Nonrelativistic-Ising superconductivity in p-wave magnets

We discuss a possibility of superconductivity in the p-wave magnets. These are recently discovered materials that have zero net magnetization by symmetry and finite non-relativistic spin splitting of electron bands, like in altermagnets. Similarly, the spin polarizations is collinear in the momentum space. Yet, as opposed to altermagnets, the magnetization is noncollinear in the real space, and the spin splitting obeys time-reversal symmetry in the momentum space. As a result, if such material harbors superconductivity (due to phonons, or any other mechanism), the only supported superconducting symmetry is Ising superconductivity, an exotic symmetry where any Cooper pair is a 50:50 mix of singlet and triplet. This unusual behavior is also in stark contrast to regular antiferromagnet, which can support Cooper pairs of any parity, and altermagnets, which can only support nonunitary triplet pairs. The presence of large triplet component and enhanced resilience against pair breaking is inherent to the p-wave magnets and as such is unconventional as it does not materialize in conventional spin-orbit coupling induced Ising superconductors.

💡 Research Summary

The authors introduce a new class of magnetic materials, termed p‑wave magnets (p‑wM), which combine three distinctive features: (i) a vanishing net magnetization enforced by symmetry, (ii) collinear spin polarization in momentum space, and (iii) a non‑relativistic spin splitting of the electronic bands that respects time‑reversal symmetry (Eₖ↑ − Eₖ↓ = E_{−k}↓ − E_{−k}↑). Unlike altermagnets, the real‑space magnetic order is non‑collinear, while the spin texture in k‑space is strictly out‑of‑plane (usually taken as the z‑axis). The spin splitting originates from a strong exchange field rather than relativistic spin‑orbit coupling (SOC), and can reach the order of electron‑volts, far exceeding the typical SOC energy scales in 3d–5d metals.

Starting from a tight‑binding model with sublattice (τ) and spin (σ) Pauli matrices, the authors derive an effective low‑energy Hamiltonian in the limit of dominant exchange (t_J ≫ t). The resulting dispersion consists of two spin‑split bands
E_{↑,↓}(k) =