  It has been recently shown that multiferroic logic - where logic bits are
encoded in the magnetization orientation of a nanoscale magnetostrictive layer
elastically coupled to a piezoelectric layer - can be Bennett clocked with
small electrostatic potentials of few tens of mV applied to the piezoelectric
layer. The potential generates stress in the magnetostrictive layer and rotates
its magnetization by a large angle to carry out Bennett clocking. This method
of clocking is far more energy-efficient than using spin transfer torque. In
order to assess if such a clocking scheme can be also reasonably fast, we have
studied the magnetization dynamics of a multiferroic logic array with nearest
neighbor dipole coupling using the Landau-Lifshitz-Gilbert (LLG) equation. We
find that switching delays of ~ 3 ns (clock rates of 0.33 GHz) can be achieved
with proper design provided we clock non-adiabatically and dissipate ~48,000 kT
(at room temperature) of energy per clock cycle per bit flip in the clocking
circuit. This dissipation far exceeds the energy barrier separating the two
logic states, which we assumed to be 32 kT to yield a bit error probability of
. Had we used spin transfer torque to switch with the same ~ 3 ns delay, the
energy dissipation would have been much larger (~ $6 \times 106$ kT). This
shows that spin transfer torque, widely used in magnetic random access memory,
is an inefficient way to switch a magnet, and multiferroic logic clocked with
voltage-induced stress is a superior nanomagnetic logic scheme.
