Steady-state Eddy-current dominated magnetic domain wall motion with severe bowing and necking

Abstract

The bowed shape and mobility of domain walls spanning metallic laminations and in steady-state eddy-current-limited motion have been calculated using a linear spline function x w( y), symmetric about the sheet centre plane y = 0, to represent the wall profile without imposing the usual constraint that x w( y) be single valued. Profiles have been calculated for all integral values of the reduced wall speed u up to 51. (Here, u = 8 VM 2 D 2/ π 3 γϱ, V) is the velocity d x/d d of the wall along sheet of thickness D and resistivity ϱ, γ is the specific surface wall energy and 2 M the change in magnetization effected by its passage). For u⩾21, profiles are multivalued with a pinched neck preceding a slightly bulbous tail. Thus, over a range of depths in the lamination, flux is reversed three times by the passage of such a “pinched” wall. The wall profiles vary very smoothly with increasing u with no trace of the oscillations obtained when they were constrained to be single valued. The results suggest that at a finite speed u c > ̆ 50 , the pinched neck ma of drop-like domains may break away from the tail.