Determination of the exchange energies in ${\mathrm{Li}}_2{\mathrm{VOSiO}}_4$ from a high-temperature series analysis of the square-lattice $J_1{-J}_2$ Heisenberg model

We present a high-temperature expansion (HTE) of the magnetic susceptibility and specific heat data of Melzi et al. on ${\mathrm{Li}}_2{\mathrm{VOSiO}}_4$ [Phys. Rev. B 64, 024409 (2001)]. The data are very well reproduced by the $J_1-J_2$ Heisenberg model on the square lattice with exchange energies $J_1=1.25\mathrm{}\pm 0.5\mathrm{K}$ and $J_2=5.95\mathrm{}\pm 0.2\mathrm{K}.$ The maximum of the specific heat $C_v^{\max }{(T}_{\max })$ is obtained as a function of $J_2{/J}_1$ from an improved method based on HTE.