Neutron scattering study of the effect of a random field on the three-dimensional dilute Ising antiferromagnet ${\mathrm{Fe}}_{0.6}$${\mathrm{Zn}}_{0.4}$${\mathrm{F}}_2$

We report a comprehensive neutron scattering study of random-field effects in the three-dimensional Ising antiferromagnet ${\mathrm{Fe}}_{0.6}$ ${\mathrm{Zn}}_{0.4}$ ${\mathrm{F}}_2$. The sample is the same one used in high-precision birefringence studies. The scattering is dependent on the prior history of the sample at all temperatures below a well-defined temperature which agrees with the phase boundary reported in the birefringence studies to within 0.2 K. When the sample is cooled in a field (FC), long-range order is not established and the scattering has a Lorentzian-squared profile with a width K≊$H^2$, as found in the three-dimensional samples studied earlier with neutron scattering techniques. On the other hand, when the sample is cooled in zero field into the Néel state, the field raised and the temperature then increased (ZFC), the scattering close to the phase boundary consists of an antiferromagnetic Bragg component superimposed on scattering which is characteristic of the FC procedure. The Bragg component is absent when the crystal is heated above the phase boundary. In addition, if after field cooling the system is heated, the width of the scattering is unchanged until the phase boundary is reached. None of the existing $d_l$=2 low-temperature theories explains such behavior in the vicinity of the phase boundary. Above the phase boundary ZFC and FC results agree, indicating that the system is always in equilibrium. We have studied the critical behavior in this region and the scattering is very different from that with H=0. Specifically, the scattering profiles show a large Lorentzian-squared component and over a limited temperature range the inverse correlation length varies linearly with temperature.