Random-field Ising ordering above magnetic vacancy percolation

The critical behavior of three dimension (d = 3) random-field Ising antiferromagnets Fe_0.87Zn_0.13F₂ and Fe_0.85Zn_0.15F₂, which have magnetic concentrations above the vacancy percolation threshold x_p = 0.76, have been studied using optical birefringence, Faraday rotation, neutron scattering and X-ray techniques in large magnetic fields up to 11 T.; The specific heat critical behavior appears to be a asymmetric cusp in zero field and a logarithmic divergence in fields up to 7 T. The measured critical exponent α = −0.07 ± 0.02 and amplitude ratio A+/A− = 1.4 ± 0.1 for H = 0, are in excellent agreement with the known d = 3 random-exchange Ising universality class.; Neutron scattering measurements do not exhibit the severe critical scattering hysteresis seen in lower concentration samples. The H = 0 data were fit to Lorentzian line shapes. The data in the field were fit to modified Tarko-Fisher and Fisher-Burford forms below and above the transition and the critical exponents were determined. The line shapes in applied fields above the transition are found to exhibit evidence for fractal spanning cluster structures.; X-ray scattering measurements were performed on Fe_0.85Zn _0.15F₂. In applied fields, the Bragg intensity vs. T goes to zero vertically in contrast to low magnetic concentration experiments. The critical exponent β = 0.16 ± 0.02 for the random-field Ising model order parameter is determined in magnetic fields up to 11 T. The crossover exponent of &phis; = 1.42 ± 0.02 is found in agreement with previous experiments and theory. The observed value of β is consistent with other experimental random-field critical exponents, but disagrees sharply with Monte Carlo and exact ground state calculations on finite-sized systems. Hysteretic behavior below the transition temperature is observed in the order parameter.; Monte Carlo simulations were used to verify the experimental results. The critical exponents for the order parameter and the shape of the specific heat agree well with the experiments. Similar hysteretic behavior to that observed in experiments is also found in the simulations upon reversing the temperature just below transition.