Topological and Chiral Spin Hall Effects

Abstract

This paper presents a theoretical analysis of the spin Hall effect driven by an asymmetrical electron scattering on chiral spin textures. It is demonstrated that in the adiabatic regime the transverse spin current is proportional to the topological charge of the spin texture and does not depend on its size. With the scattering T-matrix formalism, the reason is clarified for the spin Hall effect to vanish in the weak coupling regime while conserving the charge Hall effect. Adding a spin-independent term to the scattering potential restores the spin Hall effect. It is shown that in the weak coupling regime the scattering asymmetry vanishes in a half metallic case due to the suppression of spin-flip scattering. The existence of spin swapping effect for the exchange scattering on chiral spin textures is also demonstrated.

Chiral spin ordering of electron gas in solids with broken time reversal symmetry

“…Indeed, the topological Hall effect originates from the asymmetric scattering of electrons on chiral spin textures 16 . It has been shown that it is not limited to magnetic skyrmions possessing a topological charge but also expected for a broad range of chiral spin textures 16,57 . One possible scenario for the formation of such chiral spin textures in magnetic systems with spin-orbit interaction is suggested by the presented theory.…”

Chiral Hall Effect in Noncollinear Magnets from a Cyclic Cohomology Approach

“…The THE has been used as a proxy for the detection of a skyrmion phase since the early days of skyrmionics [15] and various theoretical approaches have been put forward in order to generalize upon its gauge-field interpretation. These are model based extensions of either the gauge-field language in the non-adiabatic regime [16,17], or on a T -matrix scattering theory operating in a weak-coupling regime [18,19]. The only approach which acknowledges the importance of SOCinduced gauge fields to linear order is that by Nakabayashi and Tatara [20].…”

“…Overall, our findings call for a re-interpretation of common transport experiments in chiral magnets. In the past, these mostly relied on phenomenological arguments based on the adiabatic theory of the topological Hall effect, which is already known to be insufficient in many cases [16][17][18][19]. Our formalism represents the first systematic derivation of corrections to the anomalous Hall effect of collinear magnets, which are in principle not restricted to the model level or the weakcoupling regime, and which can be certainly reformulated in the language of ab initio electonic structure.…”

Role of Magnetic Exchange Interactions in Chiral-Type Hall Effects of Epitaxial MnxPtSn Films

“…The well-known ordinary (OHE) and anomalous (AHE) Hall effects scale with the external magnetic field and the alignment of magnetic domains in the absence of a magnetic field, respectively . In addition, there are transport effects that are independent of the external magnetic field and net magnetization, which we group into the chiral-type Hall effects. − These chiral-type Hall effects are experimentally determined by the subtraction of the AHE and OHE from the total Hall effect and are related to the spatial variation of the local magnetic lattice in real space . The relative spatial variation gives rise to an emergent electromagnetic field, termed the Berry curvature, which is finite for localized magnetic textures with spin chirality.…”