We report on a heat capacity study of high quality single crystal samples of lcvo -- a frustrated spin $S=1/2$ chain system -- in magnetic field amounting to 3/4 of the saturation field. At low fields up to about 7~T, a linear temperature dependence
of the specific heat, $C_ppropto T$, resulting from 1D magnetic correlations in the spin chains is followed upon cooling by a sharp lambda anomaly of the transition into a 3D helical phase with $C_ppropto T^3$ behavior at low temperature. The transition from a spin liquid into a spin-modulated (SM) phase at higher fields occurs via a hump-like anomaly which, as the temperature decreases further turns into a $C_ppropto T^2$ law distinctive for a quasi-2D system. We suggest an explanation for how nonmagnetic defects in the Cu$^{2+}$ chains can suppress 3D long-range ordering in the SM phase and leave it undisturbed in a helical phase.
We report on NMR studies of the quasi--1D antiferromagnetic $S=1/2$ chain cuprate LiCuVO$_4$, focusing on the high--field spin--modulated phase observed recently in applied magnetic fields $H > H_{rm c2}$ ($mu_0H_{rm c2} approx 7.5$ T). The NMR spect
ra of $^7$Li and $^{51}$V around the transition from the ordered to the paramagnetic state were measured. It is shown that the spin--modulated magnetic structure forms with ferromagnetic interactions between spins of neighboring chains within the {bf ab}--plane at low temperatures 0.6 K $ < T < T_{rm N}$. The best fit provides evidence that the mutual orientation between spins of neighboring {bf ab}--planes is random. For elevated temperatures $T_{rm N} < T lesssim 15$ K, short--range magnetic order occurs at least on the characteristic time scale of the NMR experiment.
