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Spin-torque switching: Fokker-Planck rate calculation

D. M. Apalkov·P. B. Visscher
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Abstract

We describe a new approach to understanding and calculating magnetization switching rates and noise in the recently observed phenomenon of "spin-torque switching". In this phenomenon, which has possible applications to information storage, a large current passing from a pinned ferromagnetic (FM) layer to a free FM layer switches the free layer. Our main result is that the spin-torque effect increases the Arrhenius factor $\exp(-E/kT)$ in the switching rate, not by lowering the barrier $E$, but by raising the effective spin temperature $T$. To calculate this effect quantitatively, we extend Kramers' 1940 treatment of reaction rates, deriving and solving a Fokker-Planck equation for the energy distribution including a current-induced spin torque of the Slonczewski type. This method can be used to calculate slow switching rates without long-time simulations; in this Letter we calculate rates for telegraph noise that are in good qualitative agreement with recent experiments. The method also allows the calculation of current-induced magnetic noise in CPP (current perpendicular to plane) spin valve read heads.

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D. M. Apalkov, P. B. Visscher. 2004-06-01. Spin-torque switching: Fokker-Planck rate calculation. https://doi.org/10.1103/physrevb.72.180405

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