Effect of Coulomb interaction on the two-dimensional electronic structure of the van der Waals ferromagnet Cr$_2$Ge$_2$Te$_6$

TL;DR

This study combines ARPES measurements and DFT+U calculations to explore how Coulomb interactions influence the electronic structure and magnetic couplings in the semiconducting van der Waals ferromagnet Cr$_2$Ge$_2$Te$_6$, revealing the critical U$_{ m eff}$ values for magnetic behavior.

Contribution

It provides the first combined experimental and theoretical analysis of Coulomb interaction effects on electronic and magnetic properties of Cr$_2$Ge$_2$Te$_6$.

Findings

Valence-band maximum is 0.2 eV below Fermi level, confirming semiconducting nature.

Estimated Coulomb U$_{ m eff}$ for Cr 3d electrons is about 1.1 eV.

Intra-layer ferromagnetic coupling occurs for U$_{ m eff}$ < 3.0 eV, inter-layer ferromagnetic coupling for U$_{ m eff}$ < 1.0 eV.

Abstract

In order to investigate the electronic properties of the semiconducting van der Waals ferromagnet Cr$_2$Ge$_2$Te$_6$ (CGT), where ferromagnetic layers are bonded through van der Waals forces, we have performed angle-resolved photoemission spectroscopy (ARPES) measurements and density-functional-theory (DFT+U) calculations. The valence-band maximum at the {\Gamma} point is located $\sim$ 0.2 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$_{\rm eff}$ $\sim$ 1.1 eV. The DFT+U calculation indicates that magnetic coupling between Cr atoms within the layer is ferromagnetic if Coulomb U $_{\rm eff}$ is smaller than 3.0 eV and that the inter-layer coupling is ferromagnetic below U$_{\rm eff}$ $\sim$ 1.0 eV. We therefore conclude that, for U$_{\rm eff}$ deduced by the experiment, the intra-layer Cr-Cr coupling is ferromagnetic and the inter-layer coupling is near the boundary between ferromagnetic and antiferromagnetic, which means experimentally deduced U$_{\rm eff}$ is consistent with theoretical ferromagnetic condition.