The Formation and Coarsening of the Concertina Pattern

TL;DR

This paper investigates the formation, bifurcation, and coarsening of the concertina magnetization pattern in thin-film elements, combining experimental observations, theoretical analysis, and numerical simulations to understand its behavior and underlying mechanisms.

Contribution

It introduces a reduced asymptotic model that predicts the pattern's period and hysteresis, linking coarsening to secondary bifurcations and anisotropy effects.

Findings

Quantitative prediction of the concertina pattern period

Qualitative understanding of hysteresis in pattern formation

Identification of secondary bifurcations causing coarsening

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.