Random fields and phase transitions in model magnetic systems

Abstract

Random fields occur in a wide variety of physical systems varying from type II superconductors to two-component fluids in a random medium. However, only in model magnetic systems have systematic studies as a function of both temperature and random-field strength been possible. In this article we review recent neutron and magnetic X-ray scattering studies of the magnetic ordering processes in the antiferromagnets Mn 0.75Zn 0.25F 2, Fe 0.5Zn 0.5F 2 and Fe 0.75Co 0.25TiO 3 in an applied magnetic field. These systems should all represent realizations of the three-dimensional random-field Ising model which is the simplest version of the random-field problem in models with discrete symmetry. In all cases on field cooling (FC) the systems evolve continuously from a high-temperature paramagnetic state to a low-temperature antiferromagnetic domain state. However, on cooling to low temperatures in zero field and then applying a field (ZFC) long-range order (LRO) is obtained. On subsequent heating in the three systems the LRO vanishes continuously with a rounded power-law behavior which has been labelled trompe l'oeil critical behavior. The width of the transition region scales as H 2. Reconsideration of indirect ZFC specific-heat measurements shows that the observed peaks, previously attributed to equilibrium critical fluctuations, instead arise entirely from a LRO contribution, scaling like dM s 2/dT , to the measured quantity. Here M s is the staggered magnetization. These results thus reconcile scattering and bulk property measurements of random-field Ising systems.