Strength of effective Coulomb interaction in two-dimensional transition-metal Halides MX$_2$ and MX$_3$ (M=Ti, V, Cr, Mn, Fe, Co, Ni; X=Cl, Br, I)

Abstract

We calculate the strength of the effective onsite Coulomb interaction (Hubbard U ) in two-dimensional (2D) transition-metal (TM) dihalides MX2 and trihalides MX3 (M=Ti, V, Cr, Mn, Fe, Co, Ni; X=Cl, Br, I) from first principles using the constrained random-phase approximation. The correlated subspaces are formed from t2g or eg bands at the Fermi energy. Elimination of the efficient screening taking place in these narrow bands gives rise to sizable interaction parameters U between the localized t2g (eg) electrons. Due to this large Coulomb interaction, we find U/W >1 (with the band width W ) in most TM halides, making them strongly correlated materials. Among the metallic TM halides in paramagnetic state, the correlation strength U/W reaches a maximum in NiX2 and CrX3 with values much larger than the corresponding values in elementary TMs and other TM compounds. Based on the Stoner model and the calculated U and J values, we discuss the tendency of the electron spins to order ferromagnetically.