k (wave number)—
ω (frequency)—
Mode Energy—
The Heisenberg model: H = -J Σ Sᵢ·Sᵢ₊₁. Classical spin dynamics: dS/dt = S × B_eff where B_eff = J(Sᵢ₋₁+Sᵢ₊₁). Magnon dispersion: ω(k) = 4J sin²(k/2). At k≈0: acoustic (linear), at k=π: gapped zone-boundary magnon.