Direct observation of competition between charge order and itinerant ferromagnetism in the van der Waals crystal Fe 5 − x GeTe 2

The interplay of symmetry-breaking ordered states, such as superconductivity, charge density waves, magnetism, and pseudogaps, is a fundamental issue in correlated systems. Periodic modulation and antiferromagnetism often coexist in the proximity of phase diagram region in high-${T}_{c}$ superconductors. It is also worth noting that different order states appear in a situation on comparable temperature scales, so these orders are intertwined and competing on the same footing. The magnetism of vdW material ${\mathrm{Fe}}_{5\ensuremath{-}x}{\mathrm{GeTe}}_{2}$, with one of the highest reported bulk Curie temperatures, is found to be sensitive to thermal history and external magnetic field. However, the temperature-dependent magnetization with two characteristic points still lacks a unified picture to describe it. Using angle-resolved photoemission spectroscopy, scanning tunneling microscopy, magnetic property measurements, and first-principles calculations, the complex yet intriguing magnetic behaviors are gradually unveiled. A competition mechanism between charge order and ferromagnetism is proposed and firmly observed by experimental measurements. As the ferromagnetic order strengthens at low temperature, the charge order will be suppressed. Exchange splitting in itinerant ferromagnetism plays a significant role in the temperature evolution of band structure and causes a Lifshitz transition, which provides more control means to realize novel devices at room temperature.