Ice rule breakdown and frustrated antiferrotoroidicity in an artificial colloidal Cairo ice

Abstract

We combine experiments and numerical simulations to investigate the low
energy states and the emergence of topological defects in an artificial colloidal ice in
the Cairo geometry. This type of geometry is characterized by a mixed coordination
(z), with coexistence of both z = 3 and z = 4 vertices. We realize this particle ice by
confining field tunable paramagnetic colloidal particles within a lattice of topographic
double wells at a one to one filling using optical tweezers. By raising the interaction
strength via an applied magnetic field, we find that the ice rule breaks down, and
positive monopoles with charge q = +2 accumulate in the z = 4 vertices and are
screened by negative ones (q = −1) in the z = 3. The resulting, strongly coupled
state remains disordered. Further, via analysis of the mean chirality associated to
each pentagonal plaquette, we find that the disordered ensemble for this geometry is
massively degenerate and it corresponds to a frustrated antiferrotoroid.