  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.
