  The Kibble-Zurek mechanism describes the formation of topological defects
during spontaneous symmetry breaking for quite different systems. Shortly after
the big bang, the isotropy of the Higgs-field is broken during the expansion
and cooling of the universe. Kibble proposed the formation of monopoles,
strings, and membranes in the Higgs field since the phase of the symmetry
broken field can not switch globally to gain the same value everywhere in
space. Zurek pointed out that the same mechanism is relevant for second order
phase transitions in condensed matter systems. Every finite cooling rate
induces the system to fall out of equilibrium which is due to the critical
slowing down of order parameter fluctuations: the correlation time diverges and
the symmetry of the system can not change globally but incorporates defects
between different domains. Depending on the cooling rate the heterogeneous
order parameter pattern are a fingerprint of critical fluctuations. In the
present manuscript we show that a monolayer of superparamagnetic colloidal
particles is ideally suited to investigate such phenomena. In thermal
equilibrium the system undergos continuous phase transitions according
KTHNY-theory. If cooled rapidly across the melting temperature the final state
is a polycrystal. We show, that the observations can not be explained with
nucleation of a supercooled fluid but is compatible with the Kibble-Zurek
mechanism.
