Spin Waves & Magnon Dispersion

Ferromagnetic Spin Chain · Magnon Band · Bloch T^(3/2) Law · FMR

Exchange J/k_B (meV) 2.0

Anisotropy K_a (meV) 0.20

External field H (T) 0.30

Temperature T (K) 100

Number of spins 30

ω(k) = 2JS(1−cos ka) + gμ_B(H + K_a)

Long-wave: ω ≈ JSa²k² (quadratic dispersion)

M(T) ≈ M₀[1 − C(T/T_c)^(3/2)] Bloch law

FMR: ω_0 = gμ_B(H + K_a/M_s) uniform mode