Write error rates of in-plane spin-transfer-torque random access memory calculated from rare-event enhanced micromagnetic simulations

Pramanik, Tanmoy; Roy, Uma; Jadaun, Priyamvada; Register, Leonard F.; Banerjee, S.

doi:10.1016/j.jmmm.2018.07.042

Cited by 9 publications

(8 citation statements)

References 47 publications

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“…I J = b J /Q, 1/∆ = 2 /Q, and the unit of time is now τ Q = α/(γµ 0 M s Q). We point out that even though (20) was obtained for an in-plane STT-MRAM cell, exactly the same equation arises in the modeling of perpendicular cells [6]. Therefore, a direct comparison with the results obtained by Butler et al [6], who used the analysis of the Fokker-Planck equation is also possible.…”

Section: Induced Switchingsupporting

confidence: 51%

“…Finally, solving for ζ in (51) and substituting it back into (50), with the help of the fact that αW 1 −W 2 = √ 1 + α 2 W , where W is another Brownian motion, we obtain (20). It is interesting to note that only the contribution of the field-like spin torque appears in the reduced equation, while the contribution of the Slonczewski torque cancels out to the leading order.…”

Section: Appendixmentioning

confidence: 99%

“…Therefore, a direct comparison with the results obtained by Butler et al [6], who used the analysis of the Fokker-Planck equation is also possible. Equation (20) with 0 ≤ I J < 1 will be used as the simplest example of a stochastic micromagnetic model with bistability, for which several IS biasing strategies will be illustrated. A more realistic model of an STT-MRAM cell would need to incorporate spatial heterogeneity within the cell, which may be captured by considering a system of N exchangecoupled macrospins associated with the magnetization in each of the polycrystalline grains.…”

Section: Micromagnetic Framework and Thermally Induced Switchingmentioning

confidence: 99%

“…The exact finite time switching probability for a single macrospin exhibited by (20) can be computed by solving the backward Fokker-Planck equation for the probability P sw (θ, t) that a trajectory starting at a given value of θ ∈ (−π/2, π/2) reached the value of θ = ±π/2 by time t [43]. This probability satisfies…”

Section: Micromagnetic Framework and Thermally Induced Switchingmentioning

confidence: 99%

“…However, this may introduce large uncontrolled inaccuracies due to failure of the fitting form to capture the asymptotic behavior of the probability distribution in the small noise limit [14], [15]. Alternatively, variance reduction techniques such as importance splitting attempt to concentrate the samples generated on those with a higher likelihood of registering a rare event of interest [16], [17], [18], [19], [20].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Importance Sampling for Thermally Induced Switching and Non-Switching Probabilities in Spin-Torque Magnetic Nanodevices

Muratov

Moore

2019

IEEE Trans. Magn.

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Spin-transfer torque magnetoresistive random access memory is a potentially transformative technology in the non-volatile memory market. Its viability depends, in part, on one's ability to predictably induce or prevent switching; however, thermal fluctuations cause small but important errors in both the writing and reading processes. Computing these very small probabilities for magnetic nanodevices using naive Monte Carlo simulations is essentially impossible due to their slow statistical convergence, but variance reduction techniques can offer an effective way to improve their efficiency. Here, we provide an illustration of how importance sampling can be efficiently used to estimate low read and write soft error rates of macrospin and coupled-spin systems.

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Section: Induced Switchingsupporting

confidence: 51%

Section: Appendixmentioning

confidence: 99%

Section: Micromagnetic Framework and Thermally Induced Switchingmentioning

confidence: 99%

Section: Micromagnetic Framework and Thermally Induced Switchingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Importance Sampling for Thermally Induced Switching and Non-Switching Probabilities in Spin-Torque Magnetic Nanodevices

Muratov

Moore

2019

IEEE Trans. Magn.

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The Fouriest: High-Performance Micromagnetic Simulation of Spintronic Materials and Devices

Pershin

Knizhnik

Levchenko

et al. 2019

Advances in Intelligent Systems and Computing

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Magnetization switching in nanoelements induced by the spin-transfer torque: Study by massively parallel micromagnetic simulations

Semenova

Berkov

2019

AIP Advances

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In this paper we present a detailed numerical study of magnetization switching in shape-anisotropic thin-film nanoelements. These elements are at present of the major interest for the applied solid state magnetism as main components of a new generation of conventional and spin-transfer-torque (STT) magnetic random access memory (MRAM) cells. To conduct this study, we have developed a highly efficient method for massively parallel micromagnetic simulations of the magnetization reversal in small-size nanoelements, which allows to fully exploit the large performance gain available on the GPU architecture (usually achievable only for large systems). We apply our method to the spin-torque-induced magnetization switching in elliptical nanoelements in presence of thermal fluctuations. Being able to compute simultaneously the reversal of up to 1000 such elements, we obtain the dependence of (i) the average switching time and (ii) the distribution density of switching times for individual elements on the element size with a high statistical accuracy. Analysis of these dependencies provides important insights into the physics of magnetization reversal in such systems. Comparison with analogous simulations in the macrospin approximation allows to determine the validity limits of the macrospin model. Our methodology can be applied for the optimization of the MRAM design regarding the information life time and significantly improve the prediction accuracy of write and read error rates of conventional and STT-based MRAM cells.

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Write error rates of in-plane spin-transfer-torque random access memory calculated from rare-event enhanced micromagnetic simulations

Cited by 9 publications

References 47 publications

Importance Sampling for Thermally Induced Switching and Non-Switching Probabilities in Spin-Torque Magnetic Nanodevices

Importance Sampling for Thermally Induced Switching and Non-Switching Probabilities in Spin-Torque Magnetic Nanodevices

The Fouriest: High-Performance Micromagnetic Simulation of Spintronic Materials and Devices

Magnetization switching in nanoelements induced by the spin-transfer torque: Study by massively parallel micromagnetic simulations

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