Decay properties of microwave-magnetic-envelope solitons in yttrium iron garnet films

Abstract

Microwave magnetic envelope (MME) wave-packet propagation in a nominal 7.2-\ensuremath{\mu}m-thick yttrium iron garnet film has been investigated to determine the decay properties of linear and nonlinear MME pulses. The data were obtained in the magnetostatic backward volume wave configuration with an in-plane static field of 1088 Oe and an operating frequency of 5 GHz. Output pulse profiles, peak powers, and integrated pulse energies were measured for 13 ns wide input pulses and propagation distances from 3 to 10 mm. The pulse energy decay rate \ensuremath{\mathrm{B}} is found to be 10.6\ifmmode\times\else\texttimes\fi{}${10}^{6}$nrad/s and independent of the input power level up to 400 mW, even though the nonlinear response begins at 80 mW. This \ensuremath{\mathrm{B}} value is twice the relaxation rate \ensuremath{\eta} from ferromagnetic resonance. In the linear regime below 80 mW, the amplitude decay rate \ensuremath{\alpha} of the dynamic microwave magnetization peak amplitude is nearly constant at a value ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{low}}$\ensuremath{\approx}7.8\ifmmode\times\else\texttimes\fi{}${10}^{6}$nrad/s, which is somewhat greater than \ensuremath{\mathrm{B}}/2 and significantly less than \ensuremath{\mathrm{B}}. This ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{low}}$ is greater than the decay rate due to damping, \ensuremath{\eta}=\ensuremath{\mathrm{B}}/2, because of dispersion. With the onset of the nonlinear soliton response above 80 mW, \ensuremath{\alpha} gradually increases and saturates for input powers greater than 200 mW at a value ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{high}}$ which is equal to the energy decay rate \ensuremath{\mathrm{B}}. This result indicates that the amplitude decay rate for MME solitons is very close to twice the relaxation rate. This result is predicted in the limit of a vanishingly small damping. Experimentally, it appears to be valid even when the relaxation is significant. The transition region from ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{low}}$ to ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{high}}$ has been quantitatively modeled through the nonlinear Schr\"odinger equation, and demonstrates an explicit change in the critical propagation length for soliton formation from 8 mm at the low power end of the transition to 3 mm at the high power end.