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

Simulation of Power Gain and Simulation of Power Gain and Dissipation in Field-Coupled Dissipation in Field-Coupled

Nanomagnets Nanomagnets

OutlineOutline

The Magnetic Quantum Cellular

Automata Concept

Power Dissipation in Nanoscale

Magnets

Power Gain in Nanoscale Magnets

xL

yL

zL

in/outHinL

inV

xMV

yMV

zMV

Driver Cell Driven Cell

Main idea:Interconnection by stray fields

Coulomb-repulsion

By changing the geometry one can perform logic functions as well

The Quantum Cellular The Quantum Cellular Automata Automata

Wire

Signal in Signal out

‘1’ ‘0’

Majority gate

Input 2

Input 3

Input 1

Output

‘1’ ‘1’‘0’ ‘0’

Bistable switch:

‘1’ ‘0’

Due to shape anisotropy there is a typically few hundred room-temperature kT energy barrier between the two stationary states.

Magnetic NanopillarsMagnetic Nanopillars

En

erg

y0 90 270

Mag

neto

stat

ic e

nerg

y

0

150

300

kT

nm20

nm100

nm50 15nm

M

90 270

Interaction Between Two Interaction Between Two Nanoscale MagnetsNanoscale Magnets

mμ5.0

Signal flow

The Nanomagnet WireThe Nanomagnet Wire

t

extH

Clocking results in predictable switching dynamics

Input dot: retains its magnetization

0.5μm

Micromagnetic Simulation Micromagnetic Simulation of the Nanomagnet Wireof the Nanomagnet Wire

pumpH

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 2AND

Input 3

Input 2OR

Input 3

The Magnetic Majority GateThe Magnetic Majority Gate

Input 2

OutputInput 1

Input 3 ‘Central dot’

Top view:

Experimental Progress Experimental Progress

Fabrication and pictures by A. Imre

Investigations of permalloy nanomagnets (thermally evaporated and patterned by electron beam lithography) confirm the simulation results

Sim

ulat

ion

AF

MS

imul

ated

fiel

dM

FM

Approaches to Magnetic Approaches to Magnetic Logic DevicesLogic Devices

Soliton – propagation in coupled dots

(Cowburn, Science, 2000) (Cowburn, Science, 2002)

Manipulation of domain wall propagation

Coupling between magnetic vortices, domain walls

Joint ferro- and antiferromagnetic coupling

(Parish and Forshaw, 2003)

(Our group)

Pictures and fabrication by A. Imre

Fundamental questions from the system perspective:

•What is the amount of dissipated power?What is the amount of dissipated power?

•Do nanomagnets show power gain?Do nanomagnets show power gain?

Inputcurrents

Outputsensors

Dot Array

Small building blocks

Complex systems

?

Magnetic Signal Propagation

Larger-Scale SystemsLarger-Scale Systems

Model of Dissipation in Model of Dissipation in MagnetsMagnets

effH

eff M H

eff M M H

M

e

eff

ff

,, ,

, , , s

t t tM

tt t

t

M(r )

M

M(r ) H (

(r )M(r ) H (

)

)

r

r

Dissipative termPower density:

(i) (i) (i)diss eff eff

diss

( , ) , , ,effs

MP t H H t t t

t M

r M (r ) M (r ) H (r )

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:

Switching of a Large MagnetSwitching of a Large MagnetM

agne

tizat

ion

dyna

mic

s:

( , )tM r

Dis

sipa

ted

pow

er d

ens

ity

( , )P tr

7μm

Dissipated power:diss ( )P t

0 10 ns

710 W5

diss 1.5 10 kE T

Hysteresis curve: ( )x xM H

xH

xM

H

Dis

sipa

ted

pow

er d

ensi

ty

Simulation of a 50 nm by 20 nm permalloy strip

Dissipation in a Domain-wall Dissipation in a Domain-wall ConductorConductor 7

diss 10 WP

Minimizing the DissipationMinimizing 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)

