Topological Hall and Spin Hall Effects in Disordered Skyrmionic Textures

TL;DR

This paper investigates the topological Hall and spin Hall effects in disordered skyrmionic systems, analyzing their dependence on energy, skyrmion size, and disorder, revealing the effects' sensitivity to scattering and their relation to real-space topology.

Contribution

It provides a comprehensive analysis of topological Hall effects in disordered skyrmions using the Landauer-Büttiker formalism, highlighting the effects' dependence on size, disorder, and adiabatic conditions.

Findings

Topological Hall signals are sensitive to disorder strength.

Adiabatic approximation holds for both large and nanoscale skyrmions.

Topological Hall effect persists under certain conditions despite disorder.

Abstract

We carry out a throughout study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy band structure in the multiprobe Landauer-B\"uttiker formalism and their link to the effective magnetic field emerging from the real space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and found that the adiabatic approximation still holds for large skyrmions as well as for few atomic size-nanoskyrmions. Finally, we test the robustness of the topological signals against disorder strength and show that topological Hall effect is highly sensitive to momentum scattering.