Transition to long-range order in the three-dimensional random-field Ising model

We report both synchrotron-x-ray and neutron-diffraction studies of the magnetic ordering in a crystal of ${\mathrm{Mn}}_{0.75}$ ${\mathrm{Zn}}_{0.25}$ ${\mathrm{F}}_2$ in a magnetic field. The neutron experiments reproduce previous results showing the establishment of a short-range domain state on cooling in a field. Remarkably, the magnetic x-ray scattering shows that within a few microns of the surface there is a second-order transition to true long-range order on field cooling. Implications of these results are discussed.