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

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Syromyatnikov, A. V.

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We discuss the spin-wave interaction in two-dimensional (2D) Heisenberg
ferromagnet (FM) with dipolar forces at $T_C\gg T\ge0$ using 1/S expansion. A
comprehensive analysis is carried out of the first 1/S corrections to the
spin-wave spectrum. In particular, similar to 3D FM discussed in our previous
paper A.V. Syromyatnikov, PRB {\bf 74}, 014435 (2006), we obtain that the
spin-wave interaction leads to the {\it gap} in the spectrum $\epsilon_{\bf k}$
renormalizing greatly the bare gapless spectrum at small momenta $k$.
Expressions for the spin-wave damping $\Gamma_{\bf k}$ 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 $\Gamma_{\bf k}$ and $\Gamma_{\bf k}/\epsilon_{\bf
k}$ at small momenta. In particular, a peak appears in $\Gamma_{\bf k}$ and
$\Gamma_{\bf k}/\epsilon_{\bf k}$ at small $k$ and at any given direction of
$\bf k$. If $S\sim1$ the height of the peak in $\Gamma_{\bf k}/\epsilon_{\bf
k}$ is not larger than a value proportional to $T/D\ll1$, where $D$ is the
spin-wave stiffness. In the case of large spins $S\gg1$ the peak in
$\Gamma_{\bf k}/\epsilon_{\bf k}$ cannot be greater than that of the classical
2D FM found at $k=0$ which height is small only {\it numerically}: $\Gamma_{\bf
0}/\epsilon_{\bf 0}\approx0.16$ for the simple square lattice. Frustrating
next-nearest-neighbor exchange coupling increases $\Gamma_{\bf 0}/\epsilon_{\bf
0}$ in classical 2D FM only slightly. We find expressions for spin Green's
functions and the magnetization. The latter differs from the well-known result
by S.V. Maleev, Sov. Phys. JETP {\bf 43}, 1240 (1976). The effect of the
exchange anisotropy is also discussed briefly.

##### Keywords

Condensed Matter - Strongly Correlated Electrons