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

Content Provider	IEEE Xplore Digital Library
Author	Butler, W.H. Mewes, T. Mewes, C.K.A. Visscher, P.B. Rippard, W.H. Russek, S.E. Heindl, R.
Copyright Year	1965
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)τ] where the reduced time τ is related to the switching time, Gilbert damping and precession frequency through τ = αω₀t, and the reduced current i is the ratio of the applied current to the critical current density for switching i=I̅/I₀ . This exponentially decaying tail in WSER is not easily reduced by tilting the pinned layer magnetization.
Sponsorship	IEEE Magnetics Society
Starting Page	4684
Ending Page	4700
Page Count	17
File Size	1297887
File Format	PDF
ISSN	00189464
Volume Number	48
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-12-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Switches Mathematical model Magnetization Equations Approximation methods Films Magnetic tunneling switching distribution Error rate Fokker-Planck magnetic memory spin torque
Content Type	Text
Resource Type	Article
Subject	Electronic, Optical and Magnetic Materials Electrical and Electronic Engineering

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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