Functional properties of ferroelectric materials depend both on the residual domain states and on the mobility of domain walls in response to the applied electric and stress fi elds. This paper reviews the use of multidimensional scanning probe microscopy to assess these factors in the time-and voltage domains, with an emphasis on the manner in which domain walls respond collectively to stimuli. It is found that in many PbZr 1-x Ti x O 3 -based capacitors, domain wall motion is correlated over length scales that exceed the domain and grain sizes by orders of magnitude, suggesting emergent collective electromechanical behavior. The role of mechanical boundary conditions and fi eld history on the domain wall contributions and the stability of the ferroelectric domain state are discussed.
FEATURE ARTICLEcoeffi cient, P is the polarization, and ε 0 is the permittivity of free space. Here, ε init ′ includes contributions both from the intrinsic response and reversible motion of the interfaces, while α′ quantifi es irreversible motions of the interfaces. The intrinsic contributions arise from fi eld-induced response of an ensemble of single domains.Rayleigh behavior was fi rst observed in magnetic materials. [ 8,9 ] There is an expanding literature that demonstrates that many ferroelectric samples behave as Rayleigh-like systems for fi eld excursions up to ≈ ½ the coercive fi eld, suggesting that Rayleigh-like behavior is common in ferroic systems. [ 7 , 10,11 ] Moreover, direct confi rmation that Rayleigh behavior is associated with motion of non-180