Mode Anticipation Fields for Symmetry Breaking

The role of bias fields in micromagnetism is illustrated for some basic 3-D shapes with dimensions of the order of 100 nm. A bias field selects among possible modes that break the symmetry at critical fields and greatly decreases the time for reaching equilibrium in the vicinity of the critical fields. The magnetization reversal in a toroidal shell is discussed in detail as an example to demonstrate the importance of bias fields and to compare analytic and numerical results