Ferromagnetic Heisenberg model with the Dzyaloshinskii-Moriya interaction

TL;DR

This paper formulates a mean-field approximation of the spin-1/2 Heisenberg model incorporating Dzyaloshinskii-Moriya interactions, analyzing phase diagrams and magnetic properties under various anisotropic conditions.

Contribution

It introduces a mean-field approach to the anisotropic Heisenberg model with Dzyaloshinskii-Moriya interactions, exploring phase behavior and magnetization in detail.

Findings

Identification of ferromagnetic, paramagnetic, and random phase regions.

Discovery of an additional ferromagnetic phase with branching magnetization components.

Thermal variation analysis of magnetizations for phase diagram determination.

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 $\hat{S}_x,\hat{S}_y$ and $\hat{S}_z$ in three-dimensions. The considered Hamiltonian consists of bilinear exchange interaction parameters $(J_x,J_y,J_z)$, Dzyaloshinskii-Moriya interactions $(\Delta_x,\Delta_y,\Delta_z)$ 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 $J_x\neq J_y \neq J_z$ 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.