The analysis of eddy-current-limited magnetic domain wall motion, including severe bowing and merging

Abstract

A segmented model domain wall structure is discussed which enables an accurate theoretical analysis to be made of the motion of domain walls severely distorted by an inhomogeneous eddy current field. Methods are developed for determining the wall profile and eddy current field at successive phases of the motion, when either the applied field or the flux is a prescribed function of time. These techniques are applied to a detailed study of an isolated domain wall driven so as to generate sinusoidal flux variations. Severe wall bowing is found to reduce the relative eddy current drag very roughly as the cube root of the frequency and the square root of the amplitude. At low flux amplitudes, asymptotic agreement is found with an independent exact theory of the infinitesimal motion of a continuous quasi-plane wall. The segmented model, adapted to include interactions between walls by eddy current overlap and actual merging of neighbouring walls into cylindrical domains, is also applied to the study of saturation sinusoidal induction.Comparison with experiment is made by simulating the motion of a pair of domain walls observed by Helmiss (1969) in a detailed study of flux reversal in a single-crystal `picture- frame' specimen of 3·5% silicon-iron. Good agreement is found between the simulated eddy current losses and those reported by Helmiss. Reasonable concordance of calculated values of the surface wall velocity with those observed by Kerr magneto-optic methods is also obtained.

Generalization of the Classical Method for Calculating Dynamic Hysteresis Loops in Grain-Oriented Electrical Steels

“…The 2-D domain structures depicted play no active role in the calculations. Nevertheless, they reproduce qualitatively all characteristic features of DW behavior including the rise of wall bowing with frequency and the inverse proportionality between the DW bowing and total loss [12, p. 419], [32]. The latter phenomenon is illustrated by dotted DW profiles in Fig.…”

Correlation of magnetic Barkhausen noise with core loss in oriented 3% Si–Fe steel laminates

“…However, this neglects dynamic magnetization processes, taking place in three dimensions ͑3D͒ by which power losses may be reduced, such as domain wall bowing 11 and ruckling. 12 These processes, as well as eddy current overlap and physical merging of neighboring domain walls, 11 may also have important implications for the local eddy current field effects associated with the abrupt magnetization changes resulting from a Barkhausen event.…”

“…However, this neglects dynamic magnetization processes, taking place in three dimensions ͑3D͒ by which power losses may be reduced, such as domain wall bowing 11 and ruckling. 12 These processes, as well as eddy current overlap and physical merging of neighboring domain walls, 11 may also have important implications for the local eddy current field effects associated with the abrupt magnetization changes resulting from a Barkhausen event. The 3D behavior of microscopic eddy current processes may be even more significant since the local energy fluctuations associated with their behavior are not as strongly constrained by the sample thickness, anisotropy, and magnetization direction that modulate the bulk sample magnetization.…”

Finite frequency dynamics of magnetic domain walls

“…͑4͒ of Ref. 6 if one recognizes that the a i j in Eq. ͑6͒ there is just the discretized form for G. The ratio (‫ץ‬H/‫ץ‬t)/ٌ 2 H is of the order of (sample size/penetration depth͒ 2 and is often not negligible.…”