Harmonic Generation and Parametrically Coupled Spin Waves in Yttrium Iron Garnet

Second-harmonic generation and ferromagnetic resonance have been investigated in spheres of yttrium iron garnet (YIG) as a function of incident power above the threshold for excitation of $z$-directed spin waves by the second-order Suhl instability. The fundamental frequency was 8.42 GHz and the temperature 300 °K. The second-harmonic power output $P_{2\omega }$ has the following features above threshold: (a) $P_{2\omega }$ goes through a minimum and then a maximum as a function of incident power; (b) the line profile of $P_{2\omega }$ versus dc field $H$ shows two and then three peaks; (c) sufficiently far above threshold, $P_{2\omega }$ initially increases after the pulse of incident power is turned off. None of these effects is correlated with unusual behavior of the transverse magnetization, which always increases with power above threshold, has a single resonance line, and begins to decay as soon as incident power is turned off. The results are explained in terms of parametric coupling between the initially excited $z$-directed spin waves and other spin waves, with explicit account taken of the ensuing phase relations. These tend to make the other spin waves interfere destructively with the uniform mode ($k=0\mathrm{}$) in their contribution to $P_{2\omega }$. In this way, quantitative agreement between theory and experiment is obtained with reasonable values for two adjustable parameters. Coherent phase relations between the interacting spin waves are essential for an understanding of the results. If all $k\ne 0$ magnon interactions are lumped into effective relaxation rates, it is possible to explain the transverse resonance data, but not the second-harmonic effects.