Altermagnets and odd-parity magnets have recently emerged as important classes of magnetic materials due to their vanishing net magnetization and large, strongly momentum dependent, energy splittings between opposite spin states. Most existing theoretical research on these magnetic states stems from density functional theory (DFT). Here I present recent progress [1,2,3,4] on developing minimal, Hubbard-like, Hamiltonians for altermagnets and odd-parity magnets that faithfully reproduce important features found in DFT electronic bandstructures. These minimal models apply to a wide range of crystal classes and provide microscopic descriptions for d-wave, g-wave, and i-wave altermagnets and for p-wave, f-wave, and h-wave odd-parity magnets. Using these models we: contrast our results with related Pomeranchuk instabilities of single band theories; discuss the origin of Weyl lines; provide insight into the spin-orbit coupling enabled anomalous Hall effect; and discuss competing nematic, multiferroic, and odd-parity magnetic states.
[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, arXiv: 2402.05180 (2024).
[3] Quasi-symmetry constrained spin ferromagnetism in altermagnets, M. Roig, Y. Yu, R. C. Ekman, A. Kreisel, B.M. Andersen, D.F. Agterberg, arXiv:2412.09338 (2024).
[4] 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, arXiv:2501.02057 (2025).