Dynamical correlations in single-layer ${\mathrm{CrI}}_3$

Chromium triiodide is an intrinsically magnetic van der Waals material down to the single-layer limit. Here, we provide a first-principles description of finite-temperature magnetic and spectral properties of monolayer (ML) ${\mathrm{CrI}}_3$ based on fully charge self-consistent density functional theory (DFT) combined with dynamical mean-field theory, revealing a formation of local moments on Cr from strong local Coulomb interactions. We show that the presence of local dynamical correlations leads to a modification of the electronic structure of ferromagnetically ordered ${\mathrm{CrI}}_3$. In contrast to conventional $\mathrm{DFT}+U$ calculations, we find that the top of the valence band in ML ${\mathrm{CrI}}_3$ demonstrates essentially different orbital character for minority and majority spin states, which is closer to the standard DFT results. This leads to a strong spin polarization of the optical conductivity upon hole doping, which could be verified experimentally.

Figure 1

Comparison between the spectral densities obtained using different methods for ferromagnetic ML ${\mathrm{CrI}}_3$. The Fermi level ($E_F$) is at zero energy.

Figure 2

Spin-up and spin-down parts of the charge self-consistent $\mathrm{DFT}+\mathrm{DMFT}$-derived spectral functions for ML ${\mathrm{CrI}}_3$.

Figure 3

Comparison of the calculated optical conductivity tensor components ${\sigma }_{xx}$ and ${\sigma }_{zz}$ obtained from DFT, $\mathrm{DFT}+U$, and $\mathrm{DFT}+\mathrm{DMFT}$. Bottom panel: experimental data from Ref. [17].

Figure 4

$\mathrm{DFT}+\mathrm{DMFT}$-derived optical conductivity ${\sigma }_{xx}$ projected onto spin-up (top panel) and spin-down (bottom panel) contributions, obtained for different doping concentrations.