Renormalization of Long-Wavelength Magnons

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Abstract
The renormalization of the spin-wave frequencies in a ferromagnet, due to the thermal population of other spin waves, has been calculated taking explicit account of the effects of the dipolar coupling between the spins. The results obtained by using the Green function decoupling approximation of Tyablikov differ markedly from those obtained using the symmetric decoupling recently suggested by Callen. For purposes of comparison, the renormalization of the mode of uniform precession specifically is examined in the low-temperature limit, where it is found that the renormalization obtained using the Callen decoupling is identical to that obtained from spin-wave theory. Experiments which measure the spin-wave renormalization are discussed with regard to the theory.