Microscopic origin of $p$-wave magnetism

TL;DR

This paper explains the microscopic origin of out-of-plane spin polarization in certain antiferromagnetic materials, linking it to site-compensated spin density and providing a classification and analytic tools for understanding spin polarization in complex magnetic systems.

Contribution

It introduces a microscopic explanation for unconventional spin polarization in antiferromagnets, linking it to spin density ordering and providing a general classification and analytic expressions for spin polarization.

Findings

Out-of-plane spin polarization is proportional to the cross product of non-collinear spins.

Ab initio calculations confirm the theoretical model in CeNiAsO.

The approach distinguishes between ferro-, alter-, and antialtermagnets geometrically.

Abstract

$P$-, $f$-, or $h$-wave antialtermagnets yield large non-relativistic spin splitting with out-of-plane spin polarization in momentum space perpendicular to the coplanar non-collinear local magnetic moments. We provide a microscopic explanation of this unconventional spin polarization by linking it to a previously overlooked site-compensated spin density that orders antiparallel when projected onto opposite momenta. We verify this result both by model derivation of the out-of-plane momentum-space spin polarization being proportional to the direct-space cross product of the coplanar non-collinear spin order, as well as by ab initio calculations in the material candidate CeNiAsO. By providing a general classification and analytic expression for the spin polarization of all spinful two-site tight-binding Hamiltonians, we reveal the momentum-resolved spin polarization as a probe of the Bloch-state geometry arising from spin-site coupling. Furthermore, our approach allows for geometric distinction between ferro-, alter-, and antialtermagnets. Our results provide a quantitative guidance for quantized out-of-plane momentum-space spin polarization and large spin splitting, and construction principles for antialtermagnets.