Abstract
Scattering by multiple scatterers sometimes gives rise to nontrivial consequences such as anomalous Hall effect. We here study a mechanism for anomalous Hall effect which originates from the correlation of non-magnetic impurities and localized moments; a Hall effect induced by vector spin chirality. Using a scattering theory approach, we study the skew scattering induced by the scattering processes that involve two magnetic moments and a non-magnetic impurity, which is proportional to the vector spin chirality of the spins in the vicinity of the non-magnetic impurity. Furthermore, we show that a finite vector spin chirality naturally exists around an impurity in the usual ferromagnetic metals at finite temperature due to the local inversion-symmetry breaking by the impurity. The result is potentially relevant to magnetic oxides which the anomalous Hall effect is enhanced at finite temperatures.
Highlights
Anomalous Hall effect (AHE) in ferromagnetic materials is one of the representative examples of transport phenomena that reflects quantum nature of electrons in solids [1, 2, 3]
Extrinsic AHE by electrons with Rashba spin-orbit interaction (SOI) is studied, showing that the bulk SOI contributes to the skew scattering mechanism [12, 13, 14], and it is proposed that the Berry curvature of electronic bands leads to extrinsic AHE regardless of its microscopic origin [15, 16]
In this work, we discussed the asymmetric scattering and the anomalous Hall effect induced by the correlation of non-magnetic impurities and spins, which brings about a new mechanism for anomalous Hall effect proportional to the vector spin chirality defined anticlockwise around the impurity
Summary
Anomalous Hall effect (AHE) in ferromagnetic materials is one of the representative examples of transport phenomena that reflects quantum nature of electrons in solids [1, 2, 3]. It was later discussed that this mechanism is a distinct mechanism from the effective Peierls phase and is rather similar to the skew scattering but by multiple spins instead of non-magnetic impurities [39] This multi-spin skew scattering was studied in relation to disordered spin systems such as chiral spin glass [40], chiral magnets [37], and for the skyrmions living on the ferromagnet/semiconductor interfaces [41]. Using second Born approximation, we discuss that the skew scattering appears from the correlation between the non-magnetic impurity and vector spin chirality of spins surrounding the impurity This mechanism is in contrast to the mechanism studied in Ref. As we are interested in the ferromagnetic phase, we introduced the Zeeman shift ∆ to introduce the population difference of up spin and down spin electrons
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