Antiferromagnetic Fractons in Diluted Heisenberg Systems RbMn0.4Mg0.6F3 and Rb2Mn0.598Mg0.402F4

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The dynamical structure factors, S(q,\omega), for antiferromagnetic fractons in diluted three-dimensional (3D) and two-dimensional (2D) Heisenberg systems, RbMn0.4Mg0.6F3 and Rb2Mn0.598Mg0.402F4, respectively, with a magnetic concentration close to the percolation concentration, were observed through high-resolution (\Delta E = 17.5 μeV) inelastic neutron scattering experiments well below T_{\text{N}}. The exponents describing the peak intensity (A(q) \propto q^{-y}) and the dispersion relation (E(q) \propto q^{z}) were determined to be y = 2.9 \pm 0.1 and z = 2.5 \pm 0.1 for the 3D system and y = 2.9 \pm 0.2 and z = 1.8 \pm 0.2 for the 2D system, respectively. In addition, the validity of the single-length-scaling postulate (SLSP) was confirmed for S(q,\omega) by using the above values of y and z. We experimentally demonstrated, for the first time, that the spectral dimension, \tilde{d}_{\text{AF}} = 1, is universal and independent of the embedding Euclidean dimensions of the systems.
2011-10-15