Spin Waves — Magnon Dispersion & Exchange Stiffness

In ferromagnets, small-angle spin deviations propagate as spin waves (magnons). The Heisenberg exchange interaction gives a quadratic dispersion ω(k) = ω₀ + Dk² where D is the exchange stiffness (spin-wave stiffness constant). Magnons are bosonic quasiparticles with density of states ∝ ω^(1/2), governing low-temperature heat capacity and magnetization corrections.

Exchange J 1.00
Zeeman field H 0.30
Wavevector k (×π/a) 0.30
Temperature 0.20