Domain Growth in Random Magnets

– We study the kinetics of domain growth in ferromagnets with random exchange interactions. We present detailed Monte Carlo results for the nonconserved random-bond Ising model, which are consistent with power-law growth with a variable exponent. These results are interpreted in the context of disorder barriers with a logarithmic dependence on the domain size. Further, we clarify the implications of logarithmic barriers for both nonconserved and conserved domain growth. A homogeneous binary mixture becomes thermodynamically unstable if it is rapidly quenched below the coexistence curve. The subsequent far-from-equilibrium evolution of the system is characterized by the emergence and growth of domains enriched in the new equilibrium phases. The domain morphology is quantified by (a) the time-dependence of the domain scale R(t), where t is the time after the quench; and (b) the correlation function or its Fourier transform, the structure factor [1]. There is a good understanding of domain-growth kinetics in pure and isotropic systems, where the domain scale shows a power-law behavior, R(t) ∼ t. For the case with nonconserved order parameter, e.g., ordering of a ferromagnet into up and down phases, we have θ = 1/2. On the other hand, for the case with conserved order parameter, e.g., phase separation of a binary (AB) mixture into Aand B-rich domains, we have θ = 1/3 when growth is driven by diffusion. Of course, real experimental systems are neither pure nor isotropic. In this letter, we focus on domain growth in ferromagnets and binary alloys with quenched disorder in the form of random exchange interactions. There have been many experimental [2–4] and numerical [5–10] studies of this problem [11]. At early times, domain coarsening is not affected by disorder. Then, there is a crossover to a disorder-affected regime, which occurs earlier for higher disorder amplitudes. There have also been many studies of domain growth in spin glasses [12,13], where the amplitude of disorder is such that the local exchange coupling may be either ferromagnetic or antiferromagnetic. Inspite of this attention, the nature of asymptotic domain growth in both random magnets and spin glasses remains the subject of much controversy. The present letter resolves this controversy in the context of random magnets. We present detailed Monte Carlo (MC) results which show that asymptotic growth in these systems is consistent with a power-law behavior, with the growth exponent (θ) depending on the temperature (T ) and