Li 2 VOSiO 4 and VOMoO 4 have been proposed as realizations of the frustrated two-dimensional J 1 -J 2 quantum Heisenberg model. In this work, in order to test this picture, we study their electronic and magnetic properties by using the local-density approximation + dynamical mean-field theory method. We calculate the magnetic linear response function starting from material-specific Hubbard models and systematically map our results onto those from generalized quantum Heisenberg models. We obtain the effective local magnetic moments and the associated magnetic exchange couplings, in particular the ratio J 2 /J 1 , a measure of the frustration degree, and the ratio 2J ⊥ /(J 1 + J 2 ), measuring the three-dimensionality degree. Our results support a weak frustration picture for both materials, with small but non-negligible long-range interplane couplings, leading to three-dimensional order at low temperature. Implications for the physics of the two systems are discussed.Heisenberg model picture. In line with this view, the lattice distortions observed around T N were interpreted as frustration driven [2,3], with the degeneracy of the frustrated state perhaps lifted via the so-called spin Jahn-Teller effect [11][12][13]. Similar conclusions, although with sizably larger couplings, J 1 + J 2 ∼ 155 K, and higher critical temperature, T N ∼ 42 K, were reached for VOMoO 4 , for which it was estimated thatThis is, however, not the end of the story. Indeed, the experiments discussed above do not probe J 2 /J 1 directly, but only via the theoretical framework used in analyzing the data. In contrast to the strong frustration picture, ab initio studies [4,20,21] placed both systems in the weakly frustrated regime. As a matter of fact, these calculations, based on the local-density approximation (LDA) plus perturbation theory, yield J 2 /J 1 ∼ 12 for Li 2 VOSiO 4 (well inside the collinear regime), and J 2 /J 1 ∼ 0.2 for VOMoO 4 (well inside the
