Spin-wave interaction in two-dimensional ferromagnets with dipolar forces

We discuss the spin-wave interaction in two-dimensional (2D) Heisenberg ferromagnet (FM) with dipolar forces at T_C?T?0 using 1/S expansion. A comprehensive analysis is carried out of the first 1/S corrections to the spin-wave spectrum. In particular, we obtain that the spin-wave interaction leads to the gap in the spectrum ε_k renormalizing greatly the bare gapless spectrum at small momenta k. Expressions for the spin-wave damping Γ_k are derived self-consistently and it is concluded that magnons are well-defined quasi-particles in both quantum and classical 2D FMs at small T. We observe thermal enhancement of both Γ_k and Γ_k/ε_k at small momenta. In particular, a peak appears in Γ_k and Γ_k/ε_k at small k and at any given direction of k. If S∼1 the height of the peak in Γ_k/ε_k is not larger than a value proportional to T/D?1, where D is the spin-wave stiffness. In the case of large spins S?1 the peak in Γ_k/ε_k cannot be greater than that of the classical 2D FM found at k=0 whose height is small only numerically: Γ₀/ε₀≈0.16 for the simple square lattice.