Magnon dispersion E(k) = D·k² in ferromagnet; Bloch T^(3/2) law
Spin waves (magnons) are the collective excitations of a ferromagnet. The dispersion relation E(k) = D·k² at long wavelengths reflects the quadratic nature of the Heisenberg exchange interaction. At finite temperature T, the Bose-Einstein distribution of thermally excited magnons reduces the magnetization by ΔM ∝ T^(3/2) (Bloch 1930).