Domain wall interaction

For ferroelectrics, mainly two possible mechanisms for irreversible processes exist. First, lattice defects which interact with a domain wall and hinder it from returning into its initial position after removing the electric field that initiated the domain wall motion ( pinning ) [16]. Second, the nucleation and growth of new domains which do not disappear after the field is removed again. In ferroelectric materials the matter is further complicated by defect dipoles and free charges that also contribute to the measured polarization and can also interact with domain walls [17]. Reversible contributions in ferroelectrics are due to ionic and electronic... 

A domain wall under an external electric field moves in a statistical potential generated by their interaction with the lattice, point defects, dislocations, and neighboring walls. Reversible movement of the wall is regarded as a small displacement around a local minimum. When the driven field is high enough, irreversible jumps above the potential barrier into a neighboring local minimum occur (see Figure 1.23). 

The domain energy W consists of the depolarization field energy W,i, the energy of the domain walls Ws, and the energy, Wt, of the interaction between the electric field of the tip and the spontaneous polarization of the domain. Following Landauer [63] hereafter we assume that the domain has a shape of an elongated half-ellipsoid in the polar direction. 

The power law-type spectral dependencies of x and x" are well supported by our experiments. While the unpoled sample exhibits an exponent ft 0.2 (not shown), i. e. large poly-dispersivity, the poled sample yields ft 0.67 for both components of x (Figure 15.14 [58]). Obviously the polydispersivity is largely suppressed at low domain wall densities. This seems to show that polydispersivity is less affected by the nonlinearity in the creep regime, v oc Es, than by the mutual wall interactions in the nanodomain regime [46], Very satisfactorily, also the Cole-Cole plot, Equation (15.21), which is another independent test of the ansatz, Equation (15.18), reveals a very similar exponent, ft 0.69 (Figure 15.15 [58]). 

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