Pressure evolution of electronic structure and magnetism in the layered van der Waals ferromagnet CrGeTe$_3$

Layered van der Waals ferromagnets, which preserve their magnetic properties down to exfoliated monolayers, are fueling a bonanza of fundamental research and nanoscale device demonstration. CrGeTe$_3$ is a prime example for this class of materials. Its temperature-pressure phase diagram features an insulator-to-metal transition and a significant increase of ferromagnetic Curie-Weiss temperatures upon entering the metallic state. We use density functional theory to understand the magnetic exchange interactions in CrGeTe$_3$ at ambient and elevated pressure. We calculate Heisenberg exchange couplings, which provide the correct ferromagnetic ground state and explain the experimentally observed pressure dependence of magnetism in CrGeTe$_3$. Furthermore, we combine density functional theory with dynamical mean field theory to investigate the effects of electronic correlations and the nature of the high pressure metallic state in CrGeTe$_3$.