Reducing error rates in straintronic multiferroic nanomagnetic logic by pulse shaping

Abstract

Dipole-coupled nanomagnetic logic (NML), where nanomagnets (NMs) with bistable magnetization states act as binary switches and information is transferred between them via dipole-coupling and Bennett clocking, is a potential replacement for conventional transistor logic since magnets dissipate less energy than transistors when they switch in a logic circuit. Magnets are also 'non-volatile' and hence can store the results of a computation after the computation is over, thereby doubling as both logic and memory-a feat that transistors cannot achieve. However, dipole-coupled NML is much more error-prone than transistor logic at room temperature [Formula: see text] because thermal noise can easily disrupt magnetization dynamics. Here, we study a particularly energy-efficient version of dipole-coupled NML known as straintronic multiferroic logic (SML) where magnets are clocked/switched with electrically generated mechanical strain. By appropriately 'shaping' the voltage pulse that generates strain, we show that the error rate in SML can be reduced to tolerable limits. We describe the error probabilities associated with various stress pulse shapes and discuss the trade-off between error rate and switching speed in SML.The lowest error probability is obtained when a 'shaped' high voltage pulse is applied to strain the output NM followed by a low voltage pulse. The high voltage pulse quickly rotates the output magnet's magnetization by 90° and aligns it roughly along the minor (or hard) axis of the NM. Next, the low voltage pulse produces the critical strain to overcome the shape anisotropy energy barrier in the NM and produce a monostable potential energy profile in the presence of dipole coupling from the neighboring NM. The magnetization of the output NM then migrates to the global energy minimum in this monostable profile and completes a 180° rotation (magnetization flip) with high likelihood.

Low Energy Barrier Nanomagnet Design for Binary Stochastic Neurons: Design Challenges for Real Nanomagnets With Fabrication Defects

“…The latter are more energy-efficient, but also more error-prone. Theoretical estimates of switching errors in magneto-elastic switching (straintronics) range from 10 -3 [8] to as low as 10 -8 [9], but experiments show a much larger error probability exceeding 0.1 [10,11]. Recently, we showed that this large difference between theory and experiments accrues from the fact that real nanomagnets used in experiments invariably have structural defects and they exacerbate the switching error [12].…”

Effect of Nanomagnet Geometry on Reliability, Energy Dissipation, and Clock Speed in Strain-Clocked DC-NML

“…The effect of thermal noise is incorporated by adding an equivalent field   thermal Ht to the total effective field [11,12,15,[20][21][22]:…”

“…The Achilles' heel of strain-clocked DC-NML is its poor reliability due to high switching error rates at room temperature [10][11][12][13][14]. In this paper, we explore ways of mitigating the poor reliability, particularly through the use of appropriate geometry of the nanomagnets, and identify the metrics that have to be sacrificed to attain increased robustness.…”

Effect of temperature variations and thermal noise on the static and dynamic behavior of straintronics devices

“…Due to its crucial importance, the effect of thermal noise on the dynamic behavior of the magnetization in a nanomagnet has been the subject of study in the literature. [24][25][26][27] A general study of the dynamics in a single domain magnet under Langevin thermal noise has been published previously, 24 providing a comprehensive statistical analysis on the magnetization dynamics with and without the effect of external magnetic field. Analysis of the dynamics in strain-induced multiferroics has also been the subject of study recently.…”