Switching polarization in FE in a continuous way

Due to symmetry, domains usually occur in any ferroics. Each domain represents one episode of possible low energy configurations that are allowed by symmetry. Domains are separated by domain walls. Every wall has a definite thickness, across which the order parameter changes continuously but rather steeply. By applying an external field, the polarization of a domain can be switched, either continuously or abruptly. In this experiment [PRL 105, 167601 (2010)] on a PbTiO3 thin film, the switching takes place in a continuous way: the original polarization gradually diminishes to zero as the field increases and grows up in the other direction from zero. There is no threshold value required. It might be a very interesting question to study the general conditions for continuous and abrupt switching.