Electric Clock for NanoMagnet Logic Circuits - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 80

Table 2. Magnetic materials comparison. Ms is the saturation magnetization, ʻ 1 00
and ʻ 1 11 are the magnetostrictive coecients, while Y is the Young modulus and
˃ MAX STRUCT is the fracture stress.

Ms (10 6 A/m) ʻ S ( · 10 − 6 )Y(GPa) ˃ MAX STRUCT (MPa)

Cobalt 1.45 50 209 225

Iron 1.71 14 211 540

Nickel 0.49 33 214 100

Terfenol 0.8 600 80 28

To complete the analysis the value of maximum stress previously evaluated
( ˃ MAX PIEZO ) must be compared with the maximum stress that can be toler-
ated by the magnetic material ( ˃ MAX STRUCT ). The maximum stress that can
be applied to the circuit is therefore the minimum between these two values of
stress as shown in Eq. 6 .

˃ MAX = min ( ˃ MAX STRUCT ,˃ MAX PIEZO ) (6)

Between these two values, the lower bound is normally given by the maximum
structural stress that can be tolerated by the magnetic material ( ˃ MAX STRUCT ).
As can be seen from Table 2 this value is in the range of 28-540 MPa.
Once that the maximum stress is evaluated, the next step is to understand
the minimum stress that must be applied to the magnets to force them in the
RESET state. The minimum stress can be evaluated considering two important
properties of magnetic materials: Shape and stress anisotropy. The value of shape
anisotropy is related to the sizes and aspect ratio of magnets and can be evaluated
as shown in Eq. 7 .

E A = 1

2 μ 0 N d M 2

s V

(7)

where μ 0 is the magnetic permeability, N d is the demagnetization factor, M s is
the magnetization saturation and V is the volume. Stress anisotropy is instead
related to the applied mechanical stress and can be evaluated as shown in Eq. 8 .

E A = 3

2 ʻ s ˃V

(8)

where ʻ s is the magnetostrictive coecient of the magnetic material, ˃ is the
applied stress and V is the volume. The minimum stress is therefore the value of
stress that generates a stress anisotropy at least equal to the shape anisotropy
and can be calculated equaling Eqs. 7 and 8 , as shown in Eq. 9 .

˃ MIN = μ 0 N d M 2

s

(9)

3 ʻ s

Once the minimum and maximum stresses that can be applied are know, it it
possible to analyze different magnetic materials and to understand which of them
is suited for this kind of application. The analysis is performed using Octave,