# Critical spin fluctuation mechanism for the spin Hall effect

## TL;DR

This paper introduces mechanisms where dynamic spin fluctuations in metallic systems enhance the spin Hall effect, especially near ferromagnetic instability, with potential observation in 4d and 5d metals.

## Contribution

It proposes novel mechanisms linking spin fluctuations to the spin Hall effect, highlighting temperature dependence and potential experimental realization.

## Key findings

- Spin Hall conductivity is enhanced near ferromagnetic instability.
- Dynamical spin fluctuations cause nontrivial temperature dependence.
- Mechanisms applicable to 4d and 5d metallic compounds.

## Abstract

We propose mechanisms for the spin Hall effect in metallic systems arising from the coupling between conduction electrons and local magnetic moments that are dynamically fluctuating. Both a side-jump-type mechanism and a skew-scattering-type mechanism are considered. In either case, dynamical spin fluctuation gives rise to a nontrivial temperature dependence in the spin Hall conductivity. This leads to the enhancement in the spin Hall conductivity at nonzero temperatures near the ferromagnetic instability. The proposed mechanisms could be observed in $4d$ or $5d$ metallic compounds.