Thermal Annealing of Artificial Spin Systems: An Interplay of Three Temperatures*

Lithographically patterned arrays of magnetic nanoislands, also known as artificial spin ices, offer an exciting playground for designing, visualizing, and controlling collective magnetic behavior. The latter aspect has been predominantly achieved by subjecting these nanostructures to specific thermal and/or field protocols. This has successfully enabled access to certain parts of the phase space for some systems, while other correlated behavior remains experimentally elusive. We here propose a simple Metropolis Monte Carlo-based method for investigating the outcome of a thermal annealing protocol applied to an artificial square spin ice system. The method simulates the superparamagnetic regime of these mesoscopic systems within laboratory timescales and accounts for the temperature dependence of the magnetization. The resulting complex thermal dynamics highlight the interplay between the intrinsic reversal timescales and the potential development of correlated behavior, a kinetic interplay characterized by three temperatures: Curie, the intrinsic blocking and the ordering temperatures. This work can help establish the extent of the phase space accessible within laboratory conditions, thus inspiring optimized designs for future artificial spin systems.