# Theory of giant skew scattering by spin cluster

## TL;DR

This paper presents a non-perturbative theoretical analysis of skew scattering caused by spin clusters, revealing that three-spin clusters induce significantly larger skew angles than impurity-based mechanisms, with implications for Hall effects in complex magnets.

## Contribution

It introduces a non-perturbative T matrix approach to analyze skew scattering by spin clusters, highlighting the necessity of three spins for significant skew effects and their relation to Hall phenomena.

## Key findings

- Three-spin clusters produce large skew angles (~0.1π rad).
- Skew scattering requires at least three spins.
- Spin Hall effect is linked to three spins, while vector spin chirality involves two.

## Abstract

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