Two-dimensional (2D) robust intrinsic ferromagnetic (FM) half-metals and semiconductors exhibit widespread application prospects in spintronic and magnetic storage devices. However, designing 2D materials with high Curie temperature still faces significant challenges, as 2D crystals cannot spontaneously form long-range magnetic order at finite temperatures according to the Mermin-Wagner theorem. In this work, combining first-principles and Monte Carlo simulations, we propose a series of 2D intrinsic FM ${\mathrm{Cr}}_2{MX}_4$ ($M=\mathrm{In}$, Ge; $X=\mathrm{S}$, Te) materials with large magnetic moment ($\sim 7{\mu }_B$), high Curie temperatures ($120\sim 638$ K), sizable half-metallic and semiconducting gaps ($1.19\sim 2.94$ eV), and excellent structural stability. The superexchange mechanism mediated by Cr-$X$-Cr interaction is responsible for the FM coupling. High spin states of Cr-$d$ orbitals in the $D_{4h}$ crystal field lead to the large magnetization, the exchange splitting between the $d_{x^2-y^2}$ and $d_{xy}$ orbitals briefly induces a wide gap. Furthermore, the ${\mathrm{Cr}}_2{MX}_4$ shows out-of-plane magnetization with magnetic anisotropy energy (MAE) of $56.76\sim 434.25$ µeV/f.u., and the spin-orbit coupling plays a leading contribution compared to the magnetic dipole-dipole interaction. The origin of MAE is also unveiled by the torque method, second-order perturbation theory, and magnetic dipole-dipole interaction. Under biaxial strain of $-4\%\sim 4\%$, it is tunable for the magnetic exchange, Curie temperature, and magnetic anisotropy energy of ${\mathrm{Cr}}_2{MX}_4$, and the magnetization direction, half-metallic, or semiconducting behaviors are robustly preserved. Our results indicate that ${\mathrm{Cr}}_2{MX}_4$ is likely as candidates of spintronic and magnetic storage devices.

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• Magnetic anisotropy
• Ferromagnets
• Half-metals
• Semiconductors
• Density functional calculations