Exploration of the two-dimensional Ising magnetic materials in the triangular prismatic crystal field

Magnetic anisotropy is essential for stabilizing two-dimensional (2D) magnetism, which has significant applications in spintronics and the advancement of fundamental physics. In this work, we examine the electronic structure and magnetic properties of triangular prismatic MSi$_2$N$_4$ (M = V, Cr) monolayers, using crystal field theory, spin-orbital state analyses, and density functional calculations. Our results reveal that the pristine VSi$_2$N$_4$ monolayer exhibits magnetism with a V$^{4+}$ 3$d^1$ $S$ = 1/2 charge-spin state within the triangular prismatic crystal field. However, the strong $d$ orbital hybridization between adjacent V$^{4+}$ ions disrupts the $d$ orbital splitting in this crystal field, resulting in a relatively small in-plane magnetic anisotropy of approximately 2 $\mu$eV per V atom.In contrast, the pristine CrSi$_2$N$_4$ monolayer is nonmagnetic, characterized by the Cr$^{4+}$ 3$d^2$ $S$ = 0 state. Upon substituting nonmagnetic Cr$^{4+}$ with Si$^{4+}$, Cr$_\frac{1}{3}$Si$_\frac{8}{3}$N$_4$ transforms into an antiferromagnetic insulator with Cr$^{4+}$ 3$d^2$ $S$ = 1 state, featuring a large orbital moment of -1.06 $\mu_{\rm B}$ oriented along the $z$-axis and huge perpendicular magnetic anisotropy of 18.63 meV per Cr atom. These findings highlight the potential for further exploration of 2D Ising magnetic materials within a unique triangular prismatic crystal field.