Generalized s-d model for Wannier-Mott excitons in layered magnetic semiconductors

Abstract

The recent discovery of excitons coupled to the magnetic order, and the consequent strong magneto-optic responses, in some van der Waals magnetic semiconductors has triggered intense activity at the interface of magnetism and semiconductor optics. Here, we present an analytically tractable minimal model that describes magnetic order, electrons, holes, and excitons within a unified framework, thereby capturing a wide range of phenomena. It treats the magnetic order and itinerant carriers to be comprised by distinct electronic orbitals that are mutually coupled via orbital-dependent onsite exchange, similar to the treatment of metallic magnets using an s-d model. Investigating CrSBr bilayer as a case study, we benchmark our model and its predictions against recent experimental and ab-initio results finding good agreement as well as new insights enabled by the model's simplicity. Examining the optical selection rules, we find the conservation of a quantum number formed from a combination of spin and layer pseudospin to be a useful guiding principle, even in noncollinear magnetic configurations. Our analysis finds a series of bright and dark excitonic states in such layered A-type antiferromagnets. The presented framework should be valuable in achieving intuitive understanding of recently discovered excitonic phenomena and guiding the discovery of other excitonic states in layered magnetic semiconductors.