Magnetization dynamics, Bennett clocking and associated energy dissipation in multiferroiclogic

Abstract

It has been recently shown that the magnetization of a multiferroic nanomagnet, consistingof a magnetostrictive layer elastically coupled to a piezoelectric layer, can be rotated by a largeangle if a tiny voltage of a few tens of millivolts is applied to the piezoelectric layer. Thepotential generates stress in the magnetostrictive layer and rotates its magnetization by ∼ 90° to implement Bennett clocking in nanomagnetic logic chains. Because of the small voltageneeded, this clocking method is far more energy efficient than those that would employspin transfer torque or magnetic fields to rotate the magnetization. In order toassess if such a clocking scheme can also be reasonably fast, we have studied themagnetization dynamics of a multiferroic logic chain with nearest-neighbor dipolecoupling using the Landau–Lifshitz–Gilbert (LLG) equation. We find that clockrates of 2.5 GHz are feasible while still maintaining the exceptionally high energyefficiency. For this clock rate, the energy dissipated per clock cycle per bit flip is ∼ 52 000 kT at room temperature in the clocking circuit for properly designednanomagnets. Had we used spin transfer torque to clock at the samerate, the energy dissipated per clock cycle per bit flip would have been ∼ 4 × 108 kT, while with current transistor technology we would have expended ∼ 106 kT. For slower clock rates of 1 GHz, stress-based clocking will dissipate only ∼ 200 kT of energy per clock cycle per bit flip, while spin transfer torque would dissipate about108 kT. This shows that multiferroic nanomagnetic logic, clocked with voltage-generated stress,can emerge as a very attractive technique for computing and signal processing since it canbe several orders of magnitude more energy efficient than current technologies.