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Register a new userCalculation of the exchange constants of the Heisenberg model in the plane-wave based methods using the Greens function approach
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An approach to compute exchange parameters of the Heisenberg model in plane-wave-based methods is presented. This calculation scheme is based on the Greens function method and Wannier function projection technique. It was implemented in the framework of the pseudopotential method and tested on such materials as NiO, FeO, Li2MnO3, and KCuF3. The obtained exchange constants are in a good agreement with both the total energy calculations and experimental estimations for NiO and KCuF3. In the case of FeO our calculations explain the pressure dependence of the Neel temperature. Li2MnO3 turns out to be a Slater insulator with antiferromagnetic nearest-neighbor exchange defined by the spin splitting. The proposed approach provides a unique way to analyze magnetic interactions, since it allows one to calculate orbital contributions to the total exchange coupling and study the mechanism of the exchange coupling.
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The applicability of a broken symmetry version of the $G_0W_0$ approximation to the calculation of isotropic exchange coupling constants has been studied. Using a simple H--He--H model system the results show a significant and consistent improvement of the results over both broken symmetry Hartree--Fock and broken symmetry density functional theory. In the case of more realistic bimetallic Cu(II) complexes, inclusion of the $G_0W_0$ correction does not lead to obvious improvement in the results. The discrepancies are explained by improved description of the interactions within the magnetic orbital space upon inclusion of the $G_0W_0$ corrections but deterioration of the description of charge- and spin-polarization effects outside the magnetic orbital space. Overall the results show that computational methods based on the $GW$ method have a potential to improve computational estimates of exchange coupling constants.
Cu(pyz)(NO3)2 is a quasi one-dimensional molecular antiferromagnet that exhibits three dimensional long-range magnetic order below TN=110 mK due to the presence of weak inter-chain exchange couplings. Here we compare calculations of the three largest exchange coupling constants in this system using two techniques based on plane-wave basis-set density functional theory: (i) a dimer fragment approach and (ii) an approach using periodic boundary conditions. The calculated values of the large intrachain coupling constant are found to be consistent with experiment, showing the expected level of variation between different techniques and implementations. However, the interchain coupling constants are found to be smaller than the current limits on the resolution of the calculations. This is due to the computational limitations on convergence of absolute energy differences with respect to basis set, which are larger than the inter-chain couplings themselves. Our results imply that errors resulting from such limitations are inherent in the evaluation of small exchange constants in systems of this sort, and that many previously reported results should therefore be treated with caution.
We consider the pyrochlore-lattice quantum Heisenberg ferromagnet and discuss the properties of this spin model at arbitrary temperatures. To this end, we use the Greens function technique within the random-phase (or Tyablikov) approximation as well as the linear spin-wave theory and quantum Monte Carlo simulations. We compare our results to the ones obtained recently by other methods to corroborate our findings. Finally, we contrast our results with the ones for the simple-cubic-lattice case: both lattices are identical at the mean-field level. We demonstrate that thermal fluctuations are more efficient in the pyrochlore case (finite-temperature frustration effects). Our results may be of use for interpreting experimental data for ferromagnetic pyrochlore materials.
Starting from the three-band Hubbard model for the cuprates, we calculate analytically the four-spin cyclic exchange in the limit of infinite on-site Coulomb repulsion and zero O-O hopping $t_{pp}$ using two methods: i) perturbation theory in $t_{pd}/Delta$, where $t_{pd}$ is the Cu-O hopping and $Delta$ the Cu-O charge transfer energy and ii) exact solution of a Cu$_4$O$_4$ plaquette. The latter method coincides with the first to order eight in $t_{pd}$ and permits to extend the results to $t_{pd}/Delta$ of order one. The results are relevant to recent experimental and theoretical research that relate the splitting of certain spin excitations with $Delta$ and the superconducting critical temperature.
We investigate the interplay between spatial anisotropy and further exchange interactions in the spin-$frac{1}{2}$ Heisenberg antiferromagnetic model on a triangular lattice. We use the Schwinger boson theory by including Gaussian fluctuations above the mean-field approach. The phase diagram exhibits a strong reduction of the long range collinear and incommensurate spirals regions with respect to the mean-field ones. This reduction is accompanied by the emergence of its short range order counterparts, leaving an ample room for $0$-flux and nematic spin liquid regions. Remarkably, within the neighborhood of the spatially isotropic line, there is a range where the spirals are so fragile that only the commensurate $120^{circ}$ Neel ones survive. The good agreement with recent variational Monte Carlo predictions gives support to the rich phase diagram induced by spatial anisotropy.
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