Quadratic frequency dependence of spinwave instability thresholds from fast-relaxing ions

The effects of fast-relaxing ions on the microwave frequency dependence of the spinwave instability threshold h_c and the imaginary permeability μ" of ferrites is examined. The role of fast relaxing ions in raising spinwave instability thresholds and average power absorption in microwave ferrites is analyzed by introducing rare-earth single-ion relaxation concepts into conventional FMR (ferrimagnetic resonance) theory. The agreement between theory and earlier experimental results confirms that the increase with frequency is quadratic for h_c and inverse linear for μ"