Li${}_2$VO(Si,Ge)O${}_4$, a prototype of a two-dimensional frustrated quantum Heisenberg antiferromagnet

NMR and magnetization measurements in Li${}_2$VOSiO${}_4$ and Li${}_2$VOGeO${}_4$ are reported. The analysis of the susceptibility shows that both compounds are two-dimensional $S=1\mathrm{/}2$ Heisenberg antiferromagnets on a square lattice with a sizeable frustration induced by the competition between the superexchange couplings $J_1$ along the sides of the square and $J_2$ along the diagonal. Li${}_2$VOSiO${}_4$ undergoes a low-temperature phase transition to a collinear order, as theoretically predicted for $J_2\mathrm{/}{J}_1>0.5$. Just above the magnetic transition the degeneracy between the two collinear ground states is lifted by the onset of a structural distortion.