Analytic treatment of the precessional (ballistic) contribution to the conventional magnetic switching

We consider a uniformly magnetized particle (i.e., a macroscopic magnetic moment) with an easy axis anisotropy. The particle's moment is switched from "up" to "down" direction by an external magnetic field applied parallel to the easy axis and continuously swept from a positive to a negative value. In addition, a small constant perpendicular bias field is present. It is shown that while the driving field switches the particle's moment in a conventional damped way, the perpendicular field creates an admixture of the precessional (ballistic) switching that speeds up the switching process. Precessional contribution produces a non-monotonic dependence of the switching time on the field sweep time with a minimum at a particular sweep time value. We derive analytic expressions for the optimal point, and for the entire dependence of the switching time on the field sweep time. Our approximation is valid in a wide parameter range and can be used to engineer and optimize of the magnetic memory devices.