Anomalous Spin Diffusion on Two-Dimensional Percolating Network in Dilute Antiferromagnet Rb2Mn06Mg04F4

Inelastic neutron scattering experiments were performed on a two-dimensional dilute antiferromagnet, Rb2Mn0.6Mg0.4F4, with a magnetic concentration close to the percolation concentration, c(p) = 0.593, well above the Neel temperature, and with a high energy-resolution of Delta E = 17.5 mu eV. The energy spectrum obtained from the observed dynamical structure factor S(q, E) integrated over the wave number, q, throughout almost the entire Brillouin zone showed the power law dependence S(E) proportional to E-x. The diffusion on a percolating network is anomalous and it has been predicted that the mean square displacement of a random walker is described by < R-2(t)> proportional to t(2/(2+theta)) with an exponent, theta, as a function of the time, t. The exponent in S(E) is described as x = 1 - D-f/(2 + theta) with D-f being the fractal dimension of the medium. The observed exponent, x, was in good agreement with a theoretical value.