Reducing error rates in straintronic multiferroic nanomagnetic logic by pulse shaping

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 (> 1%) 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 degrees 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 degrees rotation (magnetization flip) with high likelihood.