Thermally assisted spin transfer torque switching in synthetic free layers

TL;DR

This paper provides a theoretical analysis of thermally assisted spin transfer torque switching in synthetic free layers, deriving analytical expressions for switching probabilities and revealing a different thermal stability dependence than previously thought.

Contribution

It offers a new analytical expression for switching probability in coupled ferromagnetic layers, correcting prior assumptions about thermal stability dependence.

Findings

Thermal stability scales with Delta_{0}(1-I/I_{c})^{2}

Derived analytical switching probability expressions for different coupling regimes

Fast switching achieved by optimal applied field direction

Abstract

We studied the magnetization reversal rates of thermally assisted spin transfer torque switching in a ferromagnetically coupled synthetic free layer theoretically. By solving the Fokker-Planck equation, we obtained the analytical expression of the switching probability for both the weak and the strong coupling limit. We found that the thermal stability is proportional to Delta_{0}(1-I/I_{c})^{2}, not Delta_{0}(1-I/I_{c}) argued by Koch et al. [Phys. Rev. Lett. 92, 088302 (2004)], where I and I_{c} are the electric current and the critical current of spin transfer torque switching at absolute zero temperature. The difference in the exponent of (1-I/I_{c}) leads to a significant underestimation of the thermal stability Delta_{0}. We also found that fast switching is achieved by choosing the appropriate direction of the applied field.