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In this paper we present an accurate numerical scheme for extractinginter-atomic exchange parameters ($J_{ij}$) of strongly correlated systems,based on first-principles full-potential electronic structure theory. Theelectronic structure is modelled with the help of a full-potential linearmuffin-tin orbital method. The effects of strong electron correlations areconsidered within the charge self-consistent density functional theory plusdynamical mean-field theory (DFT+DMFT). The exchange parameters are thenextracted using the magnetic force theorem, hence all the calculations areperformed within a single computational framework. The method allows toinvestigate how the $J_{ij}$-parameters are affected by dynamical electroncorrelations. In addition to describing the formalism and details of theimplementation, we also present magnetic properties of a few commonly discussedsystems, characterised by different degrees of electron localisation. In bcc Fewe found a minor renormalisation of the $J_{ij}$ interactions once thedynamical correlations are introduced. However, generally, if the magneticcoupling has several competing contributions from different orbitals, theredistribution of the spectral weight and changes in the exchange splitting ofthese states can lead to a dramatic modification of the total interactionparameter. In NiO we found that both static and dynamical mean-field resultsprovide an adequate description of the exchange interactions, which is somewhatsurprising given the fact that these two methods result in quite differentelectronic structures. By employing Hubbard-I approximation for the treatmentof the $4f$ states in hcp Gd we reproduce the experimentally observed multipletstructure. The calculated exchange parameters result to be rather close to theones obtained by treating the $4f$ electrons as non-interacting core states.

Exchange parameters of strongly correlated materials: extraction from spin-polarised density functional theory plus dynamical mean field theory