  In this paper we systematically evaluate the variation in the reversal delay
of a nanomagnet driven by a longitudinal spin current while under the influence
of thermal noise. We then use the results to evaluate the performance of an
All-Spin-Logic (ASL) circuit. First, we review and expand on the physics of
previously-published analytical models on stochastic nanomagnet switching. The
limits of previously established models are defined and it is shown that these
models are valid for nanomagnet reversal times < 200 ps. Second, the insight
obtained from previous models allows us to represent the probability density
function (PDF) of the nanomagnet switching delay using the double exponential
function of the Frechet distribution. The PDF of a single nanomagnet is
extended to more complex nanomagnet circuit configurations. It is shown that
the delay-variation penalty incurred by nanomagnets arranged in parallel
configuration is dwarfed by the average delay increase for nanomagnets arranged
in a series configuration. Finally, we demonstrate the impact of device-level
performance variation on the circuit behavior using ASL logic gates. While the
analysis presented in this paper uses an ASL-AND gate as the prototype
switching circuit in the spin domain, the physical concepts are generic and can
be extended to any complex spin-based circuit.
