Magnon Dispersion — Ferromagnet

Magnons are quantized spin waves — collective precession of magnetic moments in a ferromagnet. Their dispersion relation ω(k) = Dk² (at small k) reflects the quadratic, Goldstone-like nature of broken rotational symmetry.

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ω(k) = Δ + Dk² ; D = 2JSa² (Heisenberg ferromagnet, long-wavelength limit)