Coupled Oscillations of the Magnetic Domain-Domain Wall System in Substituted Garnet Thin Films

The dynamic response of parallel stripe domains in Ga substituted YIG thin films was studied using a rf spectrometer, incorporating an rf structure as the coupling device. Three signals, corresponding to the "in-phase" ((omega)('+)) and "out of phase" ((omega)('-)) domain ferromagnetic resonance and the domain wall resonance (DWR) are observed for the first time in the same frequency-field regime. As an applied in-plane field H(,P) is increased toward in -plane saturation fields, the DWR and DR signals are observed to repel each other, resulting in frequency gaps. A series of five films, with 4(pi)M ranging from 475-1275 G and H(,u) ranging from 825-450 Oe and H(,sat) in the range 190-690 Oe were examined. The frequency range studied was 10-2400 MHz for in-plane fields up to 1 K Oe. A brief discussion of the samples, experimental set up and observations are given. A unified theory is developed to account for the dynamics of a system of magnetic domains and walls. A generalized expression for free energy is written down. The resulting equations of motion, in the linear response limit, are shown to yield a 6 x 6 determinant, whose zeros determine the frequencies of coupled oscillation and hence an expression for the observed frequency gaps. The effect of demagnetization energy is taken into account and the theory of Domain Wall Resonance for bubble materials is modified to include the effects of finite value of Q. Exact calculations are carried out for such parameters as wall energy, domain wall mass, etc. A new result of this work is the lifting of the singularity in the DWR frequency as saturation is approached. Effects of cubic anisotropy energy are also discussed. The theory is seen to fit the experimental data very well upon the introduction of two phenomenological fitting parameters, H(,1) and (alpha), especially in samples with Q > 1. The agreement between the theory and the experiment is discussed.