In 2022, physicists described a new type of magnetism — alternagnetism. In it, electrons with different spin directions are split in energy depending on their direction of motion, like runners who speed up on one track and slow down on another. But spin is not the only degree of freedom particles have.

In a fresh study, researchers showed that if you replace spin with a related characteristic (eta-pseudospin, which describes pairs of electrons in superconductors) alternagnetism shows up there too. To do this, they applied a transformation discovered back in the 1970s by Japanese physicist Hiroyuki Shiba. It links models with repulsion and attraction between particles, like a translator who retells the same story in another language. As a result, ordinary antiferromagnetism turns into eta-antiferromagnetism with a uniform superconducting 'glue' of pairs and charge-density waves.

But the biggest surprise awaited in more complex lattices. When the authors added anisotropic hopping to second neighbors, the degeneracy of the eta-pseudospin was lifted, and eta-alternagnetism emerged. Depending on the lattice symmetry (checkerboard or honeycomb), the energy splitting took the form of different types of waves: p-waves, d-waves, and even f-waves. Hartree-Fock-Bogoliubov calculations confirmed these patterns.

Such 'paired' alternagnetism could be detected through features in tunneling current or neutron scattering. If experiments confirm the theory, it would give a new class of quantum materials where superconductivity and magnetic order are intertwined at a fundamental level.