Domain-wall interaction in improper ferroelectric lock-in phases

The polarization field relationship in the improper ferroelectric lock-in phase of purified Rb₂ZnCl₄ crystals is analyzed under quasistatic conditions. Domain walls are shown to interact in the same way as an ensemble of phase solitons. This justifies the application of soliton theory to derive information about the ratio n=w/x₀ between wall thickness and wall distance. Above T^'≈140K, n is found to increase with temperature and thermal hysteresis between cooling and heating data is observed. Apparently, x₀ increases via annihilation of antistripples on cooling until an equilibrium distance x₀(T) is achieved, whereas it remains constant on heating. In addition, $w(T)$ seems to be an unambiguous increasing function of temperature. However, a completely different behavior is observed below T^' where n is constant, indicating a freeze in of both x₀ and $w.$ We suggest that this may indicate a transformation from rough domain walls above T^' to flat walls at low temperatures.