The concertina pattern in elongated micromagnetic thin films

Abstract:
We consider the bifurcation of the ground state of the micromagnetic energy functional in an elongated thin film 
element. After the magnetization has been saturated by an external field in the long direction -- infinite for our 
purposes --, upon reduction and inversion of this field a bifurcation occurs. Of the four possible types of 
instabilities, each for a corresponding parameter regime, one is of special interest. This instability is of oscillatory 
type and has a characteristic wavelength which sets an intrinsic lengthscale. In a weakly nonlinear model we show that 
the bifurcation in this special regime is of the supercritical type, which makes the instability generic. Numerical 
simulations show the evolution of the instability into a pattern of well--defined magnetic domains, separated by Neel 
walls, if the external field is increased further in the inverse direction.