Dispersion relation for the domain wall motion

The dispersion relation for the domain wall motion is experimentally measured as a function of the in-plane field, Hp, for the thin films of substituted YIG by using the magnetooptical Faraday effect. A sample having a width of 190 μm is prepared by ion-etching the garnet film. Because of the discontinuity of the magnetization at the edges of the sample, it is possible to excite the standing modes of the wall across the width of the sample. These standing modes have a well defined excitation frequencies between 10 MHz and 50 MHz for the sample investigated and modes up to n = 7 have been experimentally resolved in the frequency sweep experiment. By measuring the excitation frequency for different modes, the dispersion relation is plotted. A linear dispersion relation as predicted by the rigid wall theory and the flexural wall theory is experimentally verified. From the slope of the ω-k curve, the group velocity of the domain wall modes is measured to be 550 ± 50 m/s. The experimentally measured values of the group velocity are higher than the values predicted by the two theories.