Neutron and x-ray scattering studies of field-cooled ordering in the three-dimensional random-field Ising model

We report a magnetic neutron and x-ray scattering study of the correlation length and order parameter of the random-field Ising magnets Fe0.5Zn0.5F2 and Mn0.45Zn0.55F2 on field cooling. Fitting the inverse correlation length, kappa, measured above the metastability temperature, T-M(H) in Fe0.5Zn0.5F2, at H=5 and 6 T to a power law yields the exponent nu=1.5+/-0.3 together with the equilibrium transition temperatures, T-N(H), which are found to be well below T-M(H). We also estimate gamma=2.6+/-0.5 and <(gamma)=5.7+/-1 for the connected susceptibility, chi, and the disconnected susceptibility, chi(dis), exponents, respectively. The x-ray data reveal a long range ordered component coexisting with short range magnetic order in the field-cooled state, for weak random fields in both samples. The nucleation of the long range order occurs below T-M(H). The intensity of the long range order component decreases with increasing field.