Modulated phases in a spin model with Dzyaloshinskii-Moriya interactions

TL;DR

This paper investigates the phase diagram of a classical spin model with competing isotropic and chiral interactions, revealing para-magnetic transitions and complex modulated structures including devil's staircases.

Contribution

It provides a detailed analysis of modulated phases in a spin model with Dzyaloshinskii-Moriya interactions at both mean-field and Cayley tree levels, highlighting fractal structures.

Findings

Existence of para-magnetic transition lines

Identification of modulated (helimagnetic) phases

Discovery of devil's staircase fractal structures

Abstract

We analyze the phase diagram of an elementary statistical lattice model of classical, discrete, spin variables, with nearest-neighbor ferro-magnetic isotropic interactions in competition with chiral interactions along an axis. At the mean-field level, we show the existence of para-magnetic lines of transition to a region of modulated (helimagnetic) structures. We then turn to the analysis of the analogous problem on a Cayley tree. Taking into account the simplicity introduced by the infinite-coordination limit of the tree, we explore several details of the phase diagrams in terms of temperature and a parameter of competition. In particular, we characterize sequences of modulated (helical) structures associated with devil's staircases of a fractal character.