Ab initio calculation of the effective Coulomb interactions in MX2 (M=Ti,V,Cr,Mn,Fe,Co,Ni;X=S,Se,Te) : Intrinsic magnetic ordering and Mott phase

Abstract

Correlated phenomena such as magnetism and the Mott phase are a very controversial issues in two-dimensional transition metal dichalcogenides (TMDCs). Intending to find the value of the correlation strength and understanding the origin of ferromagnetic order in TMDCs, we first identify relevant, low-energy degrees of freedom on both octahedral $1T$ and trigonal prismatic $2H$ structures in $3d\text{\ensuremath{-}}M{X}_{2}$ ($M=\mathrm{Ti},\mathrm{V},\mathrm{Cr},\mathrm{Mn},\mathrm{Fe},\mathrm{Co},\mathrm{Ni};X=\mathrm{S},\mathrm{Se},\mathrm{Te}$) and then determine the strength of the effective Coulomb interactions between localized $d$ electrons from the first principles using the constrained random-phase approximation. The on-site Coulomb interaction values lie in the range $1.4--3.7\phantom{\rule{0.16em}{0ex}}\mathrm{eV} (1.1--3.6\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$ for the $1T$ structure ($2H$ structure) and depend on the ground-state electronic structure, $d$-electron number, and correlated subspace. For most of the $3d$-TMDCs, we obtain $1<U/{W}_{b}<2$ (the bandwidth ${W}_{b}$), which turn out to be larger than the corresponding values in elementary transition metals. Based on the calculated $U$ and exchange $J$ interaction, we check the condition to be fulfilled for the formation of the ferromagnetic order by the Stoner criterion. The results indicate that experimentally observed $\mathrm{Mn}{X}_{2}$ ($X=\text{S}$, Se) and $\mathrm{V}{X}_{2}$ ($X=\text{S}$, Se) have an intrinsic ferromagnetic behavior in pristine form, although V-based materials are close in vicinity to the critical point separating the ferromagnetic from the paramagnetic phase.