Competing interactions and continuum excitations in the spin-1 triangular lattice antiferromagnet NiGa$_{2}$S$_{4}$*

In some geometrically frustrated magnets, conventional long range order is replaced by static or dynamic short range order. Quasi-2D NiGa$_{2}$S$_{4}$ is the only known S=1 antiferromagnet with an exact triangular lattice. Recent neutron scattering experiment on high quality NiGa$_{2}$S$_{4 }$single crystals revealed short range quasi-2D incommensurate spin correlation with a critical wavevector close to (1/6, 1/6, 0) [1]. Here we report a measurement of the dynamic spin correlation function through a volume of \textbf{Q}-E space for T$<<$J. A gapless spectrum was observed at the incommensurate critical wavevector while a softened but still gapped response was found at (1/3, 1/3, 0). This indicates dominant third nearest neighbor interaction and competing weaker near neighbor interactions. The excitation spectrum takes the form of a bounded continuum throughout the 2D Brillouin zone. The temperature dependence dynamic correlation length shows that short range correlation persist up to $\Theta _{cw}$=-80(2)K. \\[0pt] [1] C.Stock, \textit{et al, }Phys.Rev.Lett.105,037402 (2010)