No abstract

We studied two classical Heisenberg spin models on a lattice, with a discrete choice of spin states, with ferromagnetic interactions in competition with Dzyaloshinskii-Moriya interactions.In the first part of this work, we consider a model of four states only, which we call DM4, and which corresponds to the chiral clock model, which has been widely explored in the literature.We analyzed this DM4 model in several situations: (i) in one dimension, using the transfer matrix technique, obtaining indications about the ground state of the more realistic counterpart in three dimensions: (ii) on a Cayley tree, which leads to a phase diagram with the indication of the existence of spacial modulated structures; (iii) in a mean-field approach, in which it is relatively simple to obtain the boundaries of the disordered structures. Using the experience we have gained with the DM4 model, we have gone through the same steps to analyze a six-state model, with spin states along the Cartesian directions, which we call DM6, and which is a minimal model for a Heisenberg Hamiltonian with the addition of Dzyaloshinskii-Moriya interactions along one of the crystalline axes. We obtained several results for the global phase diagram in the limit of infinite coordination of a Cayley tree, and presented numerical evidence to show the existence of fractal structures known as "devil's staircases". In the final part of this study on the DM6 model, we sketched a mean-field solution of this problem. Also, we sketched an ongoing work, which is based on defining and analyzing a spherical version of the Heisenberg model with the addition of monoaxial interactions of the Dzyaloshinskii-Moriya type.

We analyze the thermodynamic behavior of a ferromagnetic mean-spherical model with three distinct spin components and the addition of Dzyaloshinkii–Moriya interactions. Exact calculations are performed for classical and quantum versions of this lattice model system. We show the onset of space modulated structures at low temperatures.