Ruddlesden-Popper and perovskite phases as a material platform for altermagnetism

The subclass of collinear antiferromagnets where spin Kramers degeneracy is broken -- resulting in ferromagnetic-like properties -- offers exciting new opportunities in magnetism and hence motivates the reasoned expansion of the material base for these so-called altermagnets. Here, we show that Ruddlesden-Popper and perovskite phases are generic hosts for altermagnetic behavior. Using first-principles calculations, we demonstrate altermagnetism in prototypical nickel-based systems such as La$_2$NiO$_4$ and identify additional candidates, including the superconducting La$_3$Ni$_3$O$_7$ and the multiferroic BiFeO$_3$. These materials span insulating, semiconducting, and metallic conduction types, with computed nonrelativistic spin splittings reaching up to 250~meV. Our analysis also reveals the presence of accidental nodes and distinct topologies in the spin-momentum texture at the Brillouin-zone boundary, suggesting a refined classification for altermagnetic materials beyond the $d$-wave or higher even-parity wave classes. In addition, we address formal inconsistencies in the traditional classification of magnetically ordered systems, proposing resolutions grounded in the altermagnetic framework, and point out the potential for altermagnetic behavior in systems beyond collinear antiferromagnets with perfectly compensated magnetization, broadening the scope for future exploration.