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Superconductivity via Paramagnon and Magnon Exchange in a 2D Near-Ferromagnetic Full Metal and Ferromagnetic Half-Metal

Zachary M. Raines and Andrey V. Chubukov

  • School of Physics and Astronomy and William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA

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Phys. Rev. X 16, 011059 – Published 18 March, 2026

DOI: https://doi.org/10.1103/pqq5-3n84

Abstract

We study superconductivity in paramagnetic and ferromagnetically ordered phases in a two-dimensional electron system with parabolic fermionic dispersion and short-range repulsive interaction. In the paramagnetic phase, we find that a weak momentum dependence of a paramagnon propagator parametrically reduces the onset temperature for the pairing compared to that in phenomenological theories, which assume a strong dispersion of a paramagnon, and also changes the topology of the gap function. In the ferromagnetic phase, we show that the order instantly polarizes low-energy fermionic excitations. We derive the fully renormalized pairing interaction between low-energy fermions, mediated by two transverse Goldstone modes, and show that it is attractive in a spatially odd channel. The pairing temperature in the ferromagnetic phase is found to be a fraction of the Fermi energy, significantly larger than in the paramagnetic phase near the transition. Our results are relevant for understanding superconductivity in proximity to itinerant ferromagnetism in multivalley graphene systems, particularly the ones with full valley and spin polarization.

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Predicting how superconductivity can emerge from purely repulsive interactions remains a central problem in the study of two-dimensional electron systems, especially in graphene-based materials, where a ferromagnetic order has been detected. We investigated this by theoretically analyzing a system with parabolic fermionic dispersion and short-range repulsion to determine how superconductivity arises in both paramagnetic and ferromagnetically ordered states. Our work shows that while superconductivity exists in both phases, the transition temperature is significantly higher in the ferromagnetic state, where the pairing interaction is mediated by processes involving two collective excitations—magnons. We derived magnon-mediated pairing interaction and found that it is attractive in a spatially odd p-wave channel, with a pairing temperature reaching a substantial fraction of the Fermi energy. Our results are consistent with recent experimental observations of superconductivity within ferromagnetic phases in multilayer graphene systems and provide a framework for exploring superconductivity in the ordered states of low-dimensional systems.

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Phys. Rev. X 16, 011059– Published 18 March, 2026
  • Received 1 July 2025
  • Revised 22 October 2025
  • Accepted 20 January 2026
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