Columnar domains and anisotropic growth laws in dipolar systems

Magnetic 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: ℓ_{ρ}(t)∼t^{ϕ}; ℓ_{z}(t)∼t^{ψ}, where ρ[over ⃗]=(x,y) and ℓ is the characteristic length scale; (iii) generalized dynamical scaling for the correlation function: C(ρ,z;t)=g(ρ/ℓ_{ρ},z/ℓ_{z}); and (iv) an asymptotic Porod tail in the corresponding structure factor: S(k_{ρ},0;t)∼k_{ρ}^{-3}; S(0,k_{z};t)∼k_{z}^{-2}. Our results explain the experimentally observed columnar morphologies in a wide range of dipolar systems, and they have important technological implications.