Investigation of non-Hermitian and Hermitian models of Altermagnets

Abstract: Insulating altermagnets like MnTe exhibit spin configurations where opposing spins are not only aligned antiparallel but also rotated relative to each other. This is an arrangement reminiscent of antiferromagnetism with a twist of spin canting. This study investigates a model Hamiltonian that captures the essential physics of such systems, incorporating key interactions including Dzyaloshinskii-Moriya and conventional exchange terms, relativistic spin-orbit coupling, and d-wave and g-wave orderings. Non-Hermitian dynamics are introduced through complex potentials that simulate energy dissipation and amplification. The paper delves into the behavior of the quantum geometric tensor and the emergence of the quantum anomalous Hall effect within the topologically insulating regime. It also broadens the scope to encompass non-Hermitian metallic altermagnets, focusing on phases characterized by symmetry-breaking d-wave and g-wave order parameters.