Finite frequency dynamics of magnetic domain walls

The dynamics of domain walls in an ac magnetic field is formulated. The coupled partial differential equations of the displacements of the domain wall in an external pinning potential coupled to the magnetic fields through Maxwell’s equations are obtained with proper jump conditions. These equations are solved numerically. Previous calculations are applicable only in the limit when the sample size is much less than the bare penetration depth whereas no such approximation is made in the present approach. The bowlike shape of the domain wall and its variation with time are obtained. For every point on the domain wall, its oscillation shows a phase lag which varies with time and is different from each other. Our calculation provides for an interpretation of recent experimental results that observe a peak in the ac susceptibility of soft magnets as a function of the amplitude of the external magnetic field. The effects of the surface tension, the relaxation, and the pinning potential on the permeabilities are also investigated.