Strength of effective Coulomb interaction in two-dimensional transition-metal halides <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mi>Ti</mml:mi></mml:mrow></mml:math>, V, Cr, Mn, Fe, Co, Ni; <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>Cl</mml:mi></mml:mrow></mml:math>, Br, I)
Y. Yekta, H. Hadipour, E. Şaşıoğlu, Christoph Friedrich, S. A. Jafari, Stefan Blügel, Ingrid Mertig
Abstract
We calculate the strength of the effective on-site Coulomb interaction (Hubbard $U$) in two-dimensional transition-metal (TM) dihalides $M{X}_{2}$ and trihalides $M{X}_{3}$ ($M=\mathrm{Ti}$, V, Cr, Mn, Fe, Co, Ni; $X=\mathrm{Cl}$, 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 $\mathrm{Ni}{X}_{2}$ and $\mathrm{Cr}{X}_{3}$ 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.