Simple Ising ferromagnet with chiral interactions

We introduce a minimum Ising model with two different types of ferromagnetically interacting spin variables and the addition of chiral interactions according to the suggestions of the Dzyaloshinskii-Moryia mechanism to account for the onset of helical structures in magnetic systems. The investigation of the phase diagram on a Cayley tree is reduced to the analysis of the attractors of a discrete nonlinear map. This elementary system presents a complex phase behavior, which is reminiscent of the spatially modulated structures in the well-known axial next-nearest-neighbor Ising model of magnetism. We characterize the presence of some ordered as well as a certain number of modulated structures. Also, we sketch a layer-by-layer mean-field calculation for the phase diagram of a similar monoaxial Ising system on a cubic lattice.