Coupled Spin-Orbital $p$-Wave Magnetism via Structural and Magnetic Chirality

Abstract

Helical spin textures represent the minimal realization of $p$-wave magnetism which is characterized by momentum-odd spin polarization. Independently, structurally chiral crystals exhibit momentum-odd orbital polarization arising from broken inversion symmetry. Here, we demonstrate that spin-orbit coupling couples these two independent microscopic chirality degrees of freedom, allowing the orbital polarization of a chiral crystal to generate an additional contribution to the $p$-wave spin splitting. The resulting spin-orbital state is naturally classified by the relative chirality $\eta ={\chi }_{\mathrm{c}}{\chi }_{\mathrm{m}}$, giving rise to two symmetry-distinct $p$-wave phases corresponding to homochiral and heterochiral configurations which can be directly probed by the longitudinal conductivity. These phases exhibit distinct transport signatures, establishing a unified framework linking orbitronics and unconventional magnetism through coupled spin-orbital $p$-wave order.