Electric Clock for NanoMagnet Logic Circuits - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 81

evaluating how the minimum stress changes with magnet sizes. Since in NML
circuits magnets are either 50 90 nm 2 , the shorter magnet side

is chosen equal to 50 nm, and the longest magnet side is changed from 50 nm to
100 nm, changing therefore magnets aspect ratio (from 1 to 2). Magnets thickness
is chosen equal to 10 nm, to obtain the maximum mechanical coupling between
the substrate and the magnets. Minimum and maximum stresses are therefore
evaluated for these values of magnet sizes. Figure 7 shows the results of the
analysis for two common magnetic materials, Iron and Cobalt.

100 nm 2 or 60

× ×

Fig. 7. Minimum and maximum stress evaluation changing magnets sizes for (A) Iron
and (B) Cobalt. The maximum stress is always bigger than the minimum required
stress, so these two materials cannot be used for this particular application.

To assure the magnets stability in presence of thermal noise the value of
shape anisotropy must be at least equal to 30 K b T , as shown in Eq. 10 , generating
therefore a lower bound on the value of aspect ratio:

1
2 μ 0 N d M 2

s V =30 K b T

(10)

The minimum value of aspect ratio that assures thermal stability is equal to
1.06, that means magnets must be at least 50

53 nm 2 .HoweverfromFig. 7
it is possible to see that either Iron (Fig. 7 (A)) or Cobalt (Fig. 7 (B)) cannot be
used for this application. The value of minimum stress is always bigger than the
maximum applicable stress.
Things are different if high magnetostrictive materials are considered. Figure 8
shows the analysis results applied to nickel and terfenol. Terfenol is an alloy of
Terbium, Disprosium and Iron. As can be seen Nickel shows a sizes range where
the minimum stress is effectively lower than the maximum applicable stress.
The maximum aspect ratio is 1.28, that is equal to magnets of 50

×

64 nm 2 .
Terfenol shows better performance, since the maximum aspect ratio is 1.57 that
means magnets of 50

×

78 nm 2 . It appears that Terfenol is the best choice for ×

this application.