Design and simulation of magnetic logic device for next generation data processing

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Design and simulation of magnetic logic device for
next generation data processing
Madhav Rao
International Institute of
Information Technology -Bangalore
Bangalore-560100
India
Email: mr@iiitb.ac.in
Neha Oraon
International Institute of
Information Technology -Bangalore
Bangalore-560100
India
Email: neha.oraon@iiitb.org
Ranganatha S
International Institute of
Information Technology -Bangalore
Bangalore-560100
India
Email: kamath.ranganath@gmail.com
Abstract—Next generation data processing unit requires high
computational speed with minimum power consumption. The
current technology which is driven by scaled CMOS architecture,
depends on electrical charge to create or hold one of the two
states - ”on” or ”off”. Today’s data processing unit contains
many such devices to build and store electric charges, thereby
creating excessive heat component within the computing unit.
The generated heat affects devices and thereby malfunctions the
computational process. A new generation of data processing unit
in the form of network of closely coupled ferromagnetic dots
is described in this paper. The magnetic logic device operates
by manipulating the magnetic states of closely coupled single-
domain nanomagnets. The computation takes place via magnetic
interaction between closely placed ferromagnetic dots and not by
transport of electric charge. The permalloy dots are designed in
ellipsoidal shape with dimensions of 320 nm ×120 nm and 20 nm
of thickness. The ellipsoidal shape of permalloy dots generates
single domain inherent magnetization along the major axis. The
remnant magnetization of the driver dot influences the nearby
ferromagnetic dot to align magnetic domain in either opposite or
same direction based on the coupling arrangements. Two types
of coupling: ferromagnetic and antiferromagnetic coupling in a
coplanar arrangement of dots are discussed and used to design
different logic functions in this paper. Three basic digital circuit
operations: Identity, AND, and OR are simulated using Object
Oriented Micromagnetic Framework (OOMMF). An attempt to
develop a combinational digital circuit in OOMMF simulator is
also described in this paper.
Keywords—magnetic logic gate, nanomagnets, logic devices,
data processing
I. INTRODUCTION
THE next generation data processing unit requires high
computational speed to process large data. Current CMOS
technology that works on electric charge, will dissipate exces-
sive heat for large data processing. The current CMOS circuit
consists of units of PMOS and NMOS transistors to drive
output. The leakage current generated while switching from
pull up to pull down network in a highly dense CMOS circuit
is unavoidable [1], [2]. The minute leakage current can drive
the ouput of digital circuit to a different state, yielding incorrect
logic level. Hence an alternate technology that is leakage free
during steady state needs to be developed.
The ability to pattern devices at nanoscale led to the
development of novel computational devices and circuits [3],
[4]. Alternate technologies such as single electron transistor
(SET), and quantum cellular automata (QCA) show potential.
SET device is based on the quantum mechanical behavior,
which turns ON and OFF every time an electron is added [5],
[6]. SET is an ideal replacement to conventional CMOS tech-
nologies because of low power consumption and small size,
however a complete working model at room temperature is still
not realized. QCA operates on quantum dots response to the
neighbouring charge states [7], [8]. The hopping of electrons
in QCA device is controlled by the coupling between the dots,
quantized energy level in each dot, and coulombic interaction
between electrons. QCA operation is also limited to cryogenic
temperatures and is sensitive to the slight misalignment of
quantum cells.
The magnetic logic device evolved from QCA technology
functions due to close coupling of dipoles in magnetic dots,
that are configured to behave as single domain units [9],
[10], [11], [12]. The magnetization states, instead of electric
charge, in the dot structures are used for data processing,
thereby avoiding heat dissipation in processing circuit [13],
[14]. The magnetic technology is designed to work in room
temperature and reliably overcomes the thermal fluctuations
caused to magnetic dipoles. The architecture is interconnect
free and makes the circuit more compact and wire free [15].
