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

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 (${\lambda }_{\mathrm{sk}}^{\ast }$) depends on the lifetime of itinerant electrons ($\tau$) and coupling constant between electrons and localized spins ($J$). For the former, we show that ${\lambda }_{\mathrm{sk}}^{\ast }$ is proportional to $\sqrt{\tau }$, which indicates that ${\lambda }_{\mathrm{sk}}^{\ast }$ is much less sensitive to $\tau$ than the conventional expectation that ${\lambda }_{\mathrm{sk}}^{\ast }$ 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 ${\lambda }_{\mathrm{sk}}^{\ast }$ is not so siginificant and ${\lambda }_{\mathrm{sk}}^{\ast }$ is about ten times the lattice constant in a wide range of $J$ and $\tau$.

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Cited by in corpus (1)

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