Theory of magnetic spin and orbital Hall and Nernst effects in bulk ferromagnets

TL;DR

This paper investigates the magnetic spin and orbital Hall and Nernst effects in bulk ferromagnets using ab initio calculations, revealing their magnitudes, dependencies, and potential significance for spin-orbit torques.

Contribution

It provides the first ab initio analysis of the magnetic spin and orbital Hall and Nernst effects in ferromagnets, highlighting their importance and differences from conventional effects.

Findings

MSHE in Fe and Co is comparable to SHE

MSHE can have opposite signs to SHE depending on electron lifetime

Ni exhibits larger magnetic Nernst effects than Fe and Co

Abstract

The magnetic spin Hall effect (MSHE) is an anomalous charge-to-spin conversion phenomenon which occurs in ferromagnetic materials. In contrast to the conventional spin Hall effect (SHE), being a time-reversal even effect, the magnetic counterpart is time-reversal odd. In this work, we use ab initio calculations to investigate the MSHE for the bulk ferromagnets Fe, Co, and Ni. The magnitudes of the MSHE of Fe and Co are comparable to those of the SHE, but the MSHE is strongly dependent on the electron lifetime and the MSHE and SHE can moreover have opposite signs. For Ni the MSHE is smaller than the SHE, but in general, the MSHE cannot be ignored for spin-orbit torques. Considering a charge current we analyze how both the MSHE and SHE contribute to a total Hall angle. We extend our analysis of the MSHE to its orbital counterpart, that is, the magnetic orbital Hall effect (MOHE), for which we show that the MOHE is in general smaller than the orbital Hall effect (OHE). We compute furthermore the thermal analogs, i.e., the spin and orbital Nernst effects, and their magnetic counterparts. Here our calculations show that the magnetic spin and orbital Nernst effects of Ni are substantially larger than those of Fe and Co.