DdG-like transitions in other topological spin textures

Determine what types of Dzyaloshinskii–de Gennes-like transitions arise from other topological spin textures, including skyrmions and merons, at finite temperature, in analogy with the dependence of the Lifshitz point’s upper critical dimension on the modulation dimension.

Background

The paper constructs a three-dimensional classical Heisenberg model with Dzyaloshinskii–Moriya interaction and three-state anisotropy. Its winding-to-ferromagnetic transition exhibits Dzyaloshinskii–de Gennes (DdG) or nucleation-type criticality: the transition is continuous in physical quantities and has a logarithmically diverging winding length, yet displays first-order-like critical exponents and an extensive set of free-energy minima.

The authors relate this behavior to commensurate–incommensurate transitions and to possible helical phases associated with deconfined quantum criticality. They note that the observed transition motivates investigating whether analogous DdG-like critical behavior occurs for other finite-temperature topological textures, such as skyrmions and merons, with the Lifshitz-point analogy suggesting that the relevant critical behavior may depend on the dimensionality of the modulation.