Anomalous and Topological Hall Effects in Chiral Magnets: Electric, Thermal, and Thermoelectric Transport*

Motivated by recent transport measurements of the topological Hall and Nernst effects in chiral magnets that harbor skyrmions, we extend our previous work [1, 2] to present a unified semiclassical analysis of electric, thermal, and thermoelectric transport in systems with arbitrary three-dimensional magnetic textures. We show from a controlled solution of the Boltzmann equation that the transverse thermoelectric tensor can be expressed as the sum of three contributions: an “ordinary” term arising from the external magnetic field, an “anomalous” term arising from the k-space Berry curvature in a spin-orbit coupled system with a net magnetization, and a “topological” term from the real-space Berry phase coming from the topological charge density of the spin texture. This simple result arises from a semiclassical calculation that includes effects of the Berry curvature in six-dimensional phase-space. We also show that the Wiedemann-Franz and Mott relations are obeyed in the presence of these Berry curvatures. In addition, we identify a symmetry-allowed in-plane Hall effect in materials with a sufficiently low symmetry. The ordinary, anomalous, and topological contributions to this in-plane Hall effect are all found to take a simple, unified form involving the product of a tensor containing band structure information and a time-reversal breaking pseudovector corresponding to the effective magnetic field. We will discuss conditions for the experimental detection of the in-plane Hall effect.

[1] Z. Addison, L. Keyes, and M. Randeria, Phys. Rev. B 108, 014419 (2023).

[2] N. Verma, Z. Addison, and M. Randeria, Science Adv. 8, eabq2765 (2022).