Critical enhancement of the spin Hall effect by spin fluctuations

The spin Hall (SH) effect, the conversion of the electric current to the spin current along the transverse direction, relies on the relativistic spin-orbit coupling (SOC). Here, we develop microscopic mechanisms of the SH effect in magnetic metals, where itinerant electrons are coupled with localized magnetic moments via the Hund exchange interaction and the SOC [1]. Both antiferromagnetic metals and ferromagnetic metals are considered. It is shown that the SH conductivity can be significantly enhanced by dynamical spin fluctuations when approaching the magnetic transition temperature of both cases. For antiferromagnetic metals, the pure SH effect appears in entire temperature range, while for ferromagnetic metals, the pure SH effect is expected to be replaced by the anomalous Hall effect below the transition temperature. When the magnetic transition temperature is tuned to zero temperature, i.e., approaching a quantum critical point, nontrivial temperature dependence of the SH conductivity is predicted for both ferromagnetic metals and antiferromagnetic metals. We discuss possible experimental realizations of the predicted SH effect induced by the dynamical spin fluctuations, such as antiferromagnetic metal Cr [2].

Reference

[1] S. Okamoto and N. Nagaosa, arXiv:2308.09636

[2] C. Fang, C. Wan, X. Zhang, S. Okamoto, T. Ma, J. Qin, X. Wang, C. Guo, J. Dong, G. Yu, Z. Wen, N. Tang, S. S. P. Parkin, N. Nagaosa, Y. Lu, and X. Han, arXiv:2304.13400.