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

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 $dp\ddot{I}ƒ$-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 $AB{X}_3$-type transition metal tri-chalcogenides in general.

4 pages, 3 figures