Temperature Variation of the Spin-Wave Dispersion Relation

The spin‐wave dispersion relation, including the quartic term, has been measured at 61.8 Gc/sec between 4° and 300°K by spin‐wave resonance in Permalloy films. Both the quadratic and the quatric terms vary as $T^{\frac{5}{2}}$ up to 80°K and approximately as $T^{\frac{3}{2}}$ up to room temperature. This is the same behavior previously reported for the quadratic term using a different Permalloy film at 10 Gc/sec. The long‐range exchange interaction 〈ρ²〉=ΣJ(r)r⁴/ ΣJ(r)r², where J(r) is the exchange integral between spins a distance r apart, has been obtained as a function of temperature from the ratio of the coefficient of the quatric term to the coefficient of the quadratic term.