Thermal relaxation and ground state ordering in artificial spin ice

Abstract

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.