The Antiferromagnetic Spin-1 XYZ model

Using the series expansion of exponentials for the spin matrices, the antiferromagnetic spin-1 XYZ model with Dzyaloshinskii-Moriya interaction (DMI) is investigated in the mean-field approximation (MFA). The Hamiltonian includes the bilinear interaction parameters [Formula: see text], the external magnetic field [Formula: see text], and the DMI parameter ([Formula: see text]) in three-dimensional component form. For the coordination numbers of four, their effects are taken into account for the sublattice magnetization components. In order to compute the phase diagrams on the ([Formula: see text]) and ([Formula: see text]) planes, the temperature variations of magnetizations are thoroughly investigated. Ferromagnetic (FM), antiferromagnetic (AFM), and random or oscillatory phase regions (R) are found in the model. Only when DMI is disabled does the AFM phase appear. Additionally, it is discovered that the R and AFM phases either only exhibit second-order phase transitions or are indistinguishable due to the erratic behaviors displayed by the magnetizations.