Large anomalous Hall effect and spin Hall effect by spin-cluster scattering in the strong-coupling limit

Skew scattering of electrons induced by a spin cluster is studied theoretically focusing on metals with localized magnetic moments. The probability calculated non-perturbative $T$ matrix method; this method valid for arbitrary strength electron-spin coupling. We show the three-spin produces skew angle order $0.1\pi$ rad when coupling comparable to bandwidth. This one or two orders magnitude larger than usual an impurity spin-orbit interaction. Systematic analysis one-, two-, and clusters that three spins are necessary scattering. also discuss relation between anomalous/spin Hall effects chiralities; we find effect requires while it related vector chirality defined pair spins. relevance these results large extrinsic anomalous in noncentrosymmetric and/or frustrated magnets discussed.