Collective spin precession, magnon dispersion, and BEC at k=0
Magnons are quanta of spin waves — collective precessions of magnetic moments in an ordered ferromagnet. Their dispersion relation is ω(k) = D·k² + Δ (quadratic in 3D, with anisotropy gap Δ). Like bosons, magnons can undergo BEC: at sufficient density/low T, macroscopic occupation of the k=0 mode occurs (Magnon BEC observed in YIG, Demokritov 2006). The spin-wave texture visualizes the phase of the precessing order parameter.