IEEE Circuits and Systems Magazine - Q2 2018 - 34

the temperature as a state parameter, but if the steady
state approximation does not hold for Equation 5, temperature would become a state variable for the FML,
which would then be classified as a generic (-1,0) nonlinear element. In contrast, a normal inductor (one that
does not contain a ferromagnetic core) does not exhibit an appreciable degree of non-linearity or any form
of local activity, and thereby is classified as a linear
(-1,0) element.
In conclusion, by measuring only voltage and current
simultaneously as a function of time, we were able to
compute several interesting functions from the experimental data to help analyze the nonlinear dynamical
properties of a FML. This complements the usual analysis in terms of the energy of a magnetic phase transition
as the ferromagnetic system crosses an energy barrier
between two stable equilibria, formalized by several
Mean Field theories including the Landau model. [25],
[26] We also showed that this element exhibited negative differential inductance, which is an indicator of local activity or the ability of the system to store energy
and use it to amplify small changes to the input. [12] We
analyzed a heuristic model based on an ideal voltagecontrolled non-linear (-1,0) element that approximated
the FML electronic behavior and illuminated the underlying circuit principles. We then introduced both the
flux and temperature of the FML as two important state
variables that are required to account for the complete
dynamics of its behavior in a generic non-linear (-1,0)
element model. The fact that this system has regions of
negative differential inductance and thus local activity
may be useful for constructing interesting oscillators
and observing coupled dynamics in circuits that have
not yet been explored. [19]
Acknowledgments
The authors gratefully thank Leon O. Chua for providing
constructive comments on this manuscript.
Suhas Kumar is a Researcher at Hewlett
Packard Labs, Palo Alto, CA, USA. He
earned a Ph.D. from Stanford University
in 2014. He leads a group that investigates novel physical properties of materials and devices relevant to new forms
of physics-driven and bio-inspired computing. His latest work includes a practical demonstration of the idea
of using chaos to accelerate solutions to computationally hard problems. His research has been featured in
dozens of scientific publications, conferences, patent applications, and popular media. His contributions were
recently acknowledged with the Klein Scientific Development award.
34

IEEE cIrcuIts and systEms magazInE

R. Stanley Williams (SM'08) received the
Ph.D. degree in physical chemistry from
UC Berkeley, Berkeley, CA, USA, in 1978. He
is a Hewlett Packard Enterprise Senior Fellow. He has >220 US patents and >440 publications in reviewed scientific journals.
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sEcOnd quartEr 2018



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