Measurements of the Domain Wall Area-Mobility Product during Slow Flux Reversals

A previous paper has shown that the sides of slow constant-voltage hysteresis loops on polycrystalline tape-wound cores are not smooth; instead the loop sides show irregular, imperfectly reproducible variations. These variations indicate changes in the ease of motion of the so-called transition region (the outward-moving region, formed of moving domain walls, in which the flux is changing). Such changes imply rearrangements of the domain walls within the transition region; and rearrangements of the walls imply changes in their area and mobility. Measurements have been made of a factor $K$ , defined from $e_c{\mathrm{\hspace{0.17em}=\hspace{0.17em}K(H-H}}_t)$ , where $e_c$ is the induced voltage-per-turn, $H$ is the field applied at the center of the transition region, and $H_t$ is a threshold parameter. $K$ is proportional to the average of the area-mobility product over the walls in the transition region. Using feedback of the induced voltage, $K$ was measured by modulating the applied field $H$ in such a way that the resulting modulation in $e_c$ was a small-amplitude square wave. The ratio of the modulation amplitudes in $e_c$ and $H$ gave $K$ . This technique, which is similar in principle to Becker's, has shown that the area-mobility product varies directly with the average rate of flux change and inversely with the level of prior saturation. In the 50-50 Ni-Fe grain-oriented 2-mil tape core for which results are presented, with a prior saturating field of 10 times the coercive force $H_c$ , as the average induced voltage was varied from 1.2 to 20 μv per turn, the mean value of $K$ increased from 8 to 80 μv-per-turn per ampere-turn-per-meter. With the average induced voltage at 1.2, as the prior saturating field was increased from the vicinity of the coercive force to ${\text{2H}}_c$ , $K$ dropped from 14 to 9, then remained constant at 8 as $H_S$ , the prior saturating field, was increased to ${\text{100H}}_c$ . It is shown that these results are qualitatively consistent with the results from nonmodulated measurements. It is also shown that the number of active domain walls for $\text{K\hspace{0.17em}=\hspace{0.17em}15}$ is of the order of 3, if each wall is assumed to be one wrap-of-tape long and if several other drastic assumptions are made.