Nonlinear Hall effect driven by spin-charge-coupled motive force

TL;DR

This paper investigates how localized spin dynamics influence the nonlinear Hall effect in $ ext{PT}$-symmetric magnets, revealing a significant contribution from the mixed dipole effect analogous to Berry curvature dipole.

Contribution

It provides analytical expressions for the second-order optical response in $ ext{PT}$-symmetric magnets and identifies the mixed dipole effect as a key contributor to the nonlinear Hall effect.

Findings

Localized spin dynamics affect the nonlinear Hall effect.

The mixed dipole effect is a major contribution, similar to Berry curvature dipole.

Analytical expressions for second-order optical response are derived.

Abstract

Parity-time-reversal symmetric ($\mathcal{PT}$-symmetric) magnets have garnered much attention due to their spin-charge coupled dynamics enriched by the parity-symmetry breaking. By real-time simulations, we study how localized spin dynamics can affect the nonlinear Hall effect in $\mathcal{PT}$-symmetric magnets. To identify the leading-order term, we derive analytical expressions for the second-order optical response and classify the contributions by considering their transformation properties under $\mathcal{PT}$ symmetry. Notably, our results reveal that the sizable contribution is attributed to the mixed dipole effect, which is analogous to the Berry curvature dipole term.