DocumentCode :
1558143
Title :
Switching Distributions for Perpendicular Spin-Torque Devices Within the Macrospin Approximation
Author :
Butler, W.H. ; Mewes, Tim ; Mewes, Claudia K A ; Visscher, P.B. ; Rippard, William H. ; Russek, Stephen E. ; Heindl, Ranko
Author_Institution :
Center for Mater. for Inf. Technol., Univ. of Alabama, Tuscaloosa, AL, USA
Volume :
48
Issue :
12
fYear :
2012
Firstpage :
4684
Lastpage :
4700
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=/I0 . This exponentially decaying tail in WSER is not easily reduced by tilting the pinned layer magne- ization.
Keywords :
Fokker-Planck equation; critical currents; current density; damping; magnetic film stores; magnetic switching; magnetic thin films; magnetisation; probability; spin fluctuations; torque; Fokker-Planck equation; Gilbert damping; approximate analytical expression; closed form analytical expression; critical current density; exponential decay; free-layer magnetization; macrospin approximation; perpendicular free layer; perpendicular spin-torque devices; pinned layer magnetization; precession frequency; probability distribution; random fluctuating held; short-time regime; single-macrospin Landau-Lifshitz-Gilbert equations; soft error rates; spin-torque memory devices; switching distributions; zero-temperature switching time; Approximation methods; Equations; Films; Magnetic tunneling; Magnetization; Mathematical model; Switches; Error rate; Fokker-Planck; magnetic memory; spin torque; switching distribution;
fLanguage :
English
Journal_Title :
Magnetics, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9464
Type :
jour
DOI :
10.1109/TMAG.2012.2209122
Filename :
6242414
Link To Document :
بازگشت