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

Since the first observation of the topological Hall effect (THE)[1], skyrmion systems have attracted broad interest in diverse fields, owing to its fascinating fundamental physics and the potential application in advanced spintronics devices. Recent discoveries of short-period skyrmion latteices[2] and theoretical investigations of the interplay between AHE and THE[3] revealed the importance of the comprehensive understanding of THE in a broad range of skyrmion size.
In this study, we numerically investigate THE in systems with various skyrmion sizes. We exploit kernel polynomial method to overcome the difficulty of the growing computational cost for larger skyrmions. Changing the skyrmion unit cells from 4 x 4 to 96 x 96, we numerically investigate the crossover between the two regimes described by the reciprocal space Berry curvature and the real space counterpart.

[1] A. Neubauer et al., PRL 102 186602 (2009)
[2] M. Hirschberger et al., PRL 125 076602 (2020)
[3] S. Zhang et al., PRB 101 024420 (2020)