Pair approximation method for anisotropic heisenberg system with biquadratic interaction on centered honeycomb lattice

The magnetic and thermodynamic properties of the spin-1 anisotropic Heisenberg system are studied within pair approximation method. The system contains both the bilinear and biquadratic exchange interactions between the nearest neighboring spins located on a centered honeycomb lattice. For the positive biquadratic exchange interaction parameters, the phase transition in the Heisenberg case is of both second and first order where there is a discontinuity in the thermodynamic properties at this transition temperature. For some negative biquadratic exchange interaction parameters, in both the Heisenberg and Ising cases, the ferromagnetic state changes in favor of the antiferromagnetic state. The frustrated antiferromagnetic structure created by the biquadratic exchange parameter with negative sign was shown significantly influence the magnetization, quadrupolar moment, internal energy, heat capacity, entropy and free energy of the system, where the system has an oscillating chaotic phase regime. Therefore, this study makes an important contribution to the literature in terms of demonstrating the necessary conditions of biquadratic interaction for the formation of an antiferromagnetic phase in the spin-1 Heisenberg system in the centered honeycomb lattice. A double peak behavior was observed in the specific heat, with one at the critical temperature and another at a low temperature.