Melting of Néel skyrmion lattice

Melting of a particle lattice in two dimensional systems substantially differs from the one in three dimensions. The most prominent theory of the lattice melting in 2D, formulated by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY), describes the solid-liquid phase transition as a two-step process, where the solid phase turns into the liquid via the hexatic phase. The microscopic nature of this process lies in the excitation and unbinding of topological defects in the 2D lattice. The KTHNY melting scenario has been observed in number of 2D physical systems. Here, we theoretically analyze the melting process of a N\'eel skyrmion lattice by means of numerical simulations using a model of lacunar spinel ${\mathrm{GaV}}_{4}{\mathrm{S}}_{8}$ hosting hexagonal skyrmion lattice at low temperatures. We show that topological defects are excited in such skyrmion lattice causing its melting via the hexatic phase in agreement with the KTHNY theory.