Coulomb-interaction effect on the two-dimensional electronic structure of the van der Waals ferromagnet Cr2Ge2Te6

In order to investigate the electronic properties of the semiconducting van der Waals ferromagnet $\mathrm{C}{\mathrm{r}}_{2}\mathrm{G}{\mathrm{e}}_{2}\mathrm{T}{\mathrm{e}}_{6}$ (CGT), where ferromagnetic layers are bonded through van der Waals forces, we have performed angle-resolved photoemission spectroscopy measurements and density-functional theory $(\mathrm{DFT}+U)$ calculations. The valence-band maximum at the $\mathrm{\ensuremath{\Gamma}}$ point is located $\ensuremath{\sim}0.2\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ below the Fermi level, consistent with the semiconducting property of CGT. Comparison of the experimental density of states with the DFT calculation has suggested that Coulomb interaction between the Cr $3d$ electrons ${U}_{\mathrm{eff}}\ensuremath{\sim}1.1\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$. The $\mathrm{DFT}+U$ calculation indicates that magnetic coupling between Cr atoms within the layer is ferromagnetic if Coulomb ${U}_{\mathrm{eff}}$ is smaller than 3.0 eV and that the interlayer coupling is ferromagnetic below ${U}_{\mathrm{eff}}\ensuremath{\sim}1.0\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$. We therefore conclude that, for ${U}_{\mathrm{eff}}$ deduced by the experiment, the intralayer Cr-Cr coupling is ferromagnetic and the interlayer coupling is near the boundary between ferromagnetic and antiferromagnetic, which means experimentally deduced ${U}_{\mathrm{eff}}$ is consistent with the theoretical ferromagnetic condition.