Magnetic structure and exchange interactions of transition metal dihalide monolayers: First-principles studies

Based on the first-principles linear response method and Monte Carlo simulation, we investigate the magnetic properties of single-layer transition metal dihalides $M{X}_{2}$ $(M=\mathrm{V}, \mathrm{Cr}, \mathrm{Mn}, \mathrm{Fe}, \mathrm{Co}, \mathrm{Ni}; X=\mathrm{Cl}, \mathrm{Br}, \mathrm{I})$. We calculate the magnetic exchange interactions using the first-principles linear response method and find that the third-nearest-neighbor interaction of most dihalides is very important. When spin-orbit coupling is included, $\mathrm{Fe}{X}_{2}$ and $\mathrm{Cr}{X}_{2}$ $(X=\mathrm{Cl}, \mathrm{Br}, \mathrm{I})$ are predicted to be insulators. Using the parameters of the exchange interactions and magnetic anisotropy, the magnetic ground states of transition metal dihalide monolayers are obtained by Monte Carlo simulation. Moreover, we find that the magnetic ground states of ten $M{X}_{2}$ monolayers are independent of the $U$ value. Among them, the magnetic ground state of ${\mathrm{CrI}}_{2}$ is ferromagnetic, the magnetic ground state of ${\mathrm{CrCl}}_{2}$ is collinear antiferromagnetic, the magnetic ground states of ${\mathrm{VCl}}_{2}$, ${\mathrm{FeI}}_{2}$, and $\mathrm{Co}{X}_{2}$ $(X=\mathrm{Br}, \mathrm{I})$ are ${120}^{\ensuremath{\circ}}$ antiferromagnetic, and the magnetic ground states of ${\mathrm{FeCl}}_{2}$ and $\mathrm{Ni}{X}_{2}$ $(X=\mathrm{Cl}, \mathrm{Br}, \mathrm{I})$ are helimagnetic.