Spin Wave Magnon Dispersion
Heisenberg spin chain: collective excitations and magnon band structure
Parameters
Exchange J:
1.00
Anisotropy Δ:
1.00
External field h:
0.00
Wave vector k (π units):
0.50
Lattice constant a:
1.00
Precession type:
Ferromagnet (FM)
Antiferromagnet (AFM)
Heisenberg dispersion (FM):
ω(k) = 4JS(1−cos ka) + 2hS
Antiferromagnet:
ω(k) = 4JS|sin ka|
Current k-mode:
ω =
—
Group velocity:
vg =
—
Gap at k=0:
Δ₀ =
—
The dispersion is quadratic near k=0 (FM) or linear (AFM Goldstone mode). Magnons are bosonic quasiparticles carrying spin-1.