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Spin and pair density waves in two-dimensional altermagnetic metals

Nikolaos Parthenios1,2, Pietro M. Bonetti3,1, Rafael González-Hernández4,5, Warlley H. Campos6, Libor Šmejkal6,7,8, and Laura Classen1,2

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Phys. Rev. B 112, 214410 – Published 4 December, 2025

DOI: https://doi.org/10.1103/llrq-1k9k

Abstract

Altermagnetism, a recently proposed and experimentally confirmed class of magnetic order, features collinear compensated magnetism with unconventional spin-split bands. Here, we show that in a metallic 2D d-wave altermagnet with [C2||C4] symmetry, secondary instabilities can arise. Using an unbiased functional renormalization group approach, we analyze the weak-coupling instabilities of a 2D Hubbard model with a preexisting altermagnetic order inspired by our ab initio electronic structure calculations of realistic material candidates from V2X2O (X = Te, Se) family. We identify two distinct spin-density-wave (SDW) states that break the underlying altermagnetic [C2||C4] symmetry. Additionally, we find spin-fluctuation-induced instabilities leading to a singlet d-wave superconducting state and an unconventional commensurate pair-density-wave (PDW) state with extended s-wave and spin-triplet symmetry. We analyze the pairing mechanism and characterize the excitation spectrum, which exhibits Bogoliubov Fermi surfaces or nodal points depending on the gap size.

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Phys. Rev. B 112, 214410– Published 4 December, 2025
  • Received 24 August 2025
  • Revised 24 October 2025
  • Accepted 28 October 2025
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