Thermal Hysteresis Behavior of Skyrmion Lattices in the van der Waals Ferromagnet Fe3GeTe2

Understanding the physics of phase transitions in two-dimensional (2D) systems underpins the research in diverse fields including statistical mechanics, quantum systems, nanomagnetism, and soft condensed matter. However, many fundamental aspects of 2D phase transitions are still not well understood, including the effects of interparticle potential, polydispersity, and particle shape. Magnetic skyrmions, which are non-trivial chiral spin structures, can be considered as quasi-particles that form two-dimensional lattices. Here we show, by real-space imaging using in situ cryo-Lorentz transmission electron microscopy coupled with machine learning, the ordering behavior of N\'eel skyrmion lattices in van der Waals Fe3GeTe2. We demonstrate a distinct change in the skyrmion size distribution during field-cooling, which leads to a loss of lattice order and an evolution of the skyrmion liquid phase. Remarkably, the lattice order is restored during field heating and demonstrates a thermal hysteresis. Our quantitative analysis explains this behavior based on the energy landscape of skyrmions and demonstrates the potential to control the lattice order in 2D phase transitions.