The shape, energy, eddy current loss, and relaxation damping of magnetic domain walls in glassy iron wire

A magnetostatic model is developed for extended domain boundaries of the type observed by O'Handley [1] separating opposed axially magnetized sections of glassy iron wire. The domains in any circular wire cross section are separated by a boundary that has the minimum length consistent with their areas, and the distribution of polarization over the wire length is such as to minimize the sum of the domain wall and magnetic divergence energies. The dependence of boundary length2Lon the wire diameter2a, remanent polarization JR, and domain wall energy per unit area γ, is evaluated so that γ may be obtained from measured values ofa, L, and JR. For the glassy iron material [1] γ = 0.76 mJm^-2. Eddy current loss and relaxation damping coefficients are calculated for a two-dimensional model with the same cross section and then appropriately averaged to obtain the mean coefficients for the three-dimensional model. It is shown that 55 percent of the losses observed by O'Handley are due to eddy currents, and attribution of the remainder to relaxation damping yields a value of 6.2 kgm^-2s^-1for the relaxation damping coefficient indicating a Gilbert damping coefficientalpha_{G}simeq0.06if one assumes the exchange constantA = 10^{-11}Jm^-1. De Blois' observations of domain wall motion in iron whiskers [9] are also briefly discussed.