Large anomalous Hall effect and spin Hall effect by spin-cluster scattering in the strong-coupling limit
Hiroaki Ishizuka, Naoto Nagaosa
Abstract
Skew scattering---an asymmetric scattering of electrons by impurities---is one of the major mechanisms causing anomalous/spin Hall effects. Although many microscopic mechanisms for skew scattering are known, the Hall angle of anomalous Hall effect by these mechanisms is often small, typically $\ensuremath{\theta}=0.{1}^{\ensuremath{\circ}}\ensuremath{-}{1}^{\ensuremath{\circ}}$. In this paper, we study the skew scattering by three-spin clusters focusing on the strong Kondo-coupling regime. Using a $T$-matrix formalism, we calculate the scattering probability for arbitrary strength of Kondo coupling, going beyond perturbation theory in previous studies. From a systematic analysis of the scattering probability for one-, two-, and three-spin clusters, we show that three spins are necessary for the skew scattering in the absence of spin-orbit interaction. The skew scattering by the three-spin cluster produces a skew angle on the order of $0.1\ensuremath{\pi}\phantom{\rule{0.28em}{0ex}}\mathrm{rad}\phantom{\rule{0.28em}{0ex}}(\ensuremath{\sim}{18}^{\ensuremath{\circ}})$ when the electron-spin coupling is comparable to the bandwidth. We also study the relationship between the anomalous/spin Hall effects and the spin chiralities and argue that the anomalous-(spin) Hall skew angle is approximately proportional to the scalar (net vector) spin chirality even for the strong-coupling cases. This mechanism is potentially relevant to anomalous/spin Hall effects in noncentrosymmetric and frustrated magnets.