  The magnetization reversal of Stoner particles is investigated from the point
of view of nonlinear dynamics within the Landau-Lifshitz-Gilbert formulation.
The following results are obtained. 1) We clarify that the so-called
Stoner-Wohlfarth (SW) limit becomes exact when damping constant is infinitely
large. Under the limit, the magnetization moves along the steepest energy
descent path. The minimal switching field is the one at which there is only one
stable fixed point in the system. 2) For a given magnetic anisotropy, there is
a critical value for the damping constant, above which the minimal switching
field is the same as that of the SW-limit. 3) We illustrate how fixed points
and their basins change under a field along different directions. This change
explains well why a non-parallel field gives a smaller minimal switching field
and a short switching time. 4) The field of a ballistic magnetization reversal
should be along certain direction window in the presence of energy dissipation.
The width of the window depends on both of the damping constant and the
magnetic anisotropy. The upper and lower bounds of the direction window
increase with the damping constant. The window width oscillates with the
damping constant for a given magnetic anisotropy. It is zero for both zero and
infinite damping. Thus, the perpendicular field configuration widely employed
in the current experiments is not the best one since the damping constant in a
real system is far from zero.
