SPICE Workshop on Unconventional Superconductors and Magnets May 12th - 14th, 2026
I report the results of our recent studies of magnon-mediated superconductivity in a ferromagnetically ordered state of a multi-layer graphene system. I first discuss superconductivity in a one-valley system and emphasize the crucial role of spin anisotropy. I then discuss superconductivity in a two-valley metal with small Fermi pockets and Ising spin-orbit coupling, which I use to model two and three-layer graphene systems placed in proximity to WSe2. The magnetically-ordered state in this model is a half-metal with a canted ferromagnetic order. I show the magnon spectrum and derive two types of magnon-mediated 4-fermion interactions: spin-flip interactions mediated by a single magnon and spin-preserving interactions mediated by two magnons. I argue that both have to be included into the pairing interaction between fermions from the filled bands. The full magnon-mediated interaction satisfies Adler criterion and is attractive in a spin-triplet, valley-odd and spatially-even pairing channel. The attraction is induced by spin-orbit coupling and is confined to energies which are parametrically smaller than the Fermi energy. I argue that the attraction peaks near the onset of a canted ferromagnetic order and superconductivity is confined to this range.