Magnetoelectric paramagnets: exchange-driven s-wave spin splitting in compensated magnets

In conventional antiferromagnets, local electric environments remain equivalent and combined inversion and time-reversal PT symmetry enforces spin-degenerate bands, whereas altermagnets and related compensated phases realize this inequivalence as long-range order electric environments. Materials with zero net magnetization can, nevertheless, exhibit spin-split electronic bands when the local electric environments associated with opposite magnetic moments are inequivalent. Here we this regime in which electric inequivalence arises locally from a polymorphous magnetic configuration, represented by a static, globally compensated arrangement of nonzero local moments with distinct spin neighborhoods. These neighborhoods self-consistently generate site-dependent electric offsets through the exchange-correlation potential. The correlation between these offsets and the local moments produces a finite potential-weighted Néel vector even though the net magnetization vanishes, providing a route to exchange-driven, s-wave-like spin splitting without chemical substitution, structural relaxation, heterostructures, or long-range-ordered electric inequivalence. Using spin-density functional theory for EuB6, for which previous calculations identified spin-polymorphism-induced on-site electric inequivalence, we contrast an electrically homogeneous antiferromagnetic reference with polymorphous representations of the paramagnetic state. The former remains spin degenerate, whereas the polymorphous configurations develop environment-dependent charge redistribution and finite spin splitting in the unfolded spectral function. These results establish magnetic polymorphism as an additional design axis for spin-resolved electronic structures beyond ferromagnetism, ferrimagnetism, and altermagnetism.