Electric field induced Berry curvature dipole and non-linear anomalous Hall effects in higher wave symmetric unconventional magnets

TL;DR

This paper explores how external electric fields induce Berry curvature dipoles and nonlinear Hall effects in higher-symmetry unconventional magnets, revealing new ways to probe quantum metrics and distinguish order parameter symmetries.

Contribution

It demonstrates the electric-field-induced Berry curvature dipole and nonlinear Hall effects in higher-wave symmetric magnets, including altermagnets, highlighting their potential for probing quantum geometry.

Findings

Electric fields induce nonzero Berry curvature dipoles in symmetric magnets.

Nonlinear Hall effects are generated by ac and dc electric fields.

The effects can distinguish between different order parameter symmetries.

Abstract

We investigate the second-order anomalous Hall response in two-dimensional higher-wave symmetric magnets, including the recently discovered class of collinear magnets known as altermagnets, when subjected to a symmetry-breaking external electric field. In these systems, the first- and second-order anomalous Hall responses mediated by the first- and second-order multipoles of the Berry curvature over the occupied states vanish by symmetry. However, a symmetry-breaking dc electric field can induce a nonzero Berry curvature dipole by coupling to a non-vanishing quantum metric, also known as the Berry connection polarizability. An applied ac electric field can then generate a finite nonlinear transverse Hall effect characterized by a second harmonic response. In addition, the dc field itself can generate a finite third-order transverse Hall response. We discuss this remarkable effect in a class of higher-order symmetric unconventional magnets (of $p$, $d$, $f$, $g$, $i$ symmetry), including the subclass of altermagnets. We demonstrate that the electric-field-induced anomalous Hall effect in the higher-wave-symmetric magnets can serve not only as a probe of the underlying quantum metric of the occupied states but also as a means to distinguish the even ($d$-,$g$-wave) and odd ($p$-wave) order parameter symmetries defined on the square lattice.