Measurement of the activation volume in magnetic random access memory

Abstract

Measuring thermal stability in magnetic random access memory devices is non-trivial. Recently, there has been much discussion on the appropriate model to use: single domain or domain wall nucleation. Of particular challenge is assessing the maximum size at which the single domain model can be assumed. Typically, this is estimated to be in the range of 20-30 nm based on a value of the exchange stiffness (A(ex)) that is assumed, estimated using indirect measurements or derived from significantly thicker films. In this work, it is proposed that this maximum size can be measured directly via the "activation volume" (V-act) or the "activation diameter" (D-act), which originates from the concept of magnetic viscosity. This is conducted by measuring, using the time dependence of magnetization at different applied fields, D-act in perpendicular magnetic tunnel junction pillars of varying effective anisotropy constant (K-eff) and diameter. It is shown that the trend in D-act follows root 1/K-eff dependence, in good agreement with the analytic model for the critical diameter of coherent switching. Critically, it is also found that the smallest size for which a single domain, with coherent reversal, occurs is 20 nm. Thus, in devices with technologically relevant values of K-eff, the macrospin model may only be used in 20 nm, or smaller, devices.