Coupling ferroelectric and magnetic orders would enable electrically switchable magnetism — transformative for low-dissipation electronics. But the two orders are nearly incompatible: ferroelectrics need insulating band structures, while ferromagnetism typically requires metallic bands. The few known multiferroics have weak coupling or inconvenient ordering temperatures.
This paper identifies a new route. In ferroelectrics with noncollinear magnetic sublattices, time-reversal-symmetric p-wave and f-wave spin-polarized insulating states emerge. The spin polarization has the symmetry of a p-wave or f-wave orbital — spatially varying, with nodes — while preserving the insulating gap that ferroelectricity requires. The key is that the noncollinear magnetic order breaks the right symmetries without closing the gap.
Using spin and magnetic group theory, the authors systematically classify all polar symmetry-breaking mechanisms that produce these states and identify over 50 candidate materials. First-principles calculations on GdMn₂O₅ confirm p-wave spin-polarized electronic structure that switches electrically. The p-wave order parameter can be flipped by an electric field, because the ferroelectric polarization reversal rearranges the noncollinear magnetic structure. Fifty materials is not a handful of special cases — it's a material class.