Importance of magnetic shape anisotropy in determining magnetic and electronic properties of monolayer $\mathrm{VSi_2P_4}$

TL;DR

This study reveals that magnetic shape anisotropy significantly influences the magnetic and electronic properties of monolayer VSi2P4, challenging previous assumptions that only magnetocrystalline anisotropy is relevant for 2D magnetic order.

Contribution

It demonstrates the crucial role of magnetic shape anisotropy in stabilizing magnetic phases and electronic states in monolayer VSi2P4, providing a more comprehensive understanding of its magnetic behavior.

Findings

MSA can dominate MAE at large U, leading to easy-plane anisotropy.

Monolayer VSi2P4 exhibits various magnetic and electronic phases with increasing U.

At U=3 eV, VSi2P4 behaves as a 2D XY magnet, not Ising-like, due to MSA influence.

Abstract

Two-dimensional (2D) ferromagnets have been a fascinating subject of research, and magnetic anisotropy (MA) is indispensable for stabilizing the 2D magnetic order. Here, we investigate magnetic anisotropy energy (MAE), magnetic and electronic properties of $\mathrm{VSi_2P_4}$ by using the generalized gradient approximation plus $U$ (GGA+$U$) approach. For large $U$, the magnetic shape anisotropy (MSA) energy has a more pronounced contribution to the MAE, which can overcome the magnetocrystalline anisotropy (MCA) energy to evince an easy-plane. For fixed out-of-plane MA, monolayer $\mathrm{VSi_2P_4}$ undergoes ferrovalley (FV), half-valley-metal (HVM), valley-polarized quantum anomalous Hall insulator (VQAHI), HVM and FV states with increasing $U$. However, for assumptive in-plane MA, there is no special quantum anomalous Hall (QAH) state and spontaneous valley polarization within considered $U$ range. According to the MAE and electronic structure with fixed out-of-plane or in-plane MA, the intrinsic phase diagram shows common magnetic semiconductor (CMS), FV and VQAHI in monolayer $\mathrm{VSi_2P_4}$. At representative $U$$=$3 eV widely used in references, $\mathrm{VSi_2P_4}$ can be regarded as a 2D-$XY$ magnet, not Ising-like 2D long-range order magnets predicted in previous works with only considering MCA energy. Our findings shed light on importance of MSA in determining magnetic and electronic properties of monolayer $\mathrm{VSi_2P_4}$.