Anomalous Spin Diffusion on Two-Dimensional Percolating Network in Dilute Antiferromagnet Rb2Mn0.6Mg0.4F4

Inelastic neutron scattering experiments were performed on a two-dimensional dilute antiferromagnet, Rb 2 Mn 0.6 Mg 0.4 F 4 , 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 Δ E = 17.5 µeV. 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 )∝ 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 ∝ t 2/(2+θ) with an exponent, θ, as a function of the time, t . The exponent in S ( E ) is described as x = 1 - D f /(2+θ) with D f being the fractal dimension of the medium. The observed exponent, x , was in good agreement with a theoretical value.