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

Abstract

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 $\hat{I}¼$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 $\hat{I}{¼}_{\mathrm{B}}$ 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.