Formation and coarsening of the concertina magnetization pattern in elongated thin-film elements

Abstract

The concertina is a magnetization pattern in elongated thin-film elements of a soft material. It is a ubiquitous domain pattern that occurs in the process of magnetization reversal in direction of the long axis of the small element.Van den Berg argued that this pattern grows out of the flux closure domains as the external field is reduced. Based on experimental observations and theory, we argue that in sufficiently elongated thin-film elements, the concertina pattern rather bifurcates from an oscillatory buckling mode.Using a reduced model derived by asymptotic analysis and investigated by numerical simulation, we quantitatively predict the average period of the concertina pattern and qualitatively predict its hysteresis. In particular, we argue that the experimentally observed coarsening of the concertina pattern is due to secondary bifurcations related to an Eckhaus instability.We also link the concertina pattern to the magnetization ripple and discuss the effect of a weak (crystalline or induced) anisotropy.

The magnetization ripple: A nonlocal stochastic PDE perspective

“…On these scales, the quenched noise acts like random transversal field of white-noise character (because the grains are smaller than the characteristic scales). We argue that this derivation is self-consistent (see also [21,Section V]).…”

“…Compared to [19], where similar tools are used, the main difference is that the mask ψ = ψ(x) defining the semi-group convolution family is not a Schwartz function: While being smooth, it only has mild decay due to the limited smoothness of ψ(k) in k 1 = 0, cf. (21).…”

“…Most of the arguments can be found in the physics literature [13,14]. We closely follow the set-up in [21] based on [20]. The more mathematically oriented readers could skip this section.…”

A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types

“…Concertina pattern. In a series of papers ( [20,23] among others) the formation and hysteresis of the concertina pattern in thin, sufficiently elongated ferromagnetic samples were studied. While in this case the transition layers between domains of constant magnetization are symmetric Néel walls, the program carried out for the concertina (a mixture of theoretical and numerical analysis, and comparison to experiments) serves as motivation for our work on the energy of domain walls in moderately thin films.…”

Directed self-assembly of proteins into discrete radial patterns

“…Self-assembly of soft-materials with functional groups into well-defined and discrete structures as a new form of nanofabrication has witnessed an unprecedented growth in the past decade123456. Directed self-assembly of functional molecular groups into 2D and 3D structures to produce viable nanoscale devices and sensors is an attractive goal with many potential applications.…”