Anomalous Spin Diffusion in a Two-Dimensional Percolating Ising Antiferromagnet

Anomalous diffusive motions of spins in a near-percolating Ising antiferromagnet, ${\mathrm{Rb}}_2$${\mathrm{Co}}_{0.6}$${\mathrm{Mg}}_{0.4}$${\mathrm{F}}_4$, have been observed by high-energy-resolution neutron inelastic scattering. The scattering function integrated over momentum space in the paramagnetic phase reveals a long-tailed spectrum having the form $E^{-(0.35\mathrm{}\pm 0.06)}$ superimposed on the Lorentzian line shape, which originates from the normal critical magnetic scattering. This observation of a power-law decay function is a direct measurement of anomalous diffusion in a system with fractal geometry.