Switch them slowly (use adiabatic pumping)

Dissipation is strongest around domain walls

Small magnets have no internal domain walls

Non – Adiabatic Switching of Non – Adiabatic Switching of Small MagnetsSmall Magnets

zH

E

90 90

Energy landscape of a pillar-shaped single–domain nanomagnet

0zH

smallzH

at switchingzH

Ene

rgy

barr

ier

at z

ero

fie

ld

Ene

rgy

was

ted

durin

g sw

itchi

ng

System state

Micromagnetic Simulation of the Micromagnetic Simulation of the Non-Adiabatic Switching ProcessNon-Adiabatic Switching Process

Micromagnetic simulation

( , )tM r

( )yM t

diss ( )P t

0 10 ns

710 W

0 10 ns

SM

SM

Total dissipation:

diss 4000 kE T

yH 120 nm

60 nm

20 nm

Adiabatic SwitchingAdiabatic Switching

yΗ

zH

1.

2.

3.

4.

yH

E

90 90

Ene

rgy

barr

ier

at

zero

fiel

d

1.

0yH

2. 3.

4.

By adiabatic clocking, the system can be switched with almost no dissipation, but at the expense of slower operation.

largeyH

smallyH

Dynamic simulation

( , )tM r

( )zM t

0 100 ns

SM

SM

0 100 ns

diss ( )P t

1110 W

Total dissipation:

diss 30 kE T

120 nm

60 nm

20 nm

Simulation of Adiabatic Simulation of Adiabatic SwitchingSwitching

Switching Speed vs. Dissipated PowerSwitching Speed vs. Dissipated Power

Adiabatically switched nanomagnets can dissipate at least two orders of magnitude less energy than the height of the potential barrier separating their steady-states

diss[k ]E T

rise[s]t1010 710910 810

410

310

210

110~ 20kT

120 nm

60 nm

20 nm

610

010

110 ~ 0.15 kT

Full micromagnetic model

Single-domain approx.

The Lowest Limit of Dissipation in The Lowest Limit of Dissipation in Magnetic QCA 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.

External field

Schematic:

Micromagnetic simulation:

Single-domain model

Power Gain of Adiabatically Power Gain of Adiabatically Pumped NanomagnetsPumped Nanomagnets

0 50 100 150 200 250 300 350 400 450 500

Time (ns)

-1.0

-0.5

0.0

0.5

1.0

sz MM /

Ma

gn

etiz

atio

n

How energy flows, when magnets flip to their ground state?

pumpP

in outP P

Energy of the magnetic signal increases as the soliton propagates along the wire

Detailed View of the Switching Detailed View of the Switching ProcessProcess

1.0

Z S/M M

0.0

0.0 1.00.5 nst

(1)z M

(3)zM

(2)zM

1.0

0.01

k

ns

TP

0.005

0.0 1.00.5 nst

(1)z inP

(2)z inP

(3)z inP

extz sH M

outz sM M

0 0.05 0.1

0.5

1.0

ext 0.2y si M

ext 0.25y si M

ext 0.3y si M

0.050.1

0.5

1.0

50 nm50 nm

100 nm

Hysteresis Curves of Single-Hysteresis Curves of Single-Domain Nanomagnets Domain Nanomagnets

in aci i

pump dci i

ini

pump smalli

pump largei

Low inductance

High inductance

pump dci i

in aci i

This is a circuit with a variable inductance. Does it have applications?

Inductance control

A Nanomagnet Driven by A Nanomagnet Driven by Current LoopsCurrent Loops

Magnetic AmplifiersMagnetic AmplifiersLow impedance circuit

1.Ettinger, G. M.: “Magnetic Amplifiers”, Wiley, New York, 1957

High impedance circuit

Nonlinearity of the hysteresis curve Tunable inductances Power gain

Magnetic ComputersMagnetic Computers

ini

inv

outi

outv

pumpipumpv

outv

outi

