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Understanding the physics of phase transitions in two-dimensional (2D)systems underpins the research in diverse fields including statisticalmechanics, 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 particleshape. Magnetic skyrmions, which are non-trivial chiral spin structures, can beconsidered as quasi-particles that form two-dimensional lattices. Here we show,by real-space imaging using in situ cryo-Lorentz transmission electronmicroscopy coupled with machine learning, the ordering behavior of N\'eelskyrmion lattices in van der Waals Fe3GeTe2. We demonstrate a distinct changein the skyrmion size distribution during field-cooling, which leads to a lossof lattice order and an evolution of the skyrmion liquid phase. Remarkably, thelattice order is restored during field heating and demonstrates a thermalhysteresis. Our quantitative analysis explains this behavior based on theenergy landscape of skyrmions and demonstrates the potential to control thelattice order in 2D phase transitions.

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