Low-dimensionality energy landscapes: Magnetic switching mechanisms and rates

In this paper we propose a new method for the study and visualization of dynamic processes in magnetic nanostructures, and for the accurate calculation of rates for such processes. The method is illustrated for the case of switching of a grain of an exchange-coupled recording medium, which switches through domain wall nucleation and motion, but is generalizable to other rate processes such as vortex formation and annihilation. The method involves calculating the most probable (lowest energy) switching path and projecting the motion onto that path. The motion is conveniently visualized in a two-dimensional projection parameterized by the dipole and quadrupole moments of the grain. The motion along that path can then be described by a Langevin equation, and its rate can be computed by the classic method of Kramers (1940). The rate can be evaluated numerically, or in an analytic approximation – interestingly, the analytic result for domain-wall switching is very similar to that obtained by Brown in 1963 for coherent switching, except for a factor proportional to the domain wall volume. Thus in addition to its lower coercivity, an exchange-coupled medium has the additional advantage (over a uniform medium) of greater thermal stability, for a fixed energy barrier.