Spin-transfer switching dynamics in a two-macrospin-coupled model system

A quantitative understanding of spin-torque switching of nanomagnets beyond macrospin limit and at finite temperature is important for applications such as spin-torque magnetic random access memory (STT-MRAM). Thermally activated switching of a nanomagnet under sub-threshold spintransfer- torque (STT) bias has long been used to measure the thermal activation reversal energy barrier related to memory bit’s data retention lifetime. Finite temperature write-error-rate (WER) statistics in non-macrospin systems is critically important for STT-MRAM write operation. For both thermally activated reversal and for write-error, descriptions beyond macrospin is necessary, as the macrospin-based asymptotic expressions are inaccurate beyond ∼2X for realistic experiments – doing so could cause unreliable interpretation for measurements of thermal activation probability and WER characteristics. This is because most practical spin-transfer-torque switched MTJs are not macrospins. Here using a two-macrospin coupled model as the next simplest case-study beyond a single macrospin, we demonstrate some key features of STT-biased non-macrospin dynamics – both in thermal activation region and for super-threshold fast-switching WER, and illustrate some behavioral differences of a system with more than a single macrospin’s internal degrees of freedoms. These exercises provide an understanding to the correlation of quantitative trending of device behavior with materials parameters, and help to guide further optimization of materials and device designs for switching and data-retention for nanomagnets in memory related applications.