Abstract
The dynamical structure factors, S ( q ,ω), for antiferromagnetic fractons in diluted three-dimensional (3D) and two-dimensional (2D) Heisenberg systems, RbMn 0.4 Mg 0.6 F 3 and Rb 2 Mn 0.598 Mg 0.402 F 4 , respectively, with a magnetic concentration close to the percolation concentration, were observed through high-resolution (Δ E = 17.5 µeV) inelastic neutron scattering experiments well below T N . The exponents describing the peak intensity ( A ( q ) ∝ q - y ) and the dispersion relation ( E ( q ) ∝ q z ) were determined to be y = 2.9 ±0.1 and z = 2.5 ±0.1 for the 3D system and y = 2.9 ±0.2 and z = 1.8 ±0.2 for the 2D system, respectively. In addition, the validity of the single-length-scaling postulate (SLSP) was confirmed for S ( q ,ω) 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.
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