Collective precession of magnetic moments in ferromagnets
Spin waves (magnons) are quantized collective precessions in ordered magnets. For a 1D ferromagnet, the dispersion is omega(k) = 4JS(1-cos ka) + 2KS, giving a quadratic (Goldstone) mode at k=0 for K=0. Antiferromagnets have linear dispersion omega ~ |k|, analogous to acoustic phonons.