4.2.1 Two-Dimensional Properties

The two-dimensional properties of hysteretic materials are more complex than they seem at first glance. The fact that the electric field might not only change its magnitude but also its orientation increases the complexity. These properties appear in form of a lag angle $\alpha$ between the electric field and the displacement. This effect was discovered as early as 1908 by Weiss and Planer [WP08].

So far this phenomenon has been studied only in the context of magnetism, where it is responsible for an additional energy loss [Pfü94]. For the simulation of large scale integration devices energy loss is of comparatively minor significance, but an accurate calculation of the orientations of the electric field and the displacement field is mandatory.