Electric Clock for NanoMagnet Logic Circuits - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 77

NANOMAGNETS

ELECTRODES

ELECTRIC
FIELD

A)

STRAIN
d31 COUPLING

PZT

V

VOLTAGE APPLIED

NO VOLTAGE

NANOMAGNETS

B)

PZT STRAIN

d33 COUPLING
ELECTRIC FIELD

ELECTRODES

NO VOLTAGE

V

VOLTAGE APPLIED

Fig. 6. Magnetoelastic clock system for NML logic. (A) Electrodes are placed on top
and on the bottom of the piezoelectric layer. The electric field and the piezoelectric
substrate are coupled through the d 31 coecient. Moreover electrodes interfere with
the mechanical coupling and the magnets fabrication process. (B) Electrodes are placed
on the side of the piezoelectric layer. The electric field and the piezoelectric substrate
are coupled through the d 33 coecient. Electrodes do not interfere with the mechanical
coupling and magnets fabrication.

and then to apply a voltage across them. They can be placed on top and on the
bottom of the substrate (Fig. 6 (A)) or at both sides of the substrate (Fig. 6 (B)).
The first solution was partially experimentally demonstrated in [ 34 ], success-
fully showing the magnetization control with an applied voltage. However, two
problems arise when it must be applied to NML circuits. The generated electric
field is perpendicular to the plane, while the strain of the piezoelectric layer is
directed along the plane. The consequence is that the electric field and the strain
are coupled through the d 31 coecient of the piezoelectric material. d coecients
are physical constants of piezoelectric materials that bond the mechanical stress
and the applied voltage, as can be seen from Eqs. 1 and 2 , that describe the
mathematical theory behind the piezoelectricity.

= s E ·{T }

{S} +[ d ] ·{E} (1)

= d t ·{T } + ʳ E ·{E}

{D} (2)

Equations 1 and 2 are normally called coupled equations in the strain-charge
form. They provide the link between the deformation and the electric field. S is