  Symmetry breaking phase transitions play an important role in nature. When a
system traverses such a transition at a finite rate, its causally disconnected
regions choose the new broken symmetry state independently. Where such local
choices are incompatible, defects will form with densities predicted to follow
a power law scaling in the rate of the transition. The importance of this
Kibble-Zurek mechanism (KZM) ranges from cosmology to condensed matter [1-4].
In previous tests in homogeneous systems, defect formation was seen, but weak
dependence on the transition rate and limited control of external parameters so
far prevented tests of KZM scaling. As recently predicted [5-9], in
inhomogeneous systems propagation of the critical front enhances the role of
causality and steepens scaling of defect density with the transition rate. We
use ion Coulomb crystals in a harmonic trap to demonstrate, for the first time,
scaling of the number of topological defects with the transition rate - the
central prediction of KZM - in a well-controlled environment.
