Thermal relaxation and ground state ordering in artificial spin ice

We have studied the thermal relaxation of artifcial spin ice in its two main geometries,
namely artificial square ice and artificial kagome spin ice. Using synchrotron based photoemission
electron microscopy we are able to directly observe how artificial square ice
systems find their way from an energetically excited state to one of the two degenerate
ground state configuration. On plotting vertex type populations as a function of time, we
can characterize the relaxation, which occurs in two stages, namely a string and a domain
regime. Kinetic Monte Carlo simulations agree well with the temporal evolution of the
magnetic state when including disorder, and the experimental results can be explained by
considering the effective interaction energy associated with the separation of pairs of vertex
excitations.
While a simple thermal annealing procedure, that involved one cycle of heating and
cooling the sample above and below the blocking temperature (T = 320-330 K), proved
to be very effective in achieving long-range ordered ground state configurations in artificial
square ice, the ability of achieving the same goal in artificial kagome spin ice is shown to
become increasingly difficult with increasing system size. By first focusing on the so-called
building block structures of artificial kagome spin ice, with system sizes ranging from a
single ring up to seven-ring structures, we proved that the abilitiy to access the ground
state is lost at a system size comprising seven kagome rings. Extrapolating the result
to extended arrays of artificiall kagome spin ice, we conclude that a long-range ordered
gound state is unlikely to be achieved in an infinite array of artificial kagome spin ice.
This conclusion is later confirmed by investigating thermal annealing on extended arrays
of artificial kagome spin ice.
Finally, we explored a potential optimization of thermal annealing on artificial kagome
spin ice. For this purpose, we patterned artificial kagome spin ice arrays with lower blocking
temperatures (T = 160K), hoping that the blocking temperature to be below the
predicted temperatures for phase transitions into ordered configurations. Both continuous
and stepped cooling from temperatures around 370 K down to 140 K proved to be
inefficient in achieving ground state configurations. We then applied an annealing procedure
that involved repeated heating and cooling just slightly around the blocking point
(T = 160K), thus allowing the system slow attempts in accessing ground state configurations,
while above the blocking point, and capture such configurational changes by cooling
back down below the blocking point. So far, this procedure represents the only known way
to access local ground state configurations in artificial kagome spin ice and paves the way
to explore even more sophisticated annealing procedures that remain to be discovered in
future work.