  Ferroelectric domain switching in c-axis-oriented epitaxial
Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$ thin films was studied using biased scanning
probe microscopy tips. While linear and logarithmic dependence of domain size
on tip bias and writing time, respectively, are well known, we report an
additional linear dependence on relative humidity in the 28-65% range. We map
out the switched domain size as a function of both the tip bias and the applied
pulse time and describe a growth-limited regime for very short pulses and a
nucleation-limited regime for very low tip bias. Using "interrupted-switching"
measurements, we probe the nucleation regime with subcritical pulses and
identify a surprisingly long relaxation time on the order of 100 ms, which we
relate to ionic redistribution both on the surface and within the thin film
itself.
