Collective precession of magnetic moments in a Heisenberg ferromagnet; the dispersion relation ω(k) = 4JS sin²(ka/2) for spin-S spins with exchange J defines the magnon (spin-wave quasiparticle).
Bloch (1930) showed magnons are bosonic quasiparticles. Their density of states ∝ ω^(1/2) in 3D (Bloch T^(3/2) law for magnetization reduction). In 1D and 2D, Mermin-Wagner theorem forbids long-range order at T>0. Recent experiments probe magnon spin Seebeck effect and magnon Bose-Einstein condensation.