  We show that a slowly decaying current pulse can lead to nearly deterministic
precessional switching in the presence of noise. We consider a biaxial
macrospin, with an easy axis in the plane and a hard axis out-of-the plane,
typical of thin film nanomagnets patterned into asymmetric shapes. Out-of-plane
precessional magnetization orbits are excited with a current pulse with a
component of spin polarization normal to the film plane. By numerically
integrating the stochastic Landau-Lifshitz-Gilbert-Slonczewski equation we show
that thermal noise leads to strong dephasing of the magnetization orbits.
However, an adiabatically decreasing pulse amplitude overwhelmingly leads to
magnetization reversal, with a final state that {\em only} depends on the pulse
polarity, not on the pulse amplitude. We develop an analytic model to explain
this phenomena and to determine the pulse decay time necessary for adiabatic
magnetization relaxation and thus precessional magnetization switching.
