Twin boundary profiles with linear-quadratic coupling between order parameters.

A new type of twin boundary was found when two order parameters interact by linear-quadratic coupling QP(2). In this solution, we find that a domain wall consists of two layers in which in one layer both order parameters Q and P are active while in the second layer only Q is active. The adjacent domains are equally asymmetric (Q, P) and (Q, 0) so that one phase could be polar and/or magnetic and contain a ferroelastic strain while the second layer is ferroelastic only without polar or magnetic properties. The two layers represent a stepwise transition between the two domains.We analyze the full phase diagram depending on the coupling constant and anisotropy of the gradient term, and show that in a certain regime the order parameter Q becomes activated only in the interfacial region. A common solution contains kinks and breathers whereby the width of the interface can be very wide in agreement with the first order character of the transition.