High-temperature expansions for theJ1−J2Heisenberg models: Applications toab initiocalculated models forLi2VOSiO4andLi2VOGeO4

Abstract

We develop high-temperature expansions for the uniform susceptibility and specific heat of the square-lattice ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg models. Combined with a perturbative mean-field theory, we obtain accurate results for the uniform susceptibility of the large-${J}_{2}{/J}_{1}$ Heisenberg model at all temperatures. For the specific heat, the high-temperature expansions show good convergence down to the peak temperature, where the specific heat has a maximum. Exchange couplings are calculated for ${\mathrm{Li}}_{2}{\mathrm{VOSiO}}_{4}({\mathrm{Li}}_{2}{\mathrm{VOGeO}}_{4})$ using local-density approximation (LDA) and found to be ${J}_{1}=0.75\mathrm{K}$ (1.7 K), ${J}_{2}=8.8\mathrm{K}$ (8.1 K), and ${J}_{\ensuremath{\perp}}=0.25\mathrm{K}$ (0.19 K), respectively. Using the high-temperature expansion results, we show that the specific heat and uniform susceptibility of these materials are well described by a large-${J}_{2}{/J}_{1}$ Heisenberg model in agreement with the LDA predictions. Furthermore, the measured N\'eel temperature is consistent with our LDA derived ${J}_{\ensuremath{\perp}}$ values. Further experiments which would be particularly suited to an accurate determination of the ${J}_{2}{/J}_{1}$ ratio for these systems are discussed.