The Dzyaloshinskii–Moriya interaction effects in antiferromagnetic Heisenberg model

The spin-1/2 antiferromagnetic (AFM) Heisenberg model is considered in the mean-field approximation in terms of the spin operators [Formula: see text] and [Formula: see text] in the matrix forms with the introduction of bilinear exchange interaction ([Formula: see text]), the Dzyaloshinskii–Moriya interaction (DMI) ([Formula: see text]) and external magnetic fields ([Formula: see text]) into the Hamiltonian in three dimensions. The thermal changes of sublattice magnetizations [Formula: see text] and [Formula: see text] are investigated in the isotropic case to identify the critical behaviors displayed by the system. The phase diagrams are illustrated on various planes of system parameters for given coordination numbers [Formula: see text] and 6. In addition, the graphs of the magnetization components in the same directions were drawn against each other and very interesting results were obtained. The model exhibits the ordered phases, i.e., AFM, ferromagnetic (FM), and a phase with random or oscillatory behavior (R). The phase transitions are observed between FM and R phases when for all [Formula: see text], between FM and AFM when [Formula: see text] only and, AFM and R at low temperatures for very small [Formula: see text] and [Formula: see text] values.