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We merge advanced ab initio schemes (standard density functional theory,hybrid functionals and the GW approximation) with model Hamiltonian approaches(tight-binding and Heisenberg Hamiltonian) to study the evolution of theelectronic, magnetic and dielectric properties of the manganite family RMnO3 (R= La, Pr, Nd, Sm, Eu and Gd). The link between first principles andtight-binding is established by downfolding the physically relevant subset of3d bands with e_g character by means of maximally localized Wannier functions(MLWFs) using the VASP2WANNIER90 interface. The MLWFs are then used toconstruct a tight-binding Hamiltonian. The dispersion of the TB e_g bands atall levels are found to match closely the MLWFs. We provide a complete set ofTB parameters which can serve as guidance for the interpretation of futurestudies based on many-body Hamiltonian approaches. In particular, we find thatthe Hund's rule coupling strength, the Jahn-Teller coupling strength, and theHubbard interaction parameter U remain nearly constant for all the members ofthe RMnO3 series, whereas the nearest neighbor hopping amplitudes show amonotonic attenuation as expected from the trend of the tolerance factor.Magnetic exchange interactions, computed by mapping a large set of hybridfunctional total energies onto an Heisenberg Hamiltonian, clarify the origin ofthe A-type magnetic ordering observed in the early rare-earth manganite seriesas arising from a net negative out-of-plane interaction energy. The obtainedexchange parameters are used to estimate the Neel temperature by means of MonteCarlo simulations. The resulting data capture well the monotonic decrease ofthe ordering temperature down the R series, in agreement with experiments.

Combined first-principles and model Hamiltonian study of the perovskite series RMnO3 (R = La, Pr, Nd, Sm, Eu and Gd)