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

A quantitative understanding of spin-torque switching of nanomagnets beyond a 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 a sub-threshold spin-transfer-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 are critically important for STT-MRAM write operations. For both thermally activated reversal and for write-error, descriptions beyond macrospin are necessary, as the macrospin-based asymptotic expressions are inaccurate beyond ∼ 2 X 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 a 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 freedom. These exercises provide an understanding to the correlation of quantitative trending of device behavior with material parameters and help to guide further optimization of materials and device designs for switching and data retention for nanomagnets in memory related applications.