Dynamic Fractals in Spin Ice

Fractals -- objects with non-integer dimensions -- occur in manifold settings and length scales in nature, ranging from snowflakes and lightning strikes to natural coastlines. Much effort has been expended to generate and study fractals in many-body physics, oftentimes underpinned by the presence of disorder. Here, we identify an emergent dynamical fractal in a disorder-free, stoichiometric three-dimensional magnetic crystal in thermodynamic equilibrium. The phenomenon is borne out of constraints on the dynamics of the microscopic degrees of freedom imposed by the topological nature of the system and by its characteristic point-like excitations, which at low temperatures become restricted to move on the fractal. This observation explains the anomalous exponent found in magnetic noise experiments on Dy$_2$Ti$_2$O$_7$, and it resolves a long standing puzzle about its rapidly diverging relaxation time. This is a case in point of the capacity of even simple topological many-body systems to exhibit striking phenomena in their cooperative dynamics, and of the promise they hold for further surprising discoveries.