The \(120^{0}\) ordered phase of the spin-1 \(J_{1} - J_{2}\) antiferromagnetic Heisenbeberg model on a triangular lattice

We study the effect of quantum and thermal fluctuations on the excitation energy spectrum and sublattice magnetization of the 1200 ordered phase of the spin-1 antiferromagnetic Heisenberg model on a triangular lattice with nearest J1 and next-nearest-neighbor J2 exchange interactions. The auxiliary fermionic representation of the spin operators within a functional integral formalism with an imaginary Lagrange multiplier is employed to retain an exact constraint of single particle occupancy. Representing the classical ground state by Luttinger-Tisza ordering vector Q one may consider the fluctuation contributions to the free energy of the system in the entire range of the coupling parameters. We derived the magnon spectrum in one-loop approximation and the magnetization taking into account thermal fluctuations. The obtained results are compared with the result of the linear spin-wave approximation and experimental findings on compound NiGa2S4.