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Static and dynamic properties of the quasi-two-dimensional antiferromagnetK$_2$V$_3$O$_8$ have been investigated by $^{51}$V-NMR experiments onnonmagnetic V$^{5+}$ sites. Above the structural transition temperature$T_{\rm{S}}$ = 115 K, NMR spectra are fully compatible with the $P4bm$ spacegroup symmetry. The formation of superstructure below $T_{\rm{S}}$ causessplitting of the NMR lines, which get broadened at lower temperatures so thatindividual peaks are not well resolved. Evolution of NMR spectra with magneticfield along $c$-axis below the magnetic transition temperature $T_{\rm{N}} \sim4$ K is qualitatively consistent with a simple N\'{e}el order and a spin floptransition. However, broad feature of the spectra does not rule out possibleincommensurate spin structure. The spin-lattice relaxation rate $1/T_1$ below$T_{\rm{N}}$ shows huge enhancement for a certain range of magnetic field,which is independent of temperature and attributed to cross relaxation due toanomalously large nuclear spin-spin coupling between V$^{5+}$ and magneticV$^{4+}$ sites. The results indicate strong gapless spin fluctuations, whichcould arise from incommesurate orders or complex spin textures.

51V-NMR study on the S=1/2 square lattice antiferromagnet K2V3O8