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Topological Hall effect (THE) is a recently discovered transport phenomenon occurring in various magnetic systems due to free carriers interaction with chiral magnetization textures, such as magnetic skyrmions. THE mechanism is based on exchange interaction, thus it is fundamentally different from normal Hall effect and anomalous Hall effect. THE is considered as a very perspective tool to probe topologically nontrivial spin structures as well as for potential device applications based on topology-related properties of nanostructures, one of the most popular concepts in this field is racetrack memory based on magnetic skyrmions.
Despite its great importance for fundamental and applied research, the topological Hall effect has still lacked a proper theoretical description. The existing theories of THE consider two limiting cases of either infinitely strong exchange interaction when an adiabatic Berry phase approach is applicable or the case of a weak exchange interaction allowing for perturbation theory analysis. These two theoretical approaches are known to give qualitatively different results regarding THE.
The adiabatic Berry phase approximation has revealed that THE is accompanied with a pronounced transverse spin current, so the appearance of transverse charge Hall current requires spin polarization of the carriers in the sample, similarly to the anomalous Hall effect [1]. In the opposite case of a weak exchange the transverse charge current can occur in the absence of a spin current, in this regime THE is expected even for non-polarized carriers [2]. We have developed a theory of THE based on exact solution of a problem of electron scattering on a chiral spin field. The suggested theory fills the gap between the two limiting regimes of THE. We discovered a nontrivial crossover between the two regimes, the transverse pure charge current in the weak coupling case transforms into a pronounced transverse spin current in the adiabatic regime. Thus, the apparent contradiction between the results of adiabatic and perturbative theoretical approaches to THE have been eliminated for the first time [3].
[1] P.Bruno, V.K.Dugaev, M.Taillefumier, Phys.Rev.Lett. 63, 096806 (2004).
[2] K.S. Denisov, I. V. Rozhansky, N. S. Averkiev, E. Lähderanta, Phys.Rev.Lett, 117, 027202 (2016)
[3] K.S.Denisov, I.V.Rozhansky, N.S.Averkiev, E.Lähderanta, arXiv:1702.04985 (2017).
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