Topological Hall effect of Skyrmions from First Principles

TL;DR

This paper introduces a first-principles method to calculate the topological Hall effect in magnetic materials with complex spin textures, successfully applied to skyrmions in Gd2PdSi3, aligning well with experimental observations.

Contribution

It develops a novel computational approach that models the effective magnetic field from spin textures and constructs a Wannier Hamiltonian for Hall conductivity calculations, advancing numerical techniques for magnetic systems.

Findings

Good agreement with experimental Hall effect data for Gd2PdSi3

Identifies band crossing points as key contributors to THE

Provides insights into spin texture and electronic transport interplay

Abstract

We formulate a first-principles approach for calculating the topological Hall effect (THE) in magnets with noncollinear nanoscale spin textures. We employ a modeling method to determine the effective magnetic field induced by the spin texture, thereby circumventing the computational challenges associated with superlattice calculations. Based on these results, we construct a Wannier tight-binding Hamiltonian to characterize the electronic states and calculate the Hall conductivity. Applying this approach to the skyrmion material $\rm Gd_2PdSi_3$ shows good agreement with experimental data. Our analysis in momentum space further reveals that the dominant contribution to the THE arises from the crossing points between the folded bands along high-symmetry lines in the Brillouin zone. This work advances numerical techniques for simulating general magnetic system, examplified by but not restricted to skyrmion lattice, and its result offering insights into the complex interplay between spin textures and electronic transport.