LAUSR

Fractals—objects with noninteger dimensions—occur in manifold settings and length scales in nature. In this work, we identify an emergent dynamical fractal in a disorder-free, stoichiometric, and three-dimensional magnetic crystal in thermodynamic equilibrium. The phenomenon is born from constraints on the dynamics of the magnetic monopole excitations in spin ice, which restrict them to move on the fractal. This observation explains the anomalous exponent found in magnetic noise experiments in the spin ice compound Dy2Ti2O7, and it resolves a long-standing puzzle about its rapidly diverging relaxation time. The capacity of spin ice to exhibit such notable phenomena suggests that there will be further unexpected discoveries in the cooperative dynamics of even simple topological many-body systems. Description Fractal-hopping monopoles Spin ices have crystal lattices that consist of tetrahedra of magnetic ions. In a ground state, two of the four spins on each tetrahedron point in and two point out. When an excitation called the magnetic monopole is created, this rule is violated as the monopole moves through the crystal. Monopole dynamics are reflected in quantities such as magnetic noise, the measurements of which have shown a different frequency dependence from the one that the simplest model predicts. Hallén et al. solved this puzzle by realizing that the monopole motion is more restricted than previously thought and is limited to a cluster with a fractal structure (see the Perspective by Flicker). —JS A model of monopole dynamics that restricts their motion to a fractal cluster explains anomalous magnetization noise data.