PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Leonid Berlyand.

Title:Domain and wall pattern in ferromagnets
Seminar:Marker Lecture Series
Speaker:Prof. Felix Otto, Max-Planck-Institute for Mathematics
The magnetization of ferromagnet is known to form patterns in order to minimize energy: Depending on the geometry of the sample, the magnetization features domains, in which it is nearly constant, separated by comparatively sharp transition layers ("walls"). The variational model, "micromagnetics", is an ideal test bed for an applied calculus of variations: It is easy to formulate, well-accepted, and supposedly explains a wealth of experimentally (and visually) accessible pattern. We will explain how even complicated patterns like a self-similar domain branching in strongly uniaxial bulk ferromagnets can be understood by energy minimization. As we shall explain, in samples in form of thin films,domains are formed even in absence of a crystalline anisotropy. Even in very thin films (thickness in nanometer range) of elongated cross section (width in micrometer range), the energy landscape features many local minimizers--to the effect that the switching route is complicated and hysteresis occurs. For the example of the ubiquitous "concertina pattern", a nearly periodic domain pattern in elongated thin-film elements, we developed an understanding of the cascade of bifurcation the magnetization configuration undergoes on a switching route. The secondary bifurcations are a consequence of a side band instability. The understanding arises from a combination of the rigorous derivation of suitably reduced model, and numerical simulation and qualitative analysis of this more tractable reduced model. The work on the concertina is joint work with Jutta Steiner and Rudolf Schafer (for the experiments).

Room Reservation Information

Room Number:MB114
Date:10 / 21 / 2013
Time:08:00pm - 09:00pm