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

Abstract

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: Γ 0 / ε 0 ≈ 0.16 for the simple square lattice.