Tracing the disentangled charge and spin fluctuations in ferromagnetic CrGeTe$_{3}$</inline-formula> with charge gap evolution

The interplay between electronic correlation and magnetism in transition-metal compounds is a topic of great importance in condensed matter physics.These two driving forces are often highly entangled, making it difficult to separate their effects macroscopically in real materials.Visualizing the individual influence of these mechanisms in magnetic materials has proven challenging.In this study, we propose a protocol to characterize the leading couplings in correlated magnetic materials.By combining surface electron-dosing in angle-resolved photoemission spectroscopy with advanced many-body calculations, we investigate the cooperation and competition between electronic correlation and magnetism in van der Waals (vdW) ferromagnetic CrGeTe$_{3}$.Our results on the charge-gap evolution strongly reveal the persistence of local moment fluctuations on an interacting background of electrons as the leading couplings that fundamentally determine the electronic structure.Our findings provide a realistic route to qualitatively disassemble the interplay between charge and spin fluctuations in low-dimensional ferromagnetic materials, with potential implications for spintronic applications that utilize them individually.This work represents a significant step forward in our understanding of the complex relationship between electronic correlation and magnetism in transition-metal compounds.