Magnetic domain wall bowing in a perfect metallic crystal

Publisher Website
Google Scholar
Abstract
From the equation of motion for a domain wall in a perfect crystalline sheet, expressions for the steady‐state mobility, power loss, and wall profile are calculated in terms of the magnetic eddy current field acting on the wall. An exact expression for the eddy current field for a given wall shape is derived, and an iteration procedure is used to obtain approximate results. At low wall velocity (0.16MsHAd/ε somewhat smaller than unity, where Ms is the saturation magnetization, HA is the applied field, d is the sheet thickness and ε is the wall energy per unit area) the equation for the wall profile, x=xw(y), is approximately xw= (MsHAd2/πε) [(Jm=1,3,5... 1/m3)−1 Jm=1,3,5... [sin(mπ/2) m−4](1−cosmπy/d) −(πy2/d2)], where the x axis is normal to the wall and the y axis is normal to the sheet, with the origin at the middle of the sheet. At some critical velocity, or applied field, which in rough approximation is given by 0.16MsHAd/ε equal to unity, no steady‐state solution exists. Severe wall bowing cannot occur except near this critical field, just before instability occurs.