder-induced $ ext{T}$-odd nonlinear angular-momentum currents, including both spin and orbital components, with a general scaling relation.

Findings

Orbital component can be comparable to or larger than the spin component.

Disorder mechanisms like side-jump and skew scattering significantly contribute to $ ext{T}$-odd effects.

A scaling relation helps distinguish different contributions in experiments.

Abstract

We develop a theory for the second-order time-reversal-odd ($\mathcal{T}$-odd) angular-momentum current, incorporating both spin and orbital components. We reveal that besides spin and orbital Berry curvature dipoles, $\mathcal{T}$-odd nonlinear angular-momentum current can originate from disorder-induced mechanisms including coordinate shift, side-jump spin and orbital currents, anomalous scattering amplitude, and skew scattering. A general scaling relation is derived to help distinguish some of these contributions in experiments. Model calculations demonstrate that the orbital component can be comparable to and much larger than the spin component. Our theory lays the groundwork for $\mathcal{T}$-odd nonlinear spin and orbital transport.