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Register a new userSpin and orbital exchange interactions from Dynamical Mean Field Theory
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We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of single-electron Greens functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii-Moriya interaction and other symmetric terms such as dipole-dipole interaction. We present the formulas in a format that can be used for computations via Dynamical Mean Field Theory algorithms.
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In this paper we present an accurate numerical scheme for extracting inter-atomic exchange parameters ($J_{ij}$) of strongly correlated systems, based on first-principles full-potential electronic structure theory. The electronic structure is modelled with the help of a full-potential linear muffin-tin orbital method. The effects of strong electron correlations are considered within the charge self-consistent density functional theory plus dynamical mean-field theory (DFT+DMFT). The exchange parameters are then extracted using the magnetic force theorem, hence all the calculations are performed within a single computational framework. The method allows to investigate how the $J_{ij}$-parameters are affected by dynamical electron correlations. In addition to describing the formalism and details of the implementation, we also present magnetic properties of a few commonly discussed systems, characterised by different degrees of electron localisation. In bcc Fe we found a minor renormalisation of the $J_{ij}$ interactions once the dynamical correlations are introduced. However, generally, if the magnetic coupling has several competing contributions from different orbitals, the redistribution of the spectral weight and changes in the exchange splitting of these states can lead to a dramatic modification of the total interaction parameter. In NiO we found that both static and dynamical mean-field results provide an adequate description of the exchange interactions, which is somewhat surprising given the fact that these two methods result in quite different electronic structures. By employing Hubbard-I approximation for the treatment of the $4f$ states in hcp Gd we reproduce the experimentally observed multiplet structure. The calculated exchange parameters result to be rather close to the ones obtained by treating the $4f$ electrons as non-interacting core states.
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.
In this Letter we report the first LDA+DMFT (method combining Local Density Approximation with Dynamical Mean-Field Theory) results of magnetic and spectral properties calculation for paramagnetic phases of FeO at ambient and high pressures (HP). At ambient pressure (AP) calculation gave FeO as a Mott insulator with Fe 3$d$-shell in high-spin state. Calculated spectral functions are in a good agreement with experimental PES and IPES data. Experimentally observed metal-insulator transition at high pressure is successfully reproduced in calculations. In contrast to MnO and Fe$_2$O$_3$ ($d^5$ configuration) where metal-insulator transition is accompanied by high-spin to low-spin transition, in FeO ($d^6$ configuration) average value of magnetic moment $sqrt{<mu_z^2>}$ is nearly the same in the insulating phase at AP and metallic phase at HP in agreement with X-Ray spectroscopy data (Phys. Rev. Lett. {bf83}, 4101 (1999)). The metal-insulator transition is orbital selective with only $t_{2g}$ orbitals demonstrating spectral function typical for strongly correlated metal (well pronounced Hubbard bands and narrow quasiparticle peak) while $e_g$ states remain insulating.
Although diagrammatic perturbation theory fails for the dynamical-mean field theory of the double-exchange model, the theory is nevertheless Phi-derivable and hence thermodynamically consistent, meaning that the same thermodynamic properties are obtained from either the partition function or the Greens function. We verify this consistency by evaluating the magnetic susceptibility and Curie temperature for any Hunds coupling.
We study effects of charge self-consistency within the combination of density functional theory (DFT; Wien2k) with dynamical mean field theory (DMFT; w2dynamics) in a basis of maximally localized Wannier orbitals. Using the example of two cuprates, we demonstrate that even if there is only a single Wannier orbital with fixed filling, a noteworthy charge redistribution can occur. This effect stems from a reoccupation of the Wannier orbital in k-space when going from the single, metallic DFT band to the split, insulating Hubbard bands of DMFT. We analyze another charge self-consistency effect beyond moving charge from one site to another: the correlation-enhanced orbital polarization in a freestanding layer of SrVO3.
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