Coexistence of $p$-wave magnetism and superconductivity

The symmetry requirements for realizing unconventional compensated magnets with spin-polarized bands such as altermagnets have recently been uncovered. The most recent addition to this family of magnets is parity-odd or $p$-wave magnets. We demonstrate that $p$-wave magnets are perfectly compatible with superconductivity due to the spin polarization of their electron bands and that they induce unexpected spin transport phenomena. We first show that $p$-wave magnetism can coexist with conventional superconductivity regardless of the magnitude of the spin splitting. We then predict that $p$-wave magnets induce a charge-to-spin conversion, which can be strongly enhanced by the presence of superconductivity providing a way to probe the coexistence in experiments. Our results open an avenue for material combinations with a synergetic relation between spintronics and superconductivity.