Recent Developments in Ferromagnetic Resonance at High Power Levels

The influence of inhomogeneities on the saturation of the ferromagnetic resonance is investigated. In the region of moderate power levels, the susceptibility at resonance $\mathrm{\chi \prime \prime }$ varies linearly with the square of the rf field $h$ . The magnitude of the slope ${\mathrm{\partial \chi \prime \prime /\partial h}}^2$ depends on the nature of the dominant scattering mechanism. If the uniform mode scatters primarily to spin waves of very large wavelength, the slope should be negative. Scattering to spin waves of short wavelength gives a positive contribution to the slope and can lead to a reversal of the sign. The theoretical predictions agree with measurements at X band on various polycrystalline garnets and ferrites. At very high power levels the opening angle of the precessing magnetization vector approaches a limiting value, which is related to the “line width” ${\mathrm{\Delta H}}_k$ of $z$ directed spin waves having the same frequency as the uniform mode. Experiments on single crystals and polycrystals of rare earth substituted garnets show that ${\mathrm{\Delta H}}_k$ increases approximately linearly with the rare earth content. The materials investigated contain Gd, Yb, Er, Sm, Dy, Ho, or Tb and for a given ratio of substitution ${\mathrm{\Delta H}}_k$ increases in that order. The line width ${\mathrm{\Delta H}}_k$ of $z$ directed spin waves is found to be approximately proportional to the line width $\mathrm{\Delta H}$ of the uniform mode as measured in single crystals. Experimental results on cobalt and zinc substituted nickel ferrite are reported. ${\mathrm{\Delta H}}_k$ increases linearly with the cobalt content. For the nickel-zinc ferrites with a large magnetic moment the saturation curve $\mathrm{(\chi \prime \prime \hspace{0.17em}}\mathrm{vs}{\mathrm{\hspace{0.17em}h}}^2)$ measured at X band shows a maximum well below the initial onset of nonlinearity. A theoretical explanation for this extraordinary behavior is given. A new nonlinear effect arising from spin wave instability in a microwave magnetic field applied parallel to the dc field has been observed. Spin waves which propagate in directions perpendicular to the dc field are most susceptible to this instability. The observed variation of the critical rf field strength agrees well with the theoretical predictions. It indicates that the spin-wave line width increases with increasing wave number and decreasing angle between propagation direction and dc magnetic field.