Relativistic spin-momentum locking in ferromagnets

TL;DR

This paper demonstrates the presence of relativistic spin-momentum locking in various ferromagnetic materials using density functional theory, revealing significant effects on spin responses and potential for novel spintronic applications.

Contribution

It shows relativistic spin-momentum locking occurs in ferromagnets with specific symmetries, expanding understanding beyond non-magnetic and altermagnetic materials.

Findings

Relativistic spin-momentum locking is present in several ferromagnets.

Ferromagnets can host strong spin-momentum locking effects.

Implications for spin Hall and photocurrents are significant.

Abstract

The relativistic spin-momentum locking has been proven in time-reversal-breaking classes of materials with zero net magnetization in the non-relativistic limit, such as altermagnets and other non-collinear magnets. Using density functional theory calculations, we aim to show relativistic spin-momentum locking in ferromagnets, focusing on a broad class of ferromagnetic materials with magnetic sites connected by rotational symmetry, and compare with fcc Ni. In SrRuO3, the antisymmetric exchange interaction produces a spin canting orthogonal to the easy axis, while in all other cases, spin canting is forbidden. Even when the canted magnetic moment in real space is forbidden, relativistic spin-momentum locking shows sizable contributions in k-space. Using prototypical ferromagnets such as orthorhombic SrRuO3, hexagonal CrTe and CrAs with the NiAs crystal structure, half-Heusler MnPtSb, and fcc Ni, we demonstrate that relativistic spin-momentum locking can generate strong effects in ferromagnets. Subdominant components of centrosymmetric ferro-magnetic materials with magnetic sites connected by rotational symmetry host spin-momentum locking similar to altermagnets, while noncentrosymmetric MnPtSb hosts relativistic p-wave due to the spin-orbit coupling. Fcc Ni shows a more complex behavior with a combination of two spin-momentum locking patterns characteristic of altermagnets. Because ferromagnets typically have larger bandwidths than altermagnets, they provide a promising platform for observing even-wave relativistic spin-momentum locking and associated emergent phenomena. From an application standpoint, relativistic spin-momentum locking governs symmetry-allowed spin Hall currents, spin photocurrents, and other momentum-dependent spin responses in k-space.