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Switching Distributions for Perpendicular Spin-Torque Devices Within the Macrospin Approximation

Published

Author(s)

William H. Butler, William Rippard, Stephen E. Russek, Ranko R. Heindl

Abstract

We model "soft" error rates for writing (WSER) and for reading (RSER) for spin-torque memory devices that have a free layer with easy axis perpendicular to the film plane by solving the Fokker-Planck equation for the probability distribution of the angle that the free layer magnetization makes with the normal to the plane of the film. We obtain: 1) an exact, closed form, analytical expression for the zero-temperature switching time as a function of initial angle; 2) an approximate analytical expression for the distribution function of the direction of the magnetization and the exponential decay of the WSER as a function of the time the current is applied; 3) comparison of the approximate analytical expressions for the distribution function and WSER to numerical solutions of the Fokker-Planck equation; 4) an approximate analytical expression for the distribution function and WSER for the case in which the pinned layer is not collinear with the perpendicular free layer; 5) an approximate analytical expression for the linear increase in RSER with current applied for reading; 6) comparison of the approximate analytical formula for the RSER to the numerical solution of the Fokker-Planck equation; and 7) confirmation of the accuracy of the Fokker-Planck solutions by comparison with results of direct simulation using the single-macrospin Landau-Lifshitz-Gilbert equations with a random fluctuating field in the short-time regime for which the latter is practical. We find that the WSER decays at long times as exp [-2(i - 1)tau] where the reduced time tau is related to the switching time, Gilbert damping and precession frequency through tau = alpha omega(0)t, and the reduced current is the ratio of the applied current to the critical current density for switching i = (I) over bar /I-0. This exponentially decaying tail in WSER is not easily reduced by tilting the pinned layer magnetization.
Citation
Physical Review B
Volume
48
Issue
12

Keywords

Error rate, Fokker-Planck, magnetic memory, spin torque, switching distribution

Citation

Butler, W. , Rippard, W. , Russek, S. and Heindl, R. (2012), Switching Distributions for Perpendicular Spin-Torque Devices Within the Macrospin Approximation, Physical Review B, [online], https://doi.org/10.1109/TMAG.2012.2209122, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=908646 (Accessed April 22, 2024)
Created July 16, 2012, Updated October 12, 2021