Electronic correlation and magnetic frustration inLi2VOSiO4andVOMoO4

Abstract

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

Massively parallel simulations of strong electronic correlations: Realistic Coulomb vertex and multiplet effects

“…The magnetic response function for VOMoO 4 is shown in Figure 15. Our calculations [25] support a weak frustration picture for both vanadates, with a small but non-negligible degree of three-dimensionality, which fully account for the three-dimensional magnetic order reported in experiments. Although weak, the frustration is large enough to explain the partial reduction of the ordered magnetic moments measured via neutron scattering experiments [69,70].…”

“…Finally, we use the Filon-trapezoid method to minimize the time required to perform the Fourier transform to Matsubara space as well as an extrapolation scheme to sum up Matsubara frequencies. This approach is implemented in our generalized HF-QMC solver [25].…”

Peculiarities of magnetic ordering in the S=5/2 two-dimensional square-lattice antimonate NaMnSbO4

“…The later studies of the solid solutions Li 2 V 1−x OTi x SiO 4 (for 0 ≤ x ≤ 0.2) by means of 7 Li and 29 Si NMR, muon spin relaxation (µSR), as well as magnetization [26] revealed that the ratio |J 2 /J 1 | decreases with x, and the magnetic ordering temperature decreases with reducing the spin stiffness [24] by a factor of approximately (1−x) 2 . In contrast to the case of Li 2 VOXO 4 (X = Si, Ge), the J 1 and J 2 exchanges compete in the S = 1/2 (V 4+ ) QHAF system, VOMoO 4 , [27,28] which orders at a markedly higher temperature (~ 42 K) and demonstrates a structural distortion. It is worthwhile to note that theoretical calculations [16,28] predict a quite strong interlayer exchange for both Li 2 VOXO 4 (X = Si, Ge) and VOMoO 4 .…”

Solving the strong-correlation problem in materials

“…It was shown that super-exchange yields a Fig. 4 Quasiparticles and Hubbard bands in the doped 2D Hubbard model (square lattice) with dispersion ε(k) = −2t(cos k x + cos k y ) + 4t cos k x cos k y , obtained with the dynamical mean-field theory approach [53,54]. The special points are Γ = (0, 0, 0), X = (0, π/a, 0), M = (π/a, π/a, 0), and Z = (0, 0, π/a).…”

“…Calculations were performed for U = 7 eV, t = 0.4 eV, 290 K. The quantum impurity solver adopted is the Hirsch-Fye quantum Monte Carlo [55] method in the implementation of Ref. [53]. The number of holes is indicated with x large transition temperature, but is not sufficient to explain alone the persistence of distortions till very high temperatures; in the case of ionic systems such as KCuF 3 , a new mechanism was identified [46], with the Born-Mayer repulsion playing a key role in determining the actual experimental structure (Fig.…”