Spin dynamics in two-dimensional percolating Heisenberg antiferromagnets

Inelastic neutron-scattering experiments were performed on two-dimensional Heisenberg antiferromagnets, Rb2MncMg1-cF4, with the magnetic concentrations (c = 0.598 and 0.516) just above and below the percolation threshold (c(p) = 0.593 for the square lattice). Also, the magnetic response (chi " (q, E)) was investigated over a wide temperature range. We observed an overdamped chi " (q, E), which was well fitted to a damped harmonic-oscillator scattering function. At low temperatures, chi " (q, E) is dispersive and can be described by the predicted functional form of fracton excitations. As the temperature increases, the q-dependence gradually becomes weaker, and chi " (q, E) almost becomes independent of q at temperatures higher than 150 K. The incoherent character of chi " (q, E) at high temperatures indicates that collective motions do not exist due to very small thermal correlation lengths. Fracton excitations exist only at low temperatures.