Impact of Defects on the Properties of Ferroelectric Nanoparticles

Abstract

The influence of doping effects on the polarization, the phase transition temperature and the hysteresis loop of ferroelectric nanoparticles is studied based on a modified Ising model in a transverse field. Due to the loss of translational invariance the physical quantities are figured out by a Green's function technique in real space. The spherical nanoparticles offer a shell structure starting from the center and ending with the surface shell. This assembling allows the incorporation of defect shells. Consequently, the interaction parameters are assumed to be different for defect and surface shells and are also aside from the bulk one. Depending on the kind of the doping ions the spontaneous polarization σ, the coercive field E c , the remanent polarization P r and the phase transition temperature T c can be shifted to higher or to lower values. The hysteresis loop is modified by the presence of defects. Further we demonstrate, that the changes of T c , E c , P r and σ are directly influenced by the assembling of the nanoparticles. The shifts are stronger when the shell-wise growth of defects begins from the surface. If the filling of the nanoparticles with defect shells starts from the inner part, then the increase or decrease of the physical quantities are significantly weaker. The theoretical results are in accordance with experimental data.