Topological charge and spin Hall effects due to skyrmions in canted antiferromagnets

Abstract

The topological charge-Hall effect (TCHE) and the topological spin-Hall effect (TSHE), arising from ferromagnetic (FM) and antiferromagnetic (AFM) skyrmions, respectively; can be elucidated through the emergence of spin-dependent Berry gauge fields that affect the adiabatic flow of electrons within the skyrmion texture. TCHE is absent in systems with parity-time (PT) symmetry, such as collinear AFM systems. In this paper, we theoretically study TCHE and TSHE in a canted antiferromagnetic within the diffusive transport regime. Spin canting or weak ferromagnetism in canted AFMs, which break the PT symmetry, may arise, e.g., from strong homogeneous Dzyaloshinskii-Moriya interactions. Using a semiclassical Boltzmann approach, we obtain diffusion equations for the spin and charge accumulations in the presence of finite spin-flip and spin-dependent momentum relaxation times. We show that the weak ferromagnetic moment stemming from spin canting and the subsequent breaking of parity-time symmetry results in the emergence of both finite TCHE and TSHE in AFM systems.