Gate-field controllable Zeeman-like spin splitting in layered A-type antiferromagnets

Momentum dependent spin splitting in antiferromagnetic (AFM) crystals and the resultant phenomena, such as magneto-optical and Hall effects, have attracted considerable attention for potential spintronics applications. Here, based on symmetry analysis, we proposed that specific crystal symmetry breaking through an electric field in layered A-type AFM materials results in magneto-optical (MOE) and layer-polarized anomalous Hall effects (LP-AHE). We further validate this in representative A-type AFM bilayer $\mathrm{CrP}{X}_{4}$ $(X=\mathrm{S}\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{4pt}{0ex}}\mathrm{Se})$ systems using first-principles calculations. The results demonstrate that the electric-field-induced magneto-optical effects in these bilayer systems are comparable to those of the ferromagnetic monolayer counterparts, and the spin-layer-locking character of A-type AFM gives rise to the LP-AHE. Overall, the electric field induces Zeeman-like spin splitting and the asymmetry-related spin-orbit coupling effect; the former is crucial for the manifestation of those phenomena, while the latter counts for the larger magnitude of MOE/LP-AHE. These highly tunable effects with gate voltage modulation not only offers an approach to detect and manipulate the layered AFM materials, but also expand the range of materials available for miniaturized low-dissipative spintronics based on two-dimensional antiferromagnets.