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

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 the electronic, magnetic, and dielectric properties of the manganite family RMnO3 (R = La, Pr, Nd, Sm, Eu, and Gd). The link between first principles and tight binding is established by downfolding the physically relevant subset of 3d bands with e(g) character by means of maximally localized Wannier functions (MLWFs) using the VASP2WANNIER90 interface. The MLWFs are then used to construct a general tight-binding Hamiltonian written as a sum of the kinetic term, the Hund's rule coupling, the JT coupling, and the electron-electron interaction. The dispersion of the tight-binding (TB) eg bands at all levels are found to match closely the MLWFs. We provide a complete set of TB parameters which can serve as guidance for the interpretation of future studies based on many-body Hamiltonian approaches. In particular, we find that the Hund's rule coupling strength, the Jahn-Teller coupling strength, and the Hubbard interaction parameter U remain nearly constant for all the members of the RMnO3 series, whereas the nearest-neighbor hopping amplitudes show a monotonic attenuation as expected from the trend of the tolerance factor. Magnetic exchange interactions, computed by mapping a large set of hybrid functional total energies onto an Heisenberg Hamiltonian, clarify the origin of the A-type magnetic ordering observed in the early rare-earth manganite series as arising from a net negative out-of-plane interaction energy. The obtained exchange parameters are used to estimate the Neel temperature by means of Monte Carlo simulations. The resulting data capture well the monotonic decrease of the ordering temperature down the series from R = La to Gd, in agreement with experiments. This trend correlates well with the modulation of structural properties, in particular with the progressive reduction of the Mn-O-Mn bond angle which is associated with the quenching of the volume and the decrease of the tolerance factor due to the shrinkage of the ionic radii of R going from La to Gd.