Magnons and factons in diluted antiferromagnets (invited)

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Abstract
Site-diluted antiferromagnets with short-range interactions can serve as a model magnetic percolation system. A length scale ξ exists such that for length scales (1/q)>ξ the structure is continuous (hydrodynamic limit), and the magnetic excitations are antiferromagnetic magnons, with a stiffness constant which depends critically upon the magnetic concentration. For length scales (1/q)<ξ, the structure is fractal, and the magnetic excitations are fractons, with a characteristic dispersion law. The fracton excitations are (strongly) spatially localized. The magnons are expected to be extended in the very long length scale limit, with the possibility of Anderson (weak) localization for length scales longer than ξ. The magnetic excitations cross over from magnon to fracton at an energy ωc∝ξ−[1+(θ/2)], where θ is the anomalous diffusion exponent. We have calculated the scattering form factor I(q,ω) for magnetic excitations of a d=3 simple cubic antiferromagnet within the effective medium approximation (EMA), as a function energy transfer ω and momentum transfer q. We find that at small fixed q (within the magnon regime), p>pc, I(q,ω) is sharply peaked at the magnon frequency. Near to pc, a second (but small) peak at ωc is visible on the asymmetric high-energy tail of I(q,ω). For larger fixed q (within the fracton regime), I(q,ω) is centered about the fracton frequency, although it is quite broad, reflecting the strong spatial scattering of fractons.