Continuum model for dipolar coupled planar lattices

Abstract In an effective continuum approach alike the phenomenological Landau theory, we study low energy excitations in a square lattice of dipolar coupled magnetic moments μ , over continuously degenerate microvortex (MV) ground states defined by an arbitrary angle 0 v =μ (cos θ, sin θ) and the ferromagnetic (FM) vector f = 1 2 (∂yvx, −∂xvy). The excitation energy density ∼f2 leads to a non-linear Euler equation. It allows, besides common linear waves of small amplitude, also non-linear excitations with unlimited (but slow) variation of θ( r ) . For plane wave excitations θ( r )=θ( n · r ) propagating along n = (cos ϕ, sin ϕ), exact integrals of Euler equation are found. The density of excitation states turns anisotropic in θ, conforming to the enhanced occurrence of MV-like states with θ close to 0 or π/2 in our Monte Carlo simulations of this system at low excitation energies