Spin waves in a band ferromagnet: spin-rotationally symmetric study with   self-energy and vertex corrections
  First-order quantum corrections to the transverse spin-fluctuation propagator are obtained within a systematic inverse-degeneracy 1/N expansion, which provides a spin-rotationally symmetric scheme for including self-energy and vertex corrections while preserving the Goldstone mode. An expression is obtained for the spin-wave stiffness constant including all first-order quantum corrections, and the dominant contribution is shown to yield a strong reduction due to a correlation-induced enhancement in the exchange-energy gain upon spin twisting. The quantum reduction factor U/W highlights the subtlety in the characteristic competition in a band ferromagnet between interaction U and bandwidth W. Quantum corrections also yield an intrinsic spin-wave damping mechanism due to coupling between spin and charge fluctuations. 
Avinash Singh