First- and second-order magneto-optical effects and intrinsically anomalous transport in the two-dimensional van der Waals layered magnets CrXY (X=S,Se,Te;

Recently, the two-dimensional magnetic semiconductor CrSBr has attracted considerable attention due to its excellent air-stable property and high magnetic critical temperature. Here, we systematically investigate the electronic structure, magnetocrystalline anisotropy energy, first-order magneto-optical effects (Kerr and Faraday effects), and second-order magneto-optical effects (Sch\"afer-Hubert and Voigt effects) as well as intrinsically anomalous transport properties (anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects) of two-dimensional van der Waals layered magnets $\mathrm{Cr}\mathit{XY} (X=\mathrm{S},\mathrm{Se},\mathrm{Te};Y=\mathrm{Cl},\mathrm{Br},\mathrm{I})$ by using first-principles calculations. Our results show that monolayer and bilayer $\mathrm{Cr}\mathit{XY} (X=\mathrm{S},\mathrm{Se})$ are narrow-band-gap semiconductors, whereas monolayer and bilayer $\mathrm{CrTe}Y$ are multiband metals. The magnetic ground states of bilayer $\mathrm{Cr}\mathit{XY}$ and the easy magnetization axis of monolayer and bilayer $\mathrm{Cr}\mathit{XY}$ are confirmed by the magnetocrystalline anisotropy energy calculations. Utilizing magnetic group theory analysis, the first-order magneto-optical effects as well as anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects are identified to exist in a ferromagnetic state with out-of-plane magnetization. The second-order magneto-optical effects are not restricted by the above symmetry requirements, and therefore they can arise in ferromagnetic and antiferromagnetic states with in-plane magnetization. The calculated results are compared with the available theoretical and experimental data of other two-dimensional magnets and some conventional ferromagnets. The present work reveals that monolayer and bilayer $\mathrm{Cr}\mathit{XY}$ with superior magneto-optical responses and anomalous transport properties provide an excellent material platform for the promising applications of magneto-optical devices, spintronics, and spin caloritronics.