Topical Review on Skyrmions and Hall Transport

Abstract

We review recent progresses towards an understanding of the Skyrmion Hall transport in insulating as well as conducting materials. First, we consider a theoretical breakthrough based on the quantum field theory Ward identity, a first principle analysis, relying on symmetries and conservation laws. Broken parity (inversion) symmetry plays a crucial role in Skyrmion Hall transport. In addition to the well known thermal and electric Hall conductivities, our analysis has led us to the discovery of a new and unforeseen physical quantity, Hall viscosity - an anti-symmetric part of the viscosity tensor. We propose a simple way to confirm the existence of Hall viscosity in the measurements of Hall conductivity as a function of momentum. We provide various background materials to assist the readers to understand the quantum field theory Ward identity. In the second part, we review recent theoretical and experimental advancements of the Skyrmion Hall effects and the topological (Magnon) Hall effects for conducting (insulting) magnets. For this purpose, we consider two enveloping themes: spin torque and thermo-electromagnetic effect. First, we overview various spin torques, such as spin transfer torque, spin-orbit torque, and spin Hall torque, and generalized Landau-Lifshitz-Gilbert equations and Thiele equations using a phenomenological approach. Second, we consider irreversible thermodynamics to survey possible thermo-electromagnetic effects, such as Seebeck, Peltier and Thompson effects in the presence of the electric currents, along with the Hall effects in the presence of a background magnetic field. Recently developed spin Seebeck effects are also a significant part of the survey. We also accommodate extensive background materials to make this review self-contained. Finally, we revisit the Skyrmion Hall transport from the Ward identity view point.