Dynamical fractal in spin ice

Fractals – objects with non-integer dimensions – occur in manifold settings and length scales in nature. Here, we identify an emergent dynamical fractal in a disorder-free, stoichiometric three-dimensional magnetic crystal in thermodynamic equilibrium. I will begin with a brief introduction to spin ice, focusing on the magnetic monopole excitations and their dynamics. I will then demonstrate how constraints on the monopole dynamics restrict them to move on the fractal. The fractal leaves distinct signatures in the material’s dynamics, accessible in experiments through dynamical probes. I will show that this explains the anomalous exponent found in magnetic noise experiments in the spin ice compound Dy2Ti2O7, and that it resolves a long-standing puzzle about the compound’s rapidly diverging relaxation time. The capacity of spin ice to exhibit such striking phenomena holds promise of further surprising discoveries in the cooperative dynamics of even simple topological many-body systems.