Magnetic and thermodynamic properties of ${\mathrm{Li}}_2{\mathrm{VOSiO}}_4:$ A two-dimensional $S=1/2\mathrm{}$ frustrated antiferromagnet on a square lattice

NMR, muon spin rotation $\left(\mu \mathrm{SR}\right),$ magnetization, and specific-heat measurements in ${\mathrm{Li}}_2{\mathrm{VOSiO}}_4$ powders and single crystals are reported. Specific-heat and magnetization measurements evidence that ${\mathrm{Li}}_2{\mathrm{VOSiO}}_4$ is a frustrated two-dimensional $S=1/2\mathrm{}$ Heisenberg antiferromagnet on a square lattice with a superexchange coupling $J_1,$ along the sides of the square, almost equal to $J_2,$ the one along the diagonal ${(J}_2{/J}_1=1.1\mathrm{}\pm 0.1$ with $J_2{+J}_1=8.2\mathrm{}\pm 1\hspace{0.5em}\mathrm{K}).\mathrm{}$ At $T_c\simeq 2.8\hspace{0.5em}\mathrm{K}$ a phase transition to a low-temperature collinear order is observed. $T_c$ and the sublattice magnetization, derived from NMR and $\mu \mathrm{SR},$ were found practically independent on the magnetic field intensity up to 9 T. The critical exponent of the sublattice magnetization was estimated β≃0.235, nearly coincident with the one predicted for a two-dimensional $\mathrm{XY}$ system on a finite size. The different magnetic properties found above and below $T_c$ are associated with the modifications in the spin Hamiltonian arising from a structural distortion occurring just above $T_c.$