Nonlinear Hall Effect in Antiferromagnetic Half-Heusler Materials

TL;DR

This paper proposes using the nonlinear Hall effect, influenced by symmetry, to identify topological phases and magnetic structures in antiferromagnetic half-Heusler materials, aiding in their characterization and potential applications.

Contribution

It introduces a symmetry-based method to distinguish topological phases in AFM half-Heusler compounds via the nonlinear Hall effect, supported by explicit Berry curvature dipole calculations.

Findings

Berry curvature dipole is small in triple-point semimetals.

Berry curvature dipole is large in Weyl semimetals.

Method enables identification of magnetic and topological phases.

Abstract

It has recently been demonstrated that various topological states, including Dirac, Weyl, nodal-line, and triple-point semimetal phases, can emerge in antiferromagnetic (AFM) half-Heusler compounds. However, how to determine the AFM structure and to distinguish different topological phases from transport behaviors remains unknown. We show that, due to the presence of combined time-reversal and fractional translation symmetry, the recently proposed second-order nonlinear Hall effect can be used to characterize different topological phases with various AFM configurations. Guided by the symmetry analysis, we obtain the expressions of the Berry curvature dipole for different AFM configurations. Based on the effective model, we explicitly calculate the Berry curvature dipole, which is found to be vanishingly small for the triple-point semimetal phase, and large in the Weyl semimetal phase. Our results not only put forward an effective method for the identification of magnetic orders and topological phases in AFM half-Heusler materials, but also suggest these materials as a versatile platform for engineering the non-linear Hall effect.