NMR dynamics in disordered magnets |
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Authors: | R. Orbach |
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Affiliation: | (1) Department of Physics, University of California, 90024 Los Angeles, CA, USA |
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Abstract: | The excitation dynamics of site diluted magnets can be described at low energies (long length scales) by magnons, and above a crossover frequency, ωc, (short length scales) by fractons. The density of fracton states is given by , where is the fracton dimensionality. Dilution gives rise to a characteristic length ξ∝(p−p c)ν, wherep c is the critical concentration for (magnetic) percolation. The crossover frequency ωc is proportional to ξ-1[1+(θ/2)], where θ is the rate at which the diffusion constant decays with distance for diffusion on an equivalent network. A fractal dimensionD describes the density of magnetic sites on the infinite network, and . For percolating networks, for all dimensions ≥2. Neutron scattering structure factor measurements by Uemura and Birgeneau compare well with calculations using fracton concepts. Magnons are extended at low energies, while the fracton states are geometrically localized, with a wave function envelope proportional to exp . Here, is the fracton length scale at frequency ω. The exponentd ϕ lies between 1 andd min, the chemical length index (of the order of 1.6 in three dimensions). The localization of the magnetic excitations causes a spread in the NMR relaxation rates. A given nuclear moment will experience only a limited set of fracton excitations, resulting in an overall non-exponential decay of the NMR relaxation signal. When strong cross-relaxation is present, the relaxation will be exponential, but the temperature dependence will be strongly altered from the concentrated result. |
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