"Head-to-head" and "tail-to-tail" 180-degree domain-walls in a finiteisolated ferroelectric sample are theoretically studied using Landau theory.The full set of equations, suitable for numerical calculations is developed.The explicit expressions for the polarization profile across the walls arederived for several limiting cases and wall-widths are estimated. It is shownanalytically that different regimes of screening and different dependences forwidth of charged domain walls on the temperature and parameters of the systemare possible, depending on spontaneous polarization and concentration ofcarriers in the material. It is shown that the half-width of charged domainwalls in typical perovskites is about the nonlinear Thomas-Fermiscreening-length and about one order of magnitude larger than the half-width ofneutral domain-walls. The formation energies of "head-to-head" walls underdifferent regimes of screening are obtained, neglecting the poling ability ofthe surface. It is shown that either "head-to-head" or "tail-to-tail"configuration can be energetically favorable in comparison with the monodomainstate of the ferroelectric if the poling ability of the surface is largeenough. If this is not the case, the existence of charged domain walls in bulkferroelectrics is merely a result of the domain-growth kinetics. Size-effectcorresponding to the competition between state with charged domain wall, singledomain state, multidomain state, and the state with the zero polarization isconsidered. The results obtained for the case of an isolated ferroelectricsample were compared with the results for an electroded sample. It was shownthat charged domain wall in electroded sample can be either metastable orstable, depends on the work function difference between electrodes andferroelectric and the poling ability of the electrode/ferroelectric interface.
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