Anomalous critical scattering from a three-dimensional percolating antiferromagnet RbMn_0.31Mg_0.69F₃

A neutron-diffraction experiment was performed to measure the critical scattering from a percolating antiferromagnet RbMn_0.31Mg_0.69F₃, whose magnetic concentration is just at the percolation concentration for a cubic lattice, c_p = 0.312. The magnetic scattering was observed at around the superlattice point (1/2, 1/2, 1/2). We found that the scattering function exhibits a non-Lorentzian line shape, S(q) = (q² + κ²)^-x (q and κ are the momentum transfer and the inverse correlation length, respectively), with the exponent x = 0.6 ± 0.1 at the low temperature of 1.6 K, and that the exponent is attributed to the fractal structure of the percolating network. Also, the system was found to exhibit a crossover to the homogeneous state at high temperature.