"Head-to-head" and "tail-to-tail" 180-degree domain walls in an isolated   ferroelectric
  "Head-to-head" and "tail-to-tail" 180-degree domain-walls in a finite isolated 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 are derived for several limiting cases and wall-widths are estimated. It is shown analytically that different regimes of screening and different dependences for width of charged domain walls on the temperature and parameters of the system are possible, depending on spontaneous polarization and concentration of carriers in the material. It is shown that the half-width of charged domain walls in typical perovskites is about the nonlinear Thomas-Fermi screening-length and about one order of magnitude larger than the half-width of neutral domain-walls. The formation energies of "head-to-head" walls under different regimes of screening are obtained, neglecting the poling ability of the surface. It is shown that either "head-to-head" or "tail-to-tail" configuration can be energetically favorable in comparison with the monodomain state of the ferroelectric if the poling ability of the surface is large enough. If this is not the case, the existence of charged domain walls in bulk ferroelectrics is merely a result of the domain-growth kinetics. Size-effect corresponding to the competition between state with charged domain wall, single domain state, multidomain state, and the state with the zero polarization is considered. The results obtained for the case of an isolated ferroelectric sample were compared with the results for an electroded sample. It was shown that charged domain wall in electroded sample can be either metastable or stable, depends on the work function difference between electrodes and ferroelectric and the poling ability of the electrode/ferroelectric interface. 
Maxim Y. Gureev, Alexander K. Tagantsev and Nava Setter
cond-mat.mtrl-sci