The Fundamental Lemma of Altermagnetism: Emergence of Alterferrimagnetism

Recent years have seen a proliferation in investigations on Altermagnetism due to its exciting prospects both from an applications perspective and theoretical standpoint. Traditionally, altermagnets are distinguished from collinear antiferromagnets using the central concept of halving subgroups within the spin space group formalism. In this work, we propose the Fundamental Lemma of Altermagnetism (FLAM) deriving the exact conditions required for the existence of altermagnetic phase in a magnetic material on the basis of site-symmetry groups and halving subgroups for a given crystallographic space group. The spin group formalism further clubs ferrimagnetism with ferromagnetism since the same-spin and opposite-spin sublattices lose their meaning in the presence of multiple magnetic species. As a consequence of FLAM, we further propose a class of fully compensated ferrimagnets, termed as Alterferrimagnets (AFiMs), which can show alternating momentum-dependent spin-polarized non-relativistic electronic bands within the first Brillouin zone. We show that alterferrimagnetism is a generalization of traditional collinear altermagnetism where multiple magnetic species are allowed to coexist forming fully compensated magnetic-sublattices, each with individual up-spin and down-spin sublattices.