Simulation of Power Gain and
Dissipation in Field-Coupled
Nanomagnets
G. Csaba, A. Csurgay, P. Lugli and W. Porod
University of Notre Dame
Center for Nano Science and Technology
Technische Universität München
Lehrstühl für Nanoelektronik
Outline
The Magnetic Quantum Cellular
Automata Concept
Power Dissipation in Nanoscale
Magnets


Hin/out
VM x
Lx
VM y
Ly
VM z
Lz
Lin

Vin





Power Gain in Nanoscale Magnets
The Quantum Cellular
Automata
‘1’
‘0’
‘0’
‘1’
Main idea:
Interconnection by
stray fields
Wire
Coulomb-repulsion
‘0’
‘1’
Signal in
Signal out
Majority gate
Driver Cell
Input 1
Driven Cell
By changing the geometry one
can perform logic functions as
well
Output
Input 2
Input 3
Magnetic Nanopillars
‘1’
‘0’
Due to shape anisotropy there
is a typically few hundred roomtemperature kT energy barrier
between the two stationary
states.

Energy
Bistable switch:
0
90

270
Interaction Between Two
Nanoscale Magnets
Magnetostatic energy
M

20nm
kT
100nm
50nm
300
15nm
150
0
90
270

The Nanomagnet Wire
H ext
0.5μm
Signal flow
t
Clocking results in predictable
switching dynamics
Micromagnetic Simulation
of the Nanomagnet Wire
0.5μm
H pump
Input dot: retains its magnetization
The Magnetic Majority Gate
Top view:
Input 1
Input 3
Input 2
Output
‘Central dot’
Input 1
Input 2
Input 3
Output
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1


Input 2
OR
Input 3
Input 2
AND
Input 3
Investigations of permalloy nanomagnets (thermally
evaporated and patterned by electron beam lithography)
confirm the simulation results
MFM
Fabrication and pictures by A. Imre
Simulated field
AFM
Simulation
Experimental Progress
Approaches to Magnetic
Logic Devices
Soliton – propagation
in coupled dots
Manipulation of
domain wall
propagation
(Cowburn, Science, 2000)
(Cowburn, Science, 2002)
Joint ferro- and
antiferromagnetic
coupling
Coupling between
magnetic vortices,
domain walls
(Our group)
(Parish and Forshaw, 2003)
Pictures and fabrication by A. Imre
Larger-Scale Systems
Input
currents
Dot Array
Output
sensors
Small building blocks
?
Complex systems
Magnetic Signal Propagation
Fundamental questions from the system perspective:
•What is the amount of dissipated power?
•Do nanomagnets show power gain?
Model of Dissipation in
Magnets
 M   M  H eff  
Magnetic moments (spins) of the ferromagnetic material
perform a damped precession motion around the
effective field.
The Landau-Lifschitz Equation (fundamental equation of
domain theory) gives quantitative description of this
motion:
H eff
M(r, t )
  M(r, t )  H eff (r, t )
t
  M  Heff 

M

M(r, t )   M(r, t )  H eff (r, t )  
Ms 
Dissipative term
Power density:
Pdiss (r, t )   H eff
M
t
 
M(i) (r, t )  M(i) (r, t )  H(i)
  H eff 
eff (r, t )

 Ms

diss





Switching of a Large Magnet
Magnetization dynamics:
M (r, t )
Hysteresis curve:
Mx
7μm
Hx
Dissipated power:
P(r, t )
Dissipated power density
M x (H x )
Pdiss (t )
Ediss  1.5 105 kT
107 W
H
0
10 ns
Dissipation in a Domain-wall
P  10
Conductor
7
Dissipated power density
diss
Simulation of a 50 nm by 20 nm permalloy strip
W
Minimizing the Dissipation
Rapidly moving domain walls are
the main source of dissipation in
magnetic materials
Make the magnets sufficiently
small (submicron size magnets
has no internal domain walls)
Dissipation is strongest around
domain walls
Switch them slowly (use
adiabatic pumping)
Small magnets have no internal
domain walls
Non – Adiabatic Switching of
Small Magnets

Hz  0
System state
H z small
Energy landscape of a pillar-shaped
single–domain nanomagnet
90

90
Energy wasted
during switching
H z at switching
Energy barrier
at zero field
E  
Hz
Micromagnetic Simulation of the
Non-Adiabatic Switching Process
M S
Hy
20 nm
M y (t )
120 nm
60 nm
M S
0
107 W
10 ns
Total dissipation:
Pdiss (t )
Ediss  4000 kT
Micromagnetic simulation
M (r, t )
0
10 ns
Adiabatic Switching
E  
Energy barrier at
zero field
Hy  0
1.
1.
Ηy
H y small
2.
Hz
3.
H y large
Hy
90
3.
2.

