Columnar domains and anisotropic growth laws in dipolar systems
AbstractMagnetic and dielectric solids are well-represented by the Ising model with dipolar interactions (IM+DI). The latter are long-ranged, fluctuating in sign, and anisotropic. Equilibrium studies have revealed novel consequences of these complicated interactions, but their effect on nonequilibrium behavior is not explored. We perform a deep temperature quench to study the kinetics of domain growth in the d=3 IM+DI. Our main observations are (i) the emergence of columnar domains along the z axis (Ising axis) with a transient periodicity in the xy plane; (ii) anisotropic growth laws: ℓρ(t)∼tϕ; ℓz(t)∼tψ, where ρ⃗=(x,y) and ℓ is the characteristic length scale; (iii) generalized dynamical scaling for the correlation function: C(ρ,z;t)=g(ρ/ℓρ,z/ℓz); and (iv) an asymptotic Porod tail in the corresponding structure factor: S(kρ,0;t)∼kρ−3; S(0,kz;t)∼kz−2. Our results explain the experimentally observed columnar morphologies in a wide range of dipolar systems, and they have important technological implications.