Light-Induced Even-Parity Unidirectional Spin Splitting in Coplanar Antiferromagnets

Abstract: When a coplanar antiferromagnet (AFM) with $xy$-plane magnetic moments exhibits a spin-split band structure and unidirectional spin polarization along $z$, the spin polarization is forced to be an odd function of momentum by the fundamental symmetry $[\bar{C}{2z}|\mathcal{T}]$. Coplanar AFMs displaying such odd-parity unidirectional spin splittings are known as odd-parity magnets. In this work, we propose the realization of their missing even-parity counterparts. We begin by deriving the symmetry conditions required for an even-parity, out-of-plane spin splitting. We then show that irradiating a spin-degenerate coplanar AFM with circularly polarized light lifts the $[\bar{C}{2z}|\mathcal{T}]$ constraint, dynamically generating this even-parity state. Specifically, the light-induced unidirectional spin splitting exhibits a $d$-wave texture in momentum space, akin to that of a $d$-wave altermagnet. We prove this texture's robustness against spin canting and show it yields a unique clover-like angular dependence in the Drude spin conductivity. Our work demonstrates that optical driving can generate novel spin-split phases in coplanar AFMs, thereby diversifying the landscape of materials exhibiting distinct spin splittings.