Random fields and three-dimensional Ising models:CoxZn1−xF2

Abstract

The phase transition and ordering of the $d=3\mathrm{}$ diluted Ising antiferromagnet ${\mathrm{Co}}_x{\mathrm{Zn}}_{1-x}{\mathrm{F}}_2$ has been studied using two-axis neutron diffraction for the cases (i) where $x$ is close to the percolation threshold, in zero applied magnetic field, and (ii) as a function of applied magnetic field for samples with $x=0.26\mathrm{} \mathrm{and} 0.35$. The results of the percolation study show complicated behavior, probably due to concentration gradient problems. Nevertheless, there is strong evidence that the inverse correlation length decreases to zero at the onset of long-range order. The results of the magnetic field study are compared with the theoretical predictions for the $d=3\mathrm{}$ Ising model in a random field. It is found that when the samples are cooled in even the smallest (nonzero) fields the long-range magnetic order is destroyed and that the structure factor is well described by the Lorentzian plus Lorentzian squared form. The inverse correlation length is found to have a power-law dependence on the applied magnetic field at low temperature with exponents ${\nu }_H=2.17\mathrm{}\pm 0.3$ for the $x=0.26\mathrm{}$ sample and ${\nu }_H=3.63\mathrm{}\pm 0.3$ for the $x=0.35\mathrm{}$ sample. This result is not consistent with the current theoretical predictions for the field dependence of the inverse correlation length in the $d=3\mathrm{}$ Ising model in a random field. The measurements also show that the system is frozen at low temperatures and this freezing may be responsible for the discrepancy between theory and experiment.