Designing frustration and topologically constrained disorder in artificial spin ice
We are all familiar with classical states of matter as ordered or disordered; and yet some of the most relevant phenomena in nature, from the nano-machinery of life in DNA, to the behavior of animal or human colonies, to the exotic behaviors of frustrated materials, take place at the threshold between the two states. Indeed one can think of constrained forms of disorder, where a manifold of configurations appears disordered with non-zero density of entropy, but obeys either local or global rules. The ice rule is a classical example, leading to an ice manifold of constrained disorder. We will show in this talk how novel phases of classical matter can be designed from simple mathematical models and implemented in artificial meta-materials at the nano- or micro-scale called artificial spin ices. While we started in 2006 with simple geometries (square, hexagonal, triangular), new forms of frustration, along with advances in nanofabrication and characterization allows now for the realization of more sophisticated systems described by emergent mathematical models. For instance a Shakti lattice can lead to a topologically protected constrained disorder mapping into a dimer-cover model, leading to the freeze-in of topological charges that prevent equilibration and can induce weak ergodicity breaking. Other lattices can lead to dimensional reduction in their kinetics. Others again to a disordered manifold described by fluctuating ‘polymers’ of topologically protected local excitations. We will conclude showing the first examples of ice rule fragility, in lattices where the ice rule breaks-down spontaneously.