Spin Waves & Magnon Dispersion — Heisenberg Ferromagnet

Quantized spin waves (magnons) in a Heisenberg ferromagnet have a quadratic dispersion ω∝k² at small k. The 2D simulation shows precessing spins; the dispersion diagram shows ω(k) for 1D, 2D, and with anisotropy.

Parameters

Exchange J: 1.0 Anisotropy K: 0.0 Magnon wavevec k: 0.3 Temperature: 0.3 Lattice:

Magnon Info

ω(k): —

Group vel: —

Gap (K>0): —

ω(k) = 2JS(1-cos ka) + 2KS
≈ JSa²k² + 2KS
Quadratic at small k