Abstract

The spin-1/2 antiferromagnetic (AFM) Heisenberg model is considered in the mean-field approximation in terms of the spin operators $Ŝ_{x}, Ŝ_{y}$ and $Ŝ_{z}$ in the matrix forms with the introduction of bilinear exchange interaction ( $J_{μ}$ ), the Dzyaloshinskii–Moriya interaction (DMI) ( $Δ_{μ}$ ) and external magnetic fields ( $H_{μ}$ ) into the Hamiltonian in three dimensions. The thermal changes of sublattice magnetizations $M_{μ}^{A}$ and $M_{μ}^{B}$ 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 $q = 3, 4$ 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 $Δ_{μ} \neq 0.0$ , between FM and AFM when $Δ_{μ} = 0.0$ only and, AFM and R at low temperatures for very small $Δ_{μ}$ and $H_{μ}$ values.

Keywords:

PACS: 75.10.Hk, 75.30.Kz, 75.50.Ee

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