Skyrmion-size dependence of the topological Hall effect: A real-space calculation

TL;DR

This study explores how skyrmion size influences the topological Hall effect using large-scale real-space calculations, revealing optimal conditions related to electron lifetime and coupling strength.

Contribution

It provides a detailed analysis of skyrmion-size dependence on the topological Hall effect, highlighting the roles of Berry curvature, electron lifetime, and coupling strength in a real-space framework.

Findings

Hall conductivity peaks in a crossover region involving Berry curvature.

Optimal skyrmion size scales with the square root of electron lifetime.

Non-adiabatic effects suppress the Hall effect when skyrmion-related timescales are short.

Abstract

Motivated by the recent discoveries of magnets harboring short-pitch skyrmion lattices, we investigate the skyrmion-size dependence of the topological Hall effect. By means of large-scale real-space calculations, we find that the Hall conductivity takes its extreme value in the crossover region where both the real-space and momentum-space Berry curvature play a crucial role. We also investigate how the optimum skyrmion size ($\lambda_{\rm sk}^*$) depends on the lifetime of itinerant electrons ($\tau$) and coupling constant between electrons and localized spins ($J$). For the former, we show that $\lambda_{\rm sk}^{*}$ is proportional to $\sqrt{\tau}$, which indicates that $\lambda_{\rm sk}^{*}$ is much less sensitive to $\tau$ than the conventional expectation that $\lambda_{\rm sk}^{*}$ is proportional to the mean-free path $\propto \tau$. For the latter, we show that the non-adiabaticity considerably suppresses the topological Hall effect when the time scale determined by the skyrmion size and Fermi velocity is shorter than $1/J$. However, its effect on $\lambda_{\rm sk}^{*}$ is not so siginificant and $\lambda_{\rm sk}^{*}$ is about ten times the lattice constant in a wide range of $J$ and $\tau$.