View an animated clip of the reversal process.

We have theoretically traced the dynamics of the reversal of magnetization in a ferromagnetic system by solution of the nonlinear partial differential equations of motion (Landau-Lifschitz equation) for the magnetization density M(x,t).

The figure shows three snapshots taken during the reversal process in an ellipsoid with aspect ratio 4.6:1 (chosen because experimental data is available) of gamma Fe₂O₃. The minor radius is equal to the exchange length. The unit of time is 1/gammaM_s, which is approximately 1/6 ns. No crystalline anisotropy was included in this calculation, although its inclusion is straightforward.

As the figure shows, the magnetization is initially uniformly downward. At time zero, an upward directed uniform external magnetic field is applied. The external field is gradually increased from zero to its final value of 3.4M_s (M_s is the saturation magnetization) in 2.5 ns. Two intermediate states are shown. Note that the development of the partially reversed state takes a much longer time than does almost complete reversal from that state. Eventually, of course, the magnetization becomes uniform in the upward direction.

The initial phase of the reversal progress is invisible in the kind of picture shown here, and, if the external field is a sufficiently short pulse, no reversal occurs because the initial phase is never completed, even when the height of the pulse is large.

The calculation required development of new numerical techiques, efficient in both processor time and memory usage, for treatment of the long range magnetostatic interaction and for solution of the large stiff system of differential equations resulting from finite element (Galerkin) discretization in space. The calculation shown was performed on a single IBM RS/6000 workstation.