On thermalization of magnetic nano-arrays at fabrication

We propose a model to predict and control the statistical ensemble of magnetic degrees of freedom in artificial spin ice (ASI) during thermalized adiabatic growth (Wang et al 2006 Nature 439 303; Morgan et al Nature Phys. 7 75). We predict that as-grown arrays are controlled by the temperature at fabrication and by their lattice constant, and that they can be described by an effective temperature. If the geometry is conducive to a phase transition, then the lowest-temperature phase is accessed in arrays of lattice constant smaller than a critical value, which depends on the temperature at deposition. Alternatively, for arrays of equal lattice constant, there is a temperature threshold at deposition and the lowest-temperature phase is accessed for fabrication temperatures larger rather than smaller than this temperature threshold. Finally, we show how to define and control the effective temperature of the as-grown array and how to measure critical exponents directly. We discuss the role of kinetics at the critical point, and applications to experiments, in particular to as-grown thermalized square ASI and to magnetic monopole crystallization in as-grown honeycomb ASI.