Influence of kinks on the interaction energy between ferroelastic domain walls in membranes and thin films

Abstract

In thin samples, such as membranes, kinks inside ferroelastic domain walls interact through “dipolar” interactions following a 1/d 2 decay, where d is the distance between the walls. Simultaneously, the samples relax by bending. Bending is not possible in thick samples or can be suppressed in thin films deposited on a rigid substrate. In these cases, wall-wall interactions decay as 1/d , as monopoles would do. In free-standing samples, we show a wide crossover regime between “dipolar” 1/d 2 interactions and “monopolar” 1/d interactions. The surfaces of all samples show characteristic relaxation patterns near the kink, which consists of ridges and valleys. We identify the sample bending as the relevant image force that emanates from kinks inside walls in thin samples. When samples are prevented from bending by being attached to a substrate, the dipolar force is replaced by “monopolar” forces, even in thin samples. These results are important for transmission electron microscopy imaging, where the typical sample size is in the dipolar range while it is in the monopolar range for the bulk.