Critical spin fluctuation mechanism for the spin Hall effect*

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. We consider a microscopic model proposed by Kondo [1] for the coupling between electrons and local moments and describe the fluctuation of local moments using the self-consistent renormalization method by Moriya [2]. Both a side-jump-type mechanism and a skew-scattering-type mechanism naturally arise and give rise to a nontrivial temperature dependence in the spin Hall conductivity. This leads to the enhancement in the spin Hall conductivity at non-zero temperatures near the ferromagnetic instability [3]. The proposed mechanisms could be observed in 4d or 5d metallic compounds.
[1] J. Kondo, Prog. Theor. Phys.27, 772 (1962).
[2] T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism, Solid-State Sciences 56 (Springer-Verlag, 1985).
[3] S. Okamoto, T. Egami, and N. Nagaosa, arXiv:1905.10929 (to be published).