Energy Barriers for Thermally Activated Magnetization Reversal in Perpendicular Magnetic Tunnel Junctions Nanopillars in a Transverse field

Thermally induced transitions between bistable magnetic states of magnetic tunnel junctions (MTJ) nanopillars are of interest for generating random bitstreams and for applications in stochastic computing. An applied field transverse to the easy axis of a perpendicularly magnetized MTJ (pMTJ) can lower the energy barrier (E_b) to these transitions leading to faster fluctuations. Here we present analytical and numerical calculations of E_b considering both coherent (macrospin) reversal and nonuniform magnetization reversal for a variety of nanopillar diameters and applied fields. We show that a nonuniform reversal processes dominate for larger diameters. Our macrospin reversal results are consistent with previous studies [1] but include a correction that accounts for the size-dependent demagnetization fields. Interestingly, we find that this correction results in a nonmonotonic dependence of E_b on diameter. Numerical calculations of E_b using the String-Method [2] show that the transition state is a nonuniform state with a sigmoidal magnetization profile. The latter can be described with an analytical expression that depends on only one spatial dimension, the dimension parallel to the applied field, which is also the preferred direction of profile motion during reversal. Our results provide a useful approach to determining the fluctuation rates of pMTJs as a function of the transverse field, pMTJ diameter and material characteristics.

References

[1] Garanin et al., “Thermally activated escape rates of uniaxial spin systems with transverse field: Uniaxial crossovers,” PRE 60, 6499 (1999).

[2] E, et al., “String method for the Study of Rare Events,” PRB 66, 052301 (2002)