  The polarization and strain response of ferroelectric materials at fields
below the macroscopic coercive field is of a paramount importance for the
operation of many electronic devices. The response of real ferroelectric and
related materials is in general complex and difficult to interpret. The reason
for this is that many processes in a ferroelectric material contribute to its
properties, often concurrently. Examples include motion of ferroelectric and
ferroelastic domains, presence of domains within domains, dynamics of different
types of polar nano-entities, interaction of polar nano-entities (e.g., polar
nanoregions in relaxors) with the strain and polarization within domains,
motion of defects and rearrangement of defect clusters and their interaction
with polarization and strain. One signature of these processes is nonlinearity
of the strain and polarization. Most ferroelectrics exhibit nonlinear response
at all practical field levels meaning that the apparent material coefficients
depend on the amplitude of the driving excitation. In this paper we show that
an investigation of nonlinear behavior is a sensitive way to study various
mechanisms operating in dielectric and piezoelectric materials. We review the
basic formalism of the nonlinear description of polarization and strain, give a
physical interpretation of different terms and illustrate this approach on
numerous examples of relaxors, relaxor ferroelectrics, hard and soft
ferroelectrics, and morphotropic phase boundary compositions. An experimental
approach based on a lock-in technique that is well-suited for such studies is
also discussed.
