Effect of Coulomb Interactions on the Electronic and Magnetic Properties of Two-Dimensional CrSiTe$_3$ and CrGeTe$_3$ Materials

TL;DR

This study uses first-principles calculations to explore how Coulomb interactions influence the electronic and magnetic properties of monolayer CrSiTe$_3$ and CrGeTe$_3$, revealing their ferromagnetic insulating nature and the role of hybridization.

Contribution

It provides new insights into the dependence of bandgaps and magnetic order on Coulomb interaction strength in 2D transition metal tri-chalcogenides.

Findings

CrSiTe$_3$ and CrGeTe$_3$ are ferromagnetic insulators.

Bandgaps depend on the Coulomb interaction parameter U.

Strong hybridization between Cr e_g and Te p orbitals is crucial for ferromagnetism.

Abstract

We investigate the electronic and magnetic structures of two-dimensional transition metal tri-chalcogenide CrSiTe$_{3}$ and CrGeTe$_{3}$ materials by carrying out first-principles calculations. The single-layer CrSiTe$_3$ and CrGeTe$_3$ are found to be a ferromagnetic insulator, where the presence of the strong $dp\sigma$-hybridization of Cr $e_{\mathrm{g}}$-Te $p$ plays a crucial role for the ferromagnetic coupling between Cr ions. We observe that the bandgaps and the interlayer magnetic order vary notably depending on the magnitude of on-site Coulomb interaction $U$ for Cr $d$ electrons. The bandgaps are formed between the Cr $e_{\mathrm{g}}$ conduction bands and the Te $p$ valence bands for both CrSiTe$_3$ and CrGeTe$_3$ in the majority-spin channel. The dominant Te $p$ antibonding character in the valence bands just below the Fermi level is related to the decrease of the bandgap for the increase of $U$. We elucidate the energy band diagram, which may serve to understand the electronic and magnetic properties of the $ABX_3$-type transition metal tri-chalcogenides in general.