Magnetic domain wall bowing in a perfect metallic crystal

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.