Parameters
Mode
Dispersion Relation
FM: ε(k) = 4J·sin²(k/2)
= 2J(1 − cos k)
AFM: ε(k) = 4|J|·|sin k|
(linear at small k → spinon)
Key: FM has quadratic k², AFM has linear |k| dispersion at k→0
= 2J(1 − cos k)
AFM: ε(k) = 4|J|·|sin k|
(linear at small k → spinon)
Key: FM has quadratic k², AFM has linear |k| dispersion at k→0
Physics Insight
A magnon is a quantized spin wave — a coherent precession of spins. In a ferromagnet, magnons are gapped by anisotropy; in an antiferromagnet, they are gapless (Goldstone bosons of broken SU(2)).