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

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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_{\text{p}} = 0.593, well above the Néel temperature, and with a high energy-resolution of \Delta 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)\propto 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 \langle R^{2}(t)\rangle\propto 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_{\text{f}}/(2+\theta) with D_{\text{f}} being the fractal dimension of the medium. The observed exponent, x, was in good agreement with a theoretical value.
2012-07-15