ABSTRACT
This chapter describes in some detail the results of calculations for the iron nanobrick. The calculations for the nanobrick serve as a primer on the effective use of modern codes for micromagnetism using fields from magnets and fields from electrical currents to provide symmetry breaking. In a soft magnetic material, the surface charges create fields that are approximately equal and opposite to any externally applied fields. The boundary conditions created by the magnetostatics require non-uniform magnetization patterns that decrease the parallel alignment of the electron spins, which are favored by the exchange interaction responsible for ferromagnetism. The external magnetic fields from a vortex in an ultrathin film are small because the magnetic charge on one surface cancels the effects of the charge on the other surface. When a magnetic moment is rotated with respect to the atomic lattice, there is a change in energy because of spin-orbit coupling to the lattice.
