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 fractals for use in many-body physics. Here, we identify an emergent dynamical fractal in a disorder-free, stoichiometric three-dimensional magnetic crystal in thermodynamic equilibrium. The phenomenon is borne 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. Finally, this realises a disorder-free mechanism to generate subdiffusive motion in three dimensions.

Jonathan N. Hallén, Santiago A. Grigera, D. Alan Tennant, Claudio Castelnovo, Roderich Moessner, Science 378, 1218 (2022)