Hubbard models for non-relativistic spin-splitting

Altermagnets and odd-parity magnets have recently emerged as important classes of magnetic materials for spintronics due to their vanishing net magnetization and large, strongly momentum dependent, energy splittings between opposite spin electronic states.   Here I present recent progress [1,2,3] on developing Hubbard Hamiltonians for altermagnets and odd-parity magnets. These Hubbard Hamiltonians provide microscopic descriptions for p-wave, d-wave, f-wave, g-wave, h-wave, and i-wave non-relativistic spin splittings. Using these Hubbard Hamiltonians, we provide insight into the stability of altermagnetism through both weak-coupling parquet renormalization approaches [2] and stronger coupling RPA approaches [1]. We further provide a microscopic theory for the development of odd-parity spin-splitting in lattice doubling antiferromagnets [3].

[1] Minimal models for altermagnetism, M. Roig, A. Kreisel, Y. Yu, B. M. Andersen, and D. F. Agterberg, Phys. Rev. B 110, 144412 (2024).

[2] Altermagnetism from coincident Van Hove singularities: application to κ-Cl, Y. Yu, H.G. Suh, M. Roig, and D.F. Agterberg, Nature Communications 16, 2950 (2025).

[3] Odd-parity magnetism driven by antiferromagnetic exchange, Y. Yu, M.B. Lyngby, T. Shishidou, M. Roig, A. Kreisel, M.  Weinert, B. M. Andersen, D. F. Agterberg, Phys. Rev. Lett. 135, 046701 (2025).