The power dissipation is reduced due to electrically isolated
configuration and dipole interaction that occurs when the
applied field is switched off [16], [17]. The magnetic logic
consists of input, output and a network of closely coupled
processing cells that are designed in a coplanar configuration
to yield different logic functions. The magnetic domains of
the cells arranged are aligned in either of two stable positions
based on close magnetic interaction between neighboring cells.
The magnetic logic operates by triggering a bistable physical
property of cells on one edge where the input is entered into
the system. The magnetization state of the processing cells are
disturbed by the close magnetic interaction of cells activated
by a change in state of input magnetic cell. The processing cell
changes its state till global minimum energy state is reached,
thereby driving a state in the output cell. The magnetic cell is
configured to retain either of two magnetic states, resembled as
logic ’1’ or ’0’. The physical shape of an ellipsoidal magnetic
cell restricts to the magnetization to either of two stable states
in the structure. The state of output cell is driven by the
magnetic coupling of processing cells. The magnetic state of978-1-4799-1743-3/15/$31.00 c
2015 IEEE

the input dot is controlled by magnetic field applied along the
longer dimensions of the dot [18], [19], [20], [21]. On removal
of magnetic field, the designed set of magnetic dots relaxes to
minimum energy state and a distinct output is realized. The
applied magnetic field is designed to produce the neccesary
remnant magnetization which influences the magnetic polarity
of nearby dots.
II. DESIGN AND SIMULATION OF MAGNETIC LOGIC
DEVICE
A soft magnetic material which is easily magnetized by low
magnetic field was required to design logic device. Among all
the magnetic material, Permalloy exhibits the lowest coercive
field required to overcome the remnant magnetization. The
bistable states of magnetic structures is derived from shape
anisotropy property of ferromagnetic material. The ellipse
shaped magnetic structure with dimensions of 320 nm in
length and 120 nm in width, is already proved to demonstrate
two stable states [22]. Shape anisotropy suggests the remnant
magnetization is aligned along the major length [22], [23],
[24]. The aspect ratio of magnetic dots close to 2.5 was chosen
to exhibit magnetic easy axis along the direction of their long
axis as suggested by Imre [25]. The thickness of dots were
chosen to be around 20 nm. The simulation was performed on
an open source micromagnetic simulation software OOMMF,
developed at NIST [26]. OOMMF solves a micromagnetic
problem in the form of a regular two dimensional grid and
positioning three dimensional magnetization spins at the center
of the cells. For each cell defined, the solver integrates the
Landau-Lifshitz equation stated in equation 1.
dM
dt =−γM ×Hef f −γα
Ms
M×(M×Hef f )(1)
where M is pointwise magnetization (A/m), γis gyromagnetic
ratio (m/(A.s)), αis the damping coefficient (dimensionless),
and Heff is the pointwise effective field (A/m), defined as:
Heff =−µ−1
0
∂E (M)
∂M
where µ0is magnetic permeability in vacuum and E(M) is
Landau-Lifshitz energy, which is given by
E(M) = Eexchange(M) + Eanisotropy(M) + Eapplied(M) +
Estray (M)
The simulation tool takes the geometry of the structure
in the form of an PPM image file. Characteristic material
constants, external magnetic field, anisotropy, are taken as
inputs. A damping coefficient, αof 0.5 is set, for the solver
to converge in a reasonable iterations. A default value of
2.21×105is set for γin the simulator. For permalloy material,
saturation magnetization, crystalline anisotropic constant and
exchange stiffness was set to 860×103A/m,13×10−12 J/m
and 0 J/m3respectively. Exchange stiffness, and Crystalline
anisotropic constant are used to calculate exchange energy, and
anisotropy energy for providing Landau-Lifshitz energy E(M)
component in the solver.
