On the stability of spin waves at finite temperatures

The temperature dependent exchange stiffnessD, defined for long wavelength spin waves by=Dq², is calculated for very weak itinerant ferromagnets. It is found that for a general single band of d-electrons,D reduces to a very simple form givingD(T)=D(0)/₀ in the limit₀0. The stability condition for spin waves at finite temperatures is thenD(0) > 0 and/₀ > 0, where is the relative occupation ± spin sub-bands and₀ its value at 0°K.The authors are grateful to E. P. Wohlfarth for helpful discussions.