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We study a triangular frustrated antiferromagnetic Heisenberg model withnearest-neighbor interaction $J_{1}$ and third-nearest-neighbor interactions$J_{3}$ by means of Schwinger-boson mean-field theory. It is shown that anincommensurate phase exists in a finite region in the parameter space for anantiferromagnetic $J_{3}$ while $J_{1}$ can be either positive or negtaive. Adetailed solution is presented to disclose the main features of thisincommensurate phase. A gapless dispersion of quasiparticles leads to theintrinsic $T^{2}$-law of specific heat. The local magnetization issignificantly reduced by quantum fluctuations (for S=1 case, a localmagnetization is estimated as $m=<S_{i}> \approx0.6223$). The magneticsusceptibility is linear in temperature at low temperatures. We addresspossible relevance of these results to the low-temperature properties ofNiGa$_{2}$S$_{4}$. From a careful analysis of the incommensurate spin wavevector, 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 theexperimental data.

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