Brian M. Andersen
I provide an overview of recent progress in the development of microscopic minimal models for altermagnetism [1,2]. This includes both the construction of the models, insight into the stabilization of altermagnetism, and the applicability of minimal models to address relevant physical properties. An important example pertains to the anomalous Hall effect (AHE) which share the same symmetry as the ferromagnetic spin moment, and hence are usually proportional. However, DFT calculations find that the AHE exists with negligible ferromagnetic spin moment for some altermagnets, whereas it reaches sizable values for other compounds. By examining realistic minimal models for altermagnetism in which the DFT phenomenology is captured, we uncover a general SOC-enabled quasisymmetry, the uniaxial spin space group, that provides a natural explanation for the amplitude of the ferromagnetic spin moment across the vast range of different altermagnetic materials. Finally, I address the application of minimal models to local signatures of altermagnetism near disorder sites [3], and the generic properties of superconducting gap functions arising from altermagnetic metals [4].
[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] M. Roig, Y. Yu, R. C. Ekman, A. Kreisel, B. M. Andersen, and D. F. Agterberg, Quasi-symmetry Constrained Spin Ferromagnetism in Altermagnets, Phys. Rev Lett. 135, 046701 (2025).
[3] J. Gondolf, M. Roig, Y. Yu, A. Kreisel, D. F. Agterberg, and B. M. Andersen, Local signatures of altermagnetism, Phys. Rev. B 111, 174436 (2025).
[4] C. L. H. Rasmussen, J. Gondolf, M. Barkman, M. Roig, D. F. Agterberg, A. Kreisel, and B. M. Andersen, Inherent momentum-dependent gap structure of altermagnetic superconductors, ArXiv:2509.03247