Symmetry-Enforced Nodal $f$-Wave Magnets

Abstract

Owing to their relevance for spintronics, electronic band splitting and spin-polarization textures in magnets are active areas of research. In non-collinear magnets, alternating spin textures can arise both for isolated bands and for intersecting band pairs with nodal splitting. This raises the question of whether $p,f,...$-wave magnets should be defined by their spin polarization or their band splitting. To resolve this ambiguity, we introduce spin-space symmetries that couple the spin polarization and splitting textures for all bands. Focusing on the nodal $f$-wave magnet, we construct a tight-binding model of itinerant electrons on a honeycomb bilayer coupled to a non-collinear magnetic texture. Analytic expressions for spin polarization and splitting reveal the dependence on hopping and exchange coupling. We predict a canting-induced spin conductivity arising from the nodal structure of the splitting. Furthermore, the $f$-wave magnet in the bulk can induce $p$-wave magnetism on the surface. This surface $p$-wave character leads to a bulk-forbidden Edelstein effect with $f$-wave anisotropy.