Fractal structure and critical scattering in the three-dimensional percolating antiferromagnet, RbMn_0.31 Mg_0.69 F₃

We have performed neutron scattering experiments to investigate the static magnetic structure and the magnetic critical scattering in the three-dimensional percolating Heisenberg antiferromagnet, RbMn_0.31 Mg_0.69 F₃, whose magnetic concentration is just at the percolation concentration for a cubic lattice, c_P = 0.312. Magnetic scattering was observed around the superlattice point, (frac(1, 2), frac(1, 2), frac(1, 2)). We determined the Néel temperature of this system to be T_N = 4.0 ± 0.5 K, and found that the critical scattering above T_N is similar to that observed in the homogeneous system. At T = 1.6 K well below T_N, the scattering function is described by a sum of the critical scattering and elastic scattering components, and we demonstrated that the q-variation of the intensity of the elastic scattering component can be described using the fractal dimension.