The coercive field of a single permalloy dot of dimensions
mentioned above was determined by setting up the simulation
in OOMMF. Figure 1 shows single domain magnetic alignment
with a coercive field of 120 mT to flip the magnetic domain
direction. The energy required to switch magnetic dipoles of
specified dimensions to either of the two possible states in a
single domain magnetic dot is 8×10−17J. In comparison to
a CMOS inverter gate of 65 nm process technology consumes
3×10−16Jfor a layout area of 2µm2[27]. An inverter based
on ferromagnetic dot of dimensions 320nm×120nm occupies
a footprint of 0.44µm2. In addition, the propogation delay for
a magnetic logic based inverter device is close to 3 ns. The
delay in magnetic architecture is determined as the time for
the magnetic domains to flip and settle down to minimum
energy state. Since the demagnetization energy is small for
lower dimensions of dot, the delay can be further decreased
depending on the size of the dots.
(a) (b)
Fig. 1: (a)Hystersis curve showing coercive field of 120 mT is
required to switch the domain direction and (b) representation
of magnetic domain direction in a single nanomagnet modeled
using permalloy ferromagnetic material.
Figure 2 shows that the remnant magnetic field of a
horizontally oriented magnetic dot is driving a vertically
aligned magnetic dot. The magnetic dots are designed to have
random domain directions at rest. Applied magnetic field along
horizontal direction was used to align magnetic domains of
both dots in the field direction. When the applied magnetic
field is switched off, the horizontal oriented dot, also called as
input dot, retained the domain polarity in horizontal direction
and drives the magnetic domains in the vertically oriented
processing dot in a direction, to complete magnetic flux lines.
If the applied magnetic field is less than 120 mT for the
specified dot dimensions, the input dot failed to retain remnant
magnetization and did not couple the nearby vertically aligned
dot.
A study on the scaling of the nanomagnets was performed
to observe the alignment of magnetic domains at lower dimen-
sions. The nanomagnet was modeled to various dimension and
relaxed state magnetic dipole positions were simulated. It was
observed that magnetic polarity was consistent for dots ranging
from 320nm ×120nm to 20nm ×8nm maintaining the shape
anisotropy. However a further decrease in the dot dimension
to 10nm ×4nm showed misaligned polarity of dots as shown
in Figure 3. The demagnetizing energy for a dot size of
10nm×4nm for a thickness of 2 nm was found to be 8×10−21
J which is close to thermal energy (KT) of 4.14 ×10−21
J at room temperature. The comparable thermal energy was
beieved to manipulate demagnetization driven magnetic dipole

Fig. 2: Coupling of single domain nanomagnets in the direction
of magnetic flux lines is shown.
directions in the dot. The demagnetizing energy increases
for higher dimensions of dots, hence dipole direction is less
influenced by thermal energy. The bistable dipole position is
observed for dots of size 20nm ×8nm.
Fig. 3: Magnetic domain alignment of a ferromagnetic dot of
dimension 10nm ×4nm on switching off the magnetic field
that was applied in horizontal direction.
Two types of coupling: ferromagnetic and antiferromag-
netic is applied in developing different logic functions. The fer-
romagnetic coupling through magnetostatic interactions aligns
the nearest neighbouring dot domains in same direction.
Whereas antiferromagnetically coupling aligns neighbouring
dot in opposite direction. The maximum and minimum interdot
spacing for effective ferromagnetic coupling was studied by
considering different designs of two dots, separated by varying
distances. Figure 4 represents antiferromagnetic coupling of
dots for different interdot spacing. It was observed that if the
dots were close enough, say 2 nm, then a continuous magnetic
field deters the coupling effect. However the antiferromagnetic
coupling was observed for interdot spacings of 4 to 95 nm.
Above 95 nm, the coupling effect was lost. Similar interdot
spacing effect for ferromagnetic coupling is studied as shown
in Figure 5. It was observed that ferromagnetic coupling effect
was lost for interdot spacing of more than 25 nm. With the
knowledge of dot spacing and dimensions, identity, AND, OR
and a combinational circuit was designed. Dot spacing of
20 nm was realized in simulation study, is also possible to
fabricate in an Indian academic laboratory using the existing
electron beam lithography system [28].
