Ferromagnetic Heisenberg model with the Dzyaloshinskii-Moriya interaction

Abstract

The spin-1/2 Heisenberg model is formulated in terms of a mean-field approximation (MFA) by using the matrix forms of spin operators Ŝ_x, Ŝ_y and Ŝ_z in three-dimensions. The considered Hamiltonian consists of bilinear exchange interaction parameters (J_x, J_y, J_z), Dzyaloshinskii-Moriya interactions (Δ_x, Δ_y, Δ_z) and external magnetic field components (H_x, H_y, H_z). The magnetization and its components are obtained in the MFA with the general anisotropic case with J_x ≠ J_y ≠ J_z for various values of coordination numbers q. Then, the thermal variations of magnetizations are investigated in detail to obtain the phase diagrams of the model for the isotropic case with J_x = J_y = J_z > 0. It is found that the model exhibits ferromagnetic, paramagnetic, random phase regions and an extra ferromagnetic phase at which the components of magnetizations present branching.

Keywords

• spin 1/2
• ferromagnetic
• dzyaloshinskii-moriya
• xyz model
• magnetization
• phase diagrams