90
4.
By adiabatic clocking, the system can be switched with
almost no dissipation, but at the expense of slower
operation.
4.
Simulation of Adiabatic
Switching
20 nm
M S
120 nm
M z (t )
60 nm
M S
0
100 ns
10 11 W
Total dissipation:
Ediss  30 kT
Pdiss (t )
Dynamic simulation
M (r, t )
0
100 ns
Switching Speed vs. Dissipated Power
104
20 nm
Ediss [kT ]
Full micromagnetic model
103
120 nm
60 nm
102
101
~ 20kT
Single-domain approx.
100
1010
101
109
108
107
106
trise [s]
~ 0.15 kT
Adiabatically switched nanomagnets can dissipate at least two orders of magnitude
less energy than the height of the potential barrier separating their steady-states
The Lowest Limit of Dissipation in
Magnetic QCA
Deviations from the ideal single-domain behavior  abrupt domain wall switches will always cause
dissipation (few kT)
Coupling between dots should be stronger than
few kT  dot switching cannot be arbitrarily slow
 few kT dissipation unavoidable
The minimal dissipation of nanomagnetic logic
devices is around a few kT per switching.
Power Gain of Adiabatically
Pumped Nanomagnets
Schematic:
1.0
Mz / Ms
Single-domain
model
External field
Micromagnetic
simulation:
Magnetization
0.5
How energy flows,
when magnets flip
to their ground
state?
0.0
-0.5
-1.0
0
50
100
150
200
250
300
350
Time (ns)
400
450
500
Detailed View of the Switching
Process
Pz(3)in
 kT 
P 
 ns 
Ppump
Pz(2)in
0.01
Pz(1)in
0.005
0.0
1.0
0.5
1.0
t  ns
1.0
t  ns
M z(2)
M Z / MS
Pin  Pout
Energy of the magnetic signal
increases as the soliton
propagates along the wire
M z(3)
0.0
M z(1)
1.0
0.0
0.5
Hysteresis Curves of SingleDomain Nanomagnets
1.0
M
out
z
iyext  0.3M s
Ms
iyext  0.25M s
0.5
100 nm
iyext  0.2M s
50 nm
50 nm
0.1
0.05
0
0.05
0.1
H zext M s
0.5
1.0
A Nanomagnet Driven by
Current Loops
High inductance

ipump  idc
ipump  small
Inductance control
ipump  large
iin

iin  iac
Low inductance
iin  iac
ipump  idc
This is a circuit with a variable
inductance.
Does it have applications?
Magnetic Amplifiers
Low impedance circuit
High impedance circuit
1.Ettinger, G. M.: “Magnetic Amplifiers”, Wiley, New York, 1957
Nonlinearity of the hysteresis curve  Tunable inductances  Power gain
Magnetic Computers
iin
iout
iout
idc  10 A
vout
vin
idc  0
ipump
vpump
A magnetic shift register
from Gschwind: Design of Digital Computers, 1967
Multi Apertured Device (MAD)
This three-coil device behaves like a common-base transistor amplifier
vout
Coupled Nanomagnets as
Circuits
i pump
Left neighbor
(Equivalent circuit)
Right neighbor
(Equivalent circuit)
Hy
i
in
H zin
H
out
z
i out
The origin of power gain in field-coupled nanomagnets can be understood
on the same basis as the operation of magnetic parametric amplifiers
 Nanoelectronic circuit design
Conclusions
1.0μm
Magnetic field-coupling is an idea
worth pursuing…
Low dissipation, robust operation, high
integration density and reasonably
high speed
1cm
As they are active devices, there is no
intrinsic limit to their scalability
Field-coupling is functionally equivalent
to electrically interconected device
architectures
Our Group
Prof. Vitali Metlushko
Prof. Wolfgang Porod
Prof. Paolo Lugli
Prof. Arpad Csurgay
(Circuit modeling)
Prof. Gary H. Bernstein
(Experiments)
(Fabrication)
Prof. Alexei Orlov
(Electrical measurements)
Alexandra Imre
(Fabrication, Characterization)
Ling Zhou
(Electrical measurements)
Our work was supported by the Office of Naval
Research, the National Science Foundation and the
W. M. Keck Foundation