Abstract
We propose a new theory of the topological Hall effect (THE) in systems with non-collinear magnetization textures such as magnetic skyrmions. We solve the problem of electron scattering on a magnetic skyrmion exactly, for an arbitrary strength of exchange interaction and the skyrmion size. We report the existence of different regimes of THE and resolve the apparent contradiction between the adiabatic Berry phase theoretical approach and the perturbation theory for THE. We traced how the topological charge Hall effect transforms into the spin Hall effect upon varying the exchange interaction strength or the skyrmion size. This transformation has a nontrivial character: it is accompanied by an oscillating behavior of both charge and spin Hall currents. This hallmark of THE allows one to identify the chirality driven contribution to Hall response in the experiments.
Highlights
We propose a new theory of the topological Hall effect (THE) in systems with non-collinear magnetization textures such as magnetic skyrmions
The presented analysis of microscopic electron scattering on a chiral magnetization field enabled us to formulate the following features of the topological Hall effect
In the adiabatic regime λa 1 the spin Hall effect dominates and the transverse charge current appears only if there is a substantial spin polarization of the carriers, this regime is similar to the anomalous Hall effect
Summary
We propose a new theory of the topological Hall effect (THE) in systems with non-collinear magnetization textures such as magnetic skyrmions. The hallmark of the adiabatic approximation is that this effective magnetic field is opposite for spin-up and spin-down electrons (see Fig. 1, right panel); so polarization of the electron gas is essential to produce a transverse charge current response[39,40]. The opposite limiting case corresponds to λa 1 (weak exchange interaction and small skyrmion size, typical for spin glasses and dilute magnetic semiconductors) In this case the non-adiabatic perturbation allows quantum transitions between spin sublevels split by the exchange field, so the appropriate theory should account for the spin-flip scattering[42,43,44]. In our previous work[42] we showed that in this case, when the current of non-polarized carriers flows along the sample, the transverse charge separation occurs without spin Hall effect (see Fig. 1, left panel). We have found that at λa ∼ 1 THE undergoes a nontrivial crossover: both spin and charge Hall currents exhibit oscillatory behavior, which provides a new tool for an experimental detection of THE
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