Metastability and a Temporal Phase Transition in the Random Field Ising Model

Abstract

At the preceding school in this series, we reviewed¹ the then current experimental understanding of the properties of an Ising model in a random field. Since then there have been a large number of both theoretical² and experimental studies^3,4,5,6but as we describe below the problem is still not completely understood. As reviewed in this school by Villain⁷, it is now generally accepted that the lower critical dimension in equilibrium, d_ℓ, is 2. Experiments performed by cooling random antiferromagnets in a uniform field to produce a random staggered field, have shown that long range order is not achieved in these experiments and that at low temperatures the properties are history dependent. Recently theories⁸ have been developed to reconcile these experimental results with the theoretical prediction that d_ℓ = 2, by considering the energy barriers to domain wall motion in the presence of random fields. In order to examine this problem in more detail and to test these theories in detail we have performed new measurements on the random d = 3 antiferromagnet Mn_o.75Zn_0.25F₂ and Belanger et al. have performed measurements of the d = 2^.antiferromagnet Rb₂Co_{0. 85}Mg_0.15F₄. We choose Mn_0.75Zn_0.25F₂ because the Mn_xZn_1−xF₂ system is well understood. The spins interact with Heisenberg interactions and weaker dipolar interactions, which are responsible for the uniaxial symmetry. The system therefore belongs to the Ising universality class but there are very many low energy spin waves which might be expected to relax the system towards thermodynamic equilibrium. At low temperatures and applied field H = 0, the spin wave gap is about 8 K and many of our measurements are at about 40 K.