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

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

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  • Physical Review B

    Physical Review B 104 (17), 174432-, 2021-11-23

    American Physical Society (APS)

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