Huang, PingSchonenberger, ThomasCantoni, MarcoHeinen, LukasMagrez, ArnaudRosch, AchimCarbone, FabrizioRonnow, Henrik M.2020-06-302020-06-302020-06-302020-06-1510.1038/s41565-020-0716-3https://infoscience.epfl.ch/handle/20.500.14299/169699WOS:0005404064000021807.08352While in 3D materials melting is a single, first-order phase transition, in 2D systems, it can also proceed via an intermediate phase. For a skyrmion lattice in Cu2OSeO3, magnetic field variations can tune this quasiparticle 2D solid into a skyrmion liquid via an intermediate hexatic phase with short-range translational and quasi-long-range orientational order. The phase transition most commonly observed is probably melting, a transition from ordered crystalline solids to disordered isotropic liquids. In three dimensions, melting is a single, first-order phase transition. In two-dimensional systems, however, theory predicts a general scenario of two continuous phase transitions separated by an intermediate, oriented liquid state, the so-called hexatic phase with short-range translational and quasi-long-range orientational orders. Such hexatic phases occur in colloidal systems, Wigner solids and liquid crystals, all composed of real-matter particles. In contrast, skyrmions are countable soliton configurations with non-trivial topology and these quasi-particles can form two-dimensional lattices. Here we show, by direct imaging with cryo-Lorentz transmission electron microscopy, that magnetic field variations can tune the phase of the skyrmion ensembles in Cu(2)OSeO(3)from a two-dimensional solid through the long-speculated skyrmion hexatic phase to a liquid. The local spin order persists throughout the process. Remarkably, our quantitative analysis demonstrates that the aforementioned topological-defect-induced crystal melting scenario well describes the observed phase transitions.Nanoscience & NanotechnologyMaterials Science, MultidisciplinaryScience & Technology - Other TopicsMaterials Scienceorderdisordertext::journal::journal article::research article