Electronic structure and magnetism of the Hund's insulator CrI3

${\mathrm{CrI}}_{3}$ is a two-dimensional ferromagnetic (FM) van der Waals material with a charge gap of 1.1--1.2 eV. In this paper, the electronic structure and magnetism of ${\mathrm{CrI}}_{3}$ are investigated by using density functional theory and dynamical mean-field theory. Our calculations successfully reproduce a charge gap of $\ensuremath{\sim}1.1\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ in the paramagnetic (PM) state when a Hund's coupling ${J}_{\mathrm{H}}=0.7\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ is included with an onsite Hubbard $U=5\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$. In contrast, with a large $U$ value of 8 eV and negligible Hund's coupling ${J}_{\mathrm{H}}, {\mathrm{CrI}}_{3}$ is predicted to be a moderately correlated metal in the PM state. We conclude that ${\mathrm{CrI}}_{3}$ is a Mott-Hund's insulator due to the half-filled configuration of the Cr $3d {t}_{2g}$ orbitals. The Cr $3d {e}_{g}$ orbitals are occupied by $\ensuremath{\sim}1$ electron, which leads to strong valence fluctuations so that the Cr $3d$ orbitals cannot be described by a single state. Moreover, at finite temperature, the calculated ordered static magnetic moment in the FM state is significantly larger in the $R\overline{3}$ phase than in the $C2/m$ phase. This observation indicates that the structural phase transition from the $C2/m$ phase to the $R\overline{3}$ phase with decreasing temperature is driven by FM spin fluctuations.