Numerical Fokker-Planck simulation of stochastic write error in spin torque switching with thermal noise

Emerging spintronics and nanomagnetic devices have attracted a lot of attention due to their versatility, scalability and energy efficiency. Most spintronics applications require manipulation of nano-magnet in a fast and efficient way. Spin transfer torque (STT) effect[1] is so far the most studied and well demonstrated means to switch a nano-size magnetic. Compared to traditional switching scheme by magnetic field, STT provides a scalable solution to manipulate the magnetization of a nano-sized magnet. STT based memory spin transfer torque magnetic random access memory (STT-MRAM) and spin torque oscillator (STO) have been proposed and experimentally demonstrated[2, 3]. One issue accompanies magnetic switching is the thermal noise. Under room temperature the magnetic switching under STT is susceptible to thermal fluctuation and often results in a distribution in switching current/delay. In applications like STT based memory, its stochastic nature can cause read/write error. In the case of write operation, increasing applied current or switching time can effectively reduce write error but both quantities are limited by other considerations such as energy dissipation, junction breakdown and etc. This kind of trade-off is essential in device and application design. The aim of the work is to promote numerical Fokker-Planck based framework to study thermal effect in STT switching. The comparison between numerical Fokker-Planck approach and other methods are summarized. We have also investigated write error rate (WER) in STT switching with a focus on its `slope' which is related to the write margin but not so often discussed in literature.