Description of Statistical Switching in Perpendicular STT-MRAM Within an Analytical and Numerical Micromagnetic Framework

The realistic modeling of spin-transfer torque (STT)-magnetoresistive random access memory (MRAM) for the simulations of hybrid CMOS/Spintronics devices in comprehensive simulation environments requires a full description of stochastic switching processes in the state-of-the-art STT-MRAMs. Here, we compare micromagnetic simulations with an analytical formulation that takes into account the spin-torque asymmetry of the spin-polarization function by considering the mean, standard deviation, skewness, and kurtosis. We find that, while the first and second statistical moments exhibit a very similar behavior, skewness and kurtosis are substantially different and must be taken into account in order to provide an accurate prediction of the switching performance. In fact, a reasonable fit of the probability density function (PDF) of the switching time is given by a Pearson Type IV PDF. The main achievements of this paper underline the need of data-driven design of STT-MRAM that uses a full micromagnetic simulation framework for the statistical proprieties PDF of switching processes.