In-plane anomalous and third-harmonic Hall response in an easy-plane trigonal magnet

Abstract

We report the emergence of an in-plane anomalous Hall effect (IPAHE) and a pronounced third-harmonic Hall response in an easy-plane trigonal magnetic system achieved via tuning of magnetic anisotropy. Angle-dependent Hall measurements reveal a clear departure from conventional sinusoidal behavior, revealing a strong sin(3θ) component at elevated fields, which increases as the magnetic anisotropy is reduced, accompanied by a finite in-plane Hall signal. Consistently, the observed nonlinear Hall signal exhibits a cubic field dependence, indicative of a leading third-order contribution to the transverse conductivity. The enhancement of the third harmonic reflects the evolution toward coherent in-plane magnetization and symmetry-governed nonlinear transport. These observations support an intrinsic, symmetry-controlled transport mechanism enabled by reduced magnetic anisotropy and establish a direct link between anisotropy, crystal symmetry, and higher-order Hall response.