(a) 2nm
(b) 95nm
(c) 100nm
Fig. 4: Observation of magnetic domains in a antiferromag-
netically coupled network of dots for interdot spacing of (a)
2nm, (b) 95nm, and (c) 100nm.
A. One input gate
The design of a single input logic functions was designed in
OOMMF. One input magnetic logic gate demonstrated inverter
or identity gate based on the parity of magnetic dots. Odd par-
ity suggested identity logic and even parity represented inverter
logic. The magnetic logic including identity and inverter logic

(a) 2nm (b) 25nm
(c) 27nm (d) 80nm
Fig. 5: Observation of magnetic domains in a ferromagnetically
coupled network of dots for interdot spacing of (a) 2nm, (b)
25nm, (c) 27nm, and (d) 80nm.
gate is shown in Figure 6. The design of logic gate required
minimum magnetic field of 120 mT to retain the magnetization
state of the network of dots. The hystersis loop for switching
magnetic state of dots is shown in Figure 1. Faulty operation
in the form of dots not following any ordering was observed
when the applied magnetic field was relaxed abruptly. The
applied magnetic field acted as a clock input for the designed
network of magnetic dots to trigger close coupling effect. The
magnetic field of above 120 mT was applied and restored back
to 0 with a minimum of 20 steps.
B. AND/OR logic
A logic gate comprised of two inputs was designed to
operate as AND or OR logic based on the leftmost switch
input dot. The bifunctional circuit based on magnetic material
is shown in Figure 7(a-d). An equivalent schematic of digital
circuit in CMOS logic is shown in Figure 7(e). Two input
Fig. 6: Magnetic logic based digital identity logic.
dots were fixed at the top and bottom position in the layout.
The layout was considered as multiplexer circuit representing
AND and OR logic. The antiferromagnetic ordered magnetic
input dot influences neighboring dot to align its domain in
inverse direction. The other magnetic input dots arranged in
ferromagnetic order influences the neighboring dot in same
direction. Hence the final magnetic domain orientation of the
central dot depends on dominated domain direction influnced
by three surrounded dots. The output dot is placed in series
with other dots which is antiferromagnetically coupled to
central dot.
C. Combinational circuit
A combinational circuit ((A+B).C) in the form of
network of magnetic dots as shown in Figure 8 was simulated
and designed to obtain the result.Both ferromagnetic and
antiferromagnetic coupling were applied to observe the logic
functionality in the design. The inputs: A, B and C were
configured to obtain output of ((A+B).C) expression. The
combinational circuit was verified for various input data.
III. CONCLUSIONS
Layout of logic functionalities such as identity, AND, OR
logic functions, and a combinational circuit were designed
using magnetic structures. It was demonstrated that these
structures displayed expected output provided placement is
accurate. The logic functionality was achieved by arrang-
ing the closely coupled dots in either antiferromagnetic or
ferromagnetic order. The maximum and minimum interdot
spacing for ferromagnetic and antiferromagnetic coupling was
demonstrated via simulation. Simulation study stated that the
footprint required to design inverter logic based on magnetic
architecture is was low compared to CMOS 65 nm process
technology. Experimental work in IIT-Bombay via Indian
Nanoelectronics User Program is carried and results will be
presented in the conference. An SEM image showing magnetic
dots separated by 20 nm is shown in the Figure 9. Further
experimental studies via Magnetic force microscope will verify
magnetic spin directions and logic functionalities.
ACK NOW LE DG EM EN TS
The authors would like to thank Government of India,
Science and Engineering Research Board for sponsoring the

(a) (b)
(c) (d)
(e)
Fig. 7: Bifunctional circuit in magnetic logic architecture
designed to perform (a-b) AND, (c-d) OR operation, and (e)
equivalent circuit in CMOS logic form.
research project. The authors would like to thank IIT-Bombay,
Indian Nanoelectronics Users Program (INUP) and Center of
Excellence in Nanoelectronics (CEN) for allowing to use the
facilities. We are grateful to INUP team at IIT-Bombay.
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