Topological Point Defects in Relaxor Ferroelectrics.

First-principles-based effective Hamiltonian simulations are used to reveal the hidden connection between topological defects (hedgehogs and antihedgehogs) and relaxor behavior. Such defects are discovered to predominantly lie at the border of polar nanoregions in both Ba(Zr_{0.5}Ti_{0.5})O_{3} (BZT) and Pb(Sc_{0.5}Nb_{0.5})O_{3} (PSN) systems, and the temperature dependency of their density allows us to distinguish between noncanonical (PSN) and canonical (BZT) relaxor behaviors (via the presence or absence of a crossing of a percolation threshold). This density also possesses an inflection point at precisely the temperature for which the dielectric response peaks. Moreover, hedgehogs and antihedgehogs are found to be mobile excitations, and the dynamical nature of their annihilation is demonstrated (using simple hydrodynamical arguments) to follows laws, such as those of Vogel-Fulcher and Arrhenius, that are characteristic of dipolar relaxation kinetics of relaxor ferroelectrics.