Strength of effective Coulomb interaction in two-dimensional transition-metal halides MX2 and MX3 (M = Ti, V, Cr, Mn, Fe, Co, Ni; X = Cl, Br, I)

We calculate the strength of the effective on-site Coulomb interaction (Hubbard U) in two-dimensional 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 t(2g) or e(g) 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 t(2g) (e(g)) electrons. Due to this large Coulomb interaction, we find U/W > 1 (with the bandwidth W) in most TM halides, making them strongly correlated materials. Among the metallic TM halides in the 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.