Topological defects and critical phenomena in two-dimensional frustrated helimagnets

Abstract

Using a simple model of a frustrated helimagnet, the critical behavior is numerically investigated for planar or isotropic spins, and for cases of one or two chiral order parameters. The helical structure in this model arises from the competition between exchange interactions of spins of the first two range orders in one direction (in both directions) of a square lattice. The main result is that the critical and temperature behavior is primarily determined by topological defects that are present in all cases. In the case of planar spins, vortices, fractional vortices and domain walls are present in the system. Their interaction leads to the appearance of the phase of a chiral spin liquid, or induces a single first-order transition, and in the vicinity of the Lifshitz point vortices lead to a reentrant phase transition to the phase with a collinear quasi-long-range order. When transitions in the chiral and continuous order parameters are separated in temperature, they are of the 2D Ising and Kosterlitz-Thouless types correspondingly. In the case of isotropic spins, so-called $\mathbb{Z}_2$ vortices are present. They do not lead to the appearance of a phase with long-range or quasi-long-range order in the case of one chiral order parameter. However, their interaction leads to a sharp change in the temperature dependence of the correlation length (crossover). In the case of two chiral parameters, there are long-range chiral order of the Ising type (chiral spin liquid) and domain walls. However, as a result of the interaction of vortices and walls, the crossover and chiral transition occur at the same temperature as a first-order transition.