Threshold behavior in spin lasers: Spontaneous emission and nonlinear gain

A hallmark of spin-lasers, injected with spin-polarized carriers, is their threshold behavior with the onset of stimulated emission. Unlike the single threshold in conventional lasers with unpolarized carriers, two thresholds are expected in spin lasers. With the progress in scaled-down lasers and the use of novel two-dimensional materials, it is unclear if the common description of spin lasers assuming negligible spontaneous emission and a linear optical gain remains relevant or even how to identify the lasing thresholds. Our rate-equation description addresses these questions by considering large spontaneous emission and a nonlinear optical gain. We provide a transparent approach and analytical results to explore the resulting threshold behavior, its deviation from the prior studies, as well as guide future spin-lasers as a versatile platform for spintronics beyond magnetoresistance.