Spin-transfer torque switching probability of CoFeB/MgO/CoFeB magnetic tunnel junctions beyond macrospin

We present an empirical description of experimental spin-torque switching probability for the CoFeB/MgO/CoFeB type of magnetic tunnel junctions beyond macrospin limit, parametrizing measurement data for direct comparison with the corresponding macrospin asymptote expression. We show that, near 35 nm in diameter, spin-torque switching speed in these tunnel devices is faster than macrospin-limit predictions. These devices have a faster reduction of switching error rate versus spin-torque drive amplitude than macrospin. While the functional form similar to macrospin can still describe experimental data satisfactorily, the parameters no longer correspond to materials values. Instead they reflect the nonuniform nature of the switching process. Further, the parameters depend on the resistance-area product r(A) of the junction, with higher r(A) causing a steeper slope of switching error versus switching current. This r(A) dependence could not originate from low-bias spin-dependent tunneling. These observations suggest that, in addition to nonuniform nonlinear dynamics during switching, it is also important to consider higher-order dynamic processes, including a high-bias tunnel electron's spin-flip scattering, voltage-induced change to interface magnetism, and possibly Joule heating.