Magnetization dynamics, Bennett clocking and associated energy dissipation in multiferroic logic

It has been recently shown that the magnetization of a multiferroic nanomagnet, consisting of a magnetostrictive layer elastically coupled to a piezoelectric layer, can be rotated by a large angle if a tiny voltage of a few tens of millivolts is applied to the piezoelectric layer. The potential generates stress in the magnetostrictive layer and rotates its magnetization by ∼ 900 to implement Bennett clocking in nanomagnetic logic chains. Because of the small voltage needed, this clocking method is far more energy efficient than those that would employ spin transfer torque or magnetic fields to rotate the magnetization. In order to assess if such a clocking scheme can also be reasonably fast, we have studied the magnetization dynamics of a multiferroic logic chain with nearest-neighbor dipole coupling using the Landau-Lifshitz-Gilbert (LLG) equation. We find that clock rates of 2.5 GHz are feasible while still maintaining the exceptionally high energy efficiency. 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 designed nanomagnets. Had we used spin transfer torque to clock at the same rate, the energy dissipated per clock cycle per bit flip would have been ∼ 4 x 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 about 108 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 can be several orders of magnitude more energy efficient than current technologies.