NMR in the high-field magnetic phase of LiCuVO$_4$

LiCuVO$_4$ is a quasi-one-dimensional antiferromagnetic spin-$1/2$ system with strong magnetic frustration due to competing interactions within the Cu spin chain. Consequently, a complex magnetic phase diagram with three critical magnetic field values evolves [arXiv:1005.5668]. Furthermore, spiral spin order below $T_{\mathrm{N}}$=2.7K induces ferroelectricity thus rendering LiCuVO$_4$ multiferroic. The ferroelectric polarization can be switched by reorienting the spin helix through application of external magnetic fields [PRB \textbf{77}, 144101 (2008)]. Above $H>H_{\mathrm{c}2}$ LiCuVO$_4$ becomes paraelectric and the magnetic order changes to a collinear spin-modulated phase. Employing Nuclear Magnetic Resonance we study the nature of this high-field phase by analysis of $^7$Li and $^{51}$V spectra recorded around $H>H_{\mathrm{c}2}$=7.5T. We find, together with simulations for different scenarios, that Cu-spins of neighboring planes along the c-axis have a random phase-relation thus implying a two-dimensional character of the spin order [PRB \textbf{77}, 144101 (2008)].