## Ab Initio Theory of Magnetic Spin and Orbital Hall and Nernst Effects in Metallic Ferromagnets

## Peter M. Oppeneer, Uppsala University

## June 3, 2022

Recently, an anomalous charge-to-spin conversion phenomenon, the magnetic spin Hall effect (MSHE) has been introduced [1]. The MSHE is time-reversal odd, in contrast to the spin Hall effect (SHE), which is time-reversal even or magnetization invariant. To investigate the MSHE, we use relativistic ab initio calculations to compute the SHE and MSHE for the bulk ferromagnets Fe, Co, and Ni. In contrast to the SHE, for which the electric field, spin current, and induced spin polarization are mutually orthogonal, the MSHE leads to a spin polarization parallel to the applied electric field [2]. 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. We extend our investigations to Pt/Co and Pt/Ni bilayers, typically used for spin-orbit torques (SOTs), for which we also find an unusual MSHE giving a spin polarization along the electric field [3]. Our calculations emphasize that the MSHE cannot be ignored in considerations for the SOTs in magnetic materials. We analyze how both the MSHE and SHE contribute to a total Hall angle for a charge current in a ferromagnet.

We go on to analyze the orbital counterpart of the MSHE, the as-yet unobserved magnetic orbital Hall effect (MOHE). We find that the MOHE is in general smaller than the orbital Hall effect (OHE), while the OHE is much larger than the SHE. We compute furthermore the thermal analogs, i.e., the spin Nernst and orbital Nernst effects, and their magnetic counterparts, where we predict large magnetic spin and orbital Nernst effects for ferromagnetic Ni [4].

[1] M. Kimata et al., Nature 565, 627 (2019).

[2] L. Salemi and P.M. Oppeneer, arXiv:2203.17025.

[3] L. Salemi, M. Berritta, and P.M. Oppeneer, Phys. Rev. Mater. 5, 074407 (2021).

[4] L. Salemi and P.M. Oppeneer, arXiv:2203.17037.