Ab initio study of the effective Coulomb interactions and Stoner ferromagnetism in M2C and M2CO2 MX−enes (M=Sc,Ti,V,Cr,Fe,Zr,Nb,Mo,Hf,Ta)

Abstract

The $\mathit{MX}$-enes are favorable two-dimensional materials for a wide variety of applications such as electronic and spintronic devices. The quantum confinement effects arising from reduced dimensionality and the presence of narrow $d$ bands suggest the importance of electron correlation effects in these materials. We calculate the strength of the effective screened Coulomb interaction $U$ for pristine ${M}_{2}\mathrm{C}$ and functionalized ${M}_{2}{\mathrm{CO}}_{2} (M=\mathrm{Sc},\mathrm{Ti},\mathrm{V},\mathrm{Cr},\mathrm{Fe},\mathrm{Zr},\mathrm{Nb},\mathrm{Mo},\mathrm{Hf},\mathrm{Ta}) \mathit{MX}$-enes by employing ab initio calculations in conjunction with the random-phase approximation. The calculated $U$ values lie between 1.9 and 5.2 eV and depend on the ground-state electronic structure, $d$-electron number, and chemical functionalization. The $U$ for the $3d$-based systems shows oscillation when $M$ is varied, which can be explained by the $3d$ partial density of states around the Fermi energy. For nonmetallic functionalized $\mathit{MX}$-enes ${M}_{2}{\mathrm{CO}}_{2}$, the reduced dimensionality and the existence of a band gap result in a small screening of the Coulomb interaction. The long-range Coulomb interactions for both ${M}_{2}\mathrm{C}$ and ${M}_{2}{\mathrm{CO}}_{2}$ are also reported. For metallic systems, the interactions turn out to be local, and the nonlocal part is strongly screened due to $d$ states, making metallic $\mathit{MX}$-enes correlated systems. Furthermore, on the basis of the calculated effective Coulomb parameters $U$ and $J$ we discuss the appearance of ferromagnetism at pristine and functionalized $\mathit{MX}$-enes within the Stoner model.