Cross-State Alternating Magnetism in Two-Dimensional Systems

Altermagnetism is characterized by alternating spin polarizations in both real and reciprocal spaces in a single physical state of material. Here, we introduce the physical state as a new degree of freedom and propose a theory by symmetry analysis for achieving alternating spin polarizations across two equivalent states in two-dimensional systems, which we term cross-state alternating magnetism (cs-AM). We validate the feasibility of cs-AM with a tight-binding model, showing that the requisite state transition for switching spin polarizations can be realized in altermagnets and even fully compensated ferrimagnets, via the flipping of a vertical electric polarization. Ab initio calculations demonstrate half-metallic cs-AM in a Lu₃N₂O₂ bilayer via interlayer sliding as well as a spin-valley locked altermagnetic state in a Cr₂SeO bilayer under an applied electric field. Moreover, our theory can be extended to achieve cascaded manipulation of a series of alternating spin polarizations across different symmetry-connected state pairs by, for example, the joint action of interlayer stacking and intrinsic ferroelectricity.