Skyrmions are twirling magnetic textures whose non-trivial topology leads to particle-like properties promising for information technology applications. Perhaps the most important aspect of interacting particles is their ability to form thermodynamically distinct phases from gases and liquids to crystalline solids. Dilute gases of skyrmions have been realized in artificial multilayers, and solid crystalline skyrmion lattices have been observed in bulk skyrmion hosting materials. Yet, to date melting of the skyrmion lattice into a skyrmion liquid has not been reported experimentally. Through direct imaging with cryo-Lorentz transmission electron microscopy, we demonstrate that the skyrmion lattice in the material Cu$_2$OSeO$_3$ can be dynamically melted. Remarkably, we discover this melting process to be a topological defects mediated two-step transition via a theoretically hypothesized hexatic phase to the liquid phase. The existence of hexatic and liquid phases instead of a simple fading of the local magnetic moments upon thermal excitations implies that even in bulk materials skyrmions possess considerable particle nature, which is a pre-requisite for application schemes.
Addressing the nature of an unexpected smectic-A' phase in liquid crystal 54COOBC films, we perform large scale Monte Carlo simulations of a coupled hexatic-nematic XY model. The resulting finite-temperature phase diagram reveals a small region with composite Potts $\mathbb{Z}_3$ order above the vortex binding transition; this phase is characterized by relative hexatic-nematic ordering though both variables are disordered. The system develops algebraic hexatic and nematic order only at a lower temperature. This multi-step melting scenario agrees well with the experimental observations of a sha…
In a $β$-Mn-type chiral magnet Co$_9$Zn$_9$Mn$_2$, we demonstrate that the magnetic field-driven collapse of a room temperature metastable topological skyrmion lattice passes through a regime described by a partial topological charge inversion. Using Lorentz transmission electron microscopy, the magnetization distribution was observed directly as the magnetic field was swept antiparallel to the original skyrmion core magnetization, i.e. negative magnetic fields. Due to the topological stability of skyrmions, a direct transition of the metastable skyrmion lattice to the equilibrium helical stat…
Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex superso…
We study crystal melting in two-dimensional antiferromagnets, by analyzing the statistical mechanics of the six-state clock model on a lattice in which defects (dislocations and disclinations) are allowed to appear. We show that the elementary dislocations bind to fractional magnetic vortices. We compute the phase diagram by mapping the system into a Coulomb gas model. Surprisingly, we find that in the limit of dominant magnetic interactions, antiferromagnetism can survive even in the hexatic and liquid phases. The ensuing molten antiferromagnets are topologically ordered and are characterized…
