Domain wall pinning

From what has been said it follows that small displacements of a pinned domain wall introduce restoring forces and, since the wall has inertia and its movement is accompanied by energy dissipation, an equation of motion can be written for a sinusoidal applied field ... 

Doping the PZT material with donor or acceptor ions changes its properties dramatically. Donor doping with ions such as Nb or Ta + provides soft PZTs, like PZT-5, because of the facility of domain motion due to the resulting Pb-vacancies. On the other hand, acceptor doping with Fe + or Sc + leads to hard PZTs, such as PZT-8, because the oxygen vacancies will pin domain wall motion. 

The mechanism for coercivity in the Cr—Co—Fe alloys appears to be pinning of domain walls. The magnetic domains extend through particles of both phases. The evidence from transmission electron microscopy studies and measurement of JT, and anisotropy vs T is that the walls are trapped locally by fluctuations in saturation magnetization. 

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... 

The origin of the nonlinearity and hysteresis in the films is most likely due to displacement of domain walls [4], If domain walls move in a medium with a random distribution of pinning center, the response of the material can be described, in the first approximation by Rayleigh relations. We next demostrate how optical interferometry can be sued to verify whether this particular model applies to the investigated pzt thin film. In the case of the converse piezoelectric effect, when the driving field E is varied between — Eo and Eo, the piezoelectric strain x is hysteretic and can be expressed by the following Rayleigh relations ... 

D. Sander, R. Skomski, C. Schmidthals, A. Enders, and J. Kirschner, Film Stress and Domain Wall Pinning in Sesquilayer Iron Films on W(110) , Phys. Rev. Lett. 77, 2566(1996). 

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