Microscopic mechanism for intrinsic nonlinear anomalous Hall conductivity in noncollinear antiferromagnetic metals

Abstract

We theoretically investigate an intrinsic nonlinear anomalous Hall effect (INAHE) in space-time (PT ) symmetric antiferromagnetic metals. The INAHE is characterized by an asymmetric and nondissipative part of the second-order electric conductivity tensor in the clean limit in contrast to the Drude-type symmetric conductivity tensor with dissipation. By introducing a multipole description, we show that the emergence of the INAHE is due to active odd-parity magnetic quadrupoles or magnetic toroidal dipoles under magnetic orderings. In order to clarify the microscopic origin of the INAHE, we specifically consider a fundamental tight-binding model of a three-dimensional tetragonal system. We demonstrate that the INAHE arises from the effective coupling between magnetic ordering and antisymmetric spin-orbit interaction. We also discuss essential electron hopping paths driving the INAHE.

Electric Ferro-Axial Moment as Nanometric Rotator and Source of Longitudinal Spin Current

“…The sublattice-dependent antisymmetric spin-orbit in-teraction has been recently studied in various contexts in condensed matter physics, since it becomes the origin of various electronic orderings, such as odd-parity magnetic multipole orderings [70,71,[73][74][75][76][77], skyrmion crystals [78][79][80][81], and exotic superconducting states [82][83][84][85][86][87][88][89][90][91][92][93]. For example, the relevance with magnetic odd-parity multipole orderings is understood from the symmetry correspondence as follows:…”