Incommensurate Phase of a Triangular Frustrated Heisenberg Model Studied via Schwinger-Boson Mean-Field Theory

We study a triangular frustrated antiferromagnetic Heisenberg model with nearest-neighbor interaction $J_{1}$ and third-nearest-neighbor interactions $J_{3}$ by means of Schwinger-boson mean-field theory. It is shown that an incommensurate phase exists in a finite region in the parameter space for an antiferromagnetic $J_{3}$ while $J_{1}$ can be either positive or negtaive. A detailed solution is presented to disclose the main features of this incommensurate phase. A gapless dispersion of quasiparticles leads to the intrinsic $T^{2}$-law of specific heat. The local magnetization is significantly reduced by quantum fluctuations (for S=1 case, a local magnetization is estimated as $m=<S_{i}> \approx0.6223$). The magnetic susceptibility is linear in temperature at low temperatures. We address possible relevance of these results to the low-temperature properties of NiGa$_{2}$S$_{4}$. From a careful analysis of the incommensurate spin wave vector, the interaction parameters for NiGa$_{2}% $S$_{4}$ are estimated as, $J_{1}\approx-3.8755$K and $J_{3}\approx14.0628$K, in order to account for the experimental data.