  In all-perpendicular spin valve nanopillars the probability density of the
free-layer magnetization is independent of the azimuthal angle and its
evolution equation simplifies considerably compared to the general,
nonaxisymmetric geometry. Expansion of the time-dependent probability density
to Legendre polynomials enables analytical integration of the evolution
equation and yields a compact expression for the practically relevant switching
probability. This approach is valid when the free layer behaves as a
single-domain magnetic particle and it can be readily applied to fitting
experimental data.

Mesoscale and Nanoscale Physics