  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 (Schafer-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 CrXY (X = S, Se, Te; Y = Cl, Br, I) by using the first-principles
calculations. Our results show that monolayer and bilayer CrXY (X = S, Se) are
narrow band gap semiconductors, whereas monolayer and bilayer CrTeY are
multi-band metals. The magnetic ground states of bilayer CrXY and the easy
magnetization axis of monolayer and bilayer CrXY 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 ferromagnetic state with out-of-plane magnetization. The second-order
magneto-optical effects are not restricted by the above symmetry requirements,
and therefore 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
CrXY 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.
