Spin waves in the 1D Heisenberg ferromagnet
In the 1D Heisenberg ferromagnet (H = −J∑SᵢSᵢ₊₁), magnons (spin waves) are the elementary excitations. The dispersion relation is ε(k) = 2JS(1−cos(ka)) + gμ_B·h. With XXZ anisotropy Δ the ferromagnetic dispersion acquires a gap: ε(k) = 2JS(Δ − cos(ka)). Below we show spin precession at wavevector k and the full dispersion curve.