Magnon Spectrum

Spin waves in a ferromagnet — collective magnetic excitations

Magnons are quasiparticles representing quantized spin waves. In a ferromagnet, the dispersion is ω(k) = Δ + Dk² (quadratic, unlike phonons which are linear). The stiffness D relates to the exchange interaction J and lattice constant a: D = 2JSa². The density of states g(ω) ∝ ω^(1/2) leads to the Bloch T^(3/2) law for magnetization: M(T) = M₀[1 − C·T^(3/2)].