Condensed Matter Seminars

Topological spin textures like magnetic skyrmions exhibit a stable particle nature due to their topological protection, leading to their utilization as an information carrier in magnetic memory devices. Although exploring the fundamental current-induced dynamics is a pivotal topic for such applications, the studies have been mostly limited to two-dimensional skyrmions [1] and the systematic investigation for three-dimensional (3D) magnetic hedgehogs remains largely unexplored. The topological defect at the core of the hedgehog where spin length vanishes, corresponding to monopoles of the emergent magnetic field for electrons, could bring about current-induced dynamics distinct from skyrmions [2]. 
In this study, we theoretically investigate the drift motions of the hedgehogs caused by an electric current, focusing on periodic arrangements of hedgehogs and antihedgehogs called the hedgehog lattices (HLs) [2]. Through the numerical simulations based on the Landau-Lifshitz-Gilbert equation, we find that a drift motion of the HLs requires a nonzero threshold current density depending on the magnetic field and the direction of the electric current relative to the Dirac strings connecting the hedgehogs and antihedgehogs. Furthermore, we reveal that the HLs exhibit a drift motion transverse to the current direction, which we call the monopole Hall effect. Notably, the threshold current for the transverse motion can be smaller than that of the longitudinal motion, resulting in the “perfect” monopole Hall effect with the maximally large Hall angle of π/2. Our study makes an important step toward understanding the current-induced dynamics of the HLs and would shed light on the applications of the 3D topological spin textures to novel spintronic devices.
[1] F. Jonietz et al., Science 330, 1648 (2010). 
[2] N. Kanazawa et al., Nat. Commun. 7, 11622 (2016).