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A microscopic model for describing ferroelectric nanoparticles is proposedwhich allows us to calculate the polarization as a function of an externalelectric field, the temperature, the defect concentration and the particlesize. The interaction of the constituents of the material, arranged in layers,depends on both the coupling strength at the surface and that of defect shellsin addition to the bulk values. The analysis is based on an Ising model in atransverse field, modified in such a manner to study the influence of size anddoping effects on the hysteresis loop of the nanoparticles. Using a Greenfunction technique in real space we find the coercive field, the remanentpolarization and the critical temperature which differ significantly from thebulk behavior. Depending on the varying coupling strength due to the kind ofdoping ions and the surface configuration, the coercive field and the remanentpolarization can either increase or decrease in comparison to the bulkbehavior. The theoretical results are compared with a variety of differentexperimental data.Comment: 16 pages, 7 figure

Size and doping effects on the coercive field of ferroelectric nanoparticles: A microscopic model