We report electronic structure calculations for the multiferroic ferromagnetoelectric perovskite PbFe1/2Ta1/2O3, within density functional theory in the local spin density approximation (LSDA) and within the LSD+U approach. Our results, corresponding to several possible crystallographic and magnetic orderings, show the link between short range cation coordination and magnetic properties. In particular, the existence of two different Neel ordering temperatures, experimentally evidenced, is explained in terms of different superexchange paths introduced by crystallographic orderings certainly present, locally, in the real samples. The introduction of ferroelectric displacements, which are found to be in good agreement with experiment, do not bring about large changes in the electronic structure of this system.
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