Polarization Closure in PbZr_(0.42)Ti_(0.58)O₃ Nanodots

Abstract

Domain states in PbZr((0.42))Ti((0.58))O(3) single-crystal ferroelectric nanodots, formed on cooling through the Curie temperature, were imaged by transmission electron microscopy. In the majority of cases, 90° stripe domains were found to form into four distinct "bundles" or quadrants. Detailed analysis of the dipole orientations in the system was undertaken, using both dark-field imaging and an assumption that charged domain walls were energetically unfavorable in comparison to uncharged walls. On this basis, we conclude that the dipoles in these nanodots are arranged such that the resultant polarizations, associated with the four quadrant domain bundles, form into a closed loop. This "polarization closure" pattern is reminiscent of the flux-closure already commonly observed in soft ferromagnetic microdots but to date unseen in analogous ferroelectric dots.