Theory of Domain-Wall Mobility in Ferromagnetic Insulators

Abstract

The motion of a 180° domain-wall in pure yttrium iron garnet has been investigated, using the Winter-Janak domain-wall excitation spectrum. In particular, the domain-wall mobility as a function of temperature has been thoroughly studied. It is shown that the demagnetization energy due to the surface roughness of the sample where the domain-wall plane crosses the sample surface is the main source of resistance to domain-wall motion; the two-body part of the surface roughness causes transitions from a uniform translational domain-wall magnon mode to a degenerate domain-wall translational magnon mode, and is the predominant process that leads to the domain-wall motion relaxation. The four-body interaction intrinsic process contributes very little even at higher temperatures (about 10% of the two-body interaction at 300°K, much less at lower temperatures). The two-body process being considered here is, in some sense, similar to the Sparks-Loudon-Kittel calculations in which each pit is assumed to scatter independently; in the present case, however, we find it essential to take into account the mutual energy between pits. For a checker-board like surface corresponding to grit diameter R≈0.25 μ−0.30 μ(μ=10−4 cm), it is found that the domain-wall mobilities are 720, 740, 1200, and 5000 cm/sec-Oe at temperatures 4.2°, 77°, 195°, and 300°K, respectively. These numbers are of the same order of magnitude as the experimental results reported by Wanas and by Hagedorn and Gyorgy. We also show that the domain-wall mobility depends upon the size of the sample; the bigger the sample, the larger the mobility. Pseudodipolar fluctuation effects are negligible in YIG, but are important in ferrites with an inverted spinel structure. Assuming the pseudodipolar fluctuation field is about 105 Oe at 0°K, we show that this along with the surface roughness effect yields the same order of domain-wall mobilities as Dillon and Earl experimentally observed in manganese ferrite.