Vortex Ferroelectric Domains
  We show experimental switching data on microscale capacitors of lead-zirconate-titanate (PZT), which reveal time-resolved domain behavior during switching on a 100-ns scale. For small circular capacitors, an unswitched domain remains in the center while complete switching is observed in square capacitors. The observed effect is attributed to the formation of vortex domain during polarization switching in circular capacitors. This dynamical behavior is modeled using the Landau-Liftshitz-Gilbert equations and found to be in detailed agreement with experiment. This simulation implies rotational motion of polarization in the xy-plane, a Heisenberg-like result supported by the recent model of Naumov and Fu [Phys. Rev. Lett. 98, 077603 (2007)], although not directly measurable by the present quasi-static measurements. 
A. Gruverman, D. Wu, H.-J. Fan, I. Vrejoiu, M. Alexe, R. J. Harrison,   and J. F. Scott