Symmetry Dictionary on Charge and Spin Nonlinear Responses for All Magnetic Point Groups with Nontrivial Topological Nature

TL;DR

This paper provides a comprehensive symmetry analysis of all 122 magnetic point groups to identify their potential for nonlinear charge and spin transport related to topological properties, offering a foundational theoretical framework.

Contribution

It introduces a symmetry-based dictionary for nonlinear responses in all magnetic point groups, linking topological features with specific nonlinear transport tensors.

Findings

Identifies magnetic point groups supporting nonlinear responses

Provides symmetry constraints for Berry curvature dipole and related tensors

Establishes a theoretical basis for nonlinear transport in topological materials

Abstract

Recently, charge or spin nonlinear transport with nontrivial topological properties in crystal materials has attracted much attention. In this paper, we perform a comprehensive symmetry analysis for all 122 magnetic point groups (MPGs) and provide a useful dictionary for charge and spin nonlinear transport from Berry curvature dipole, Berry connection polarization and Drude term with nontrivial topological nature. The results are obtained by making a full symmetry investigation on matrix representations of six nonlinear response tensors. We further identify every MPG that can accommodate two or three of the nonlinear tensors. The present work gives a solid theoretical basis for overall understanding the second-order nonlinear responses in realistic materials.