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.   Most existing theoretical research on these magnetic states stems from density functional theory (DFT). Here I present recent progress [1,2,3] on developing Hubbard Hamiltonians for non-relativistic spin-splitting with an emphasis on odd-parity magnets. These Hubbard Hamiltonians realize lattice doubling antiferromagnet states that provide microscopic descriptions for p-wave, f-wave, and h-wave odd-parity magnets. We provide insight into the stability, the microscopic origin of the odd-parity electronic spin-textures, and response properties of these 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] 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).
[3] Odd-Parity Magnetism in Fe-Based Superconductors, R. Dsouza, A. Kreisel, B. M. Andersen, D. F. Agterberg, and M. H. Christensen, arXiv:2508.21673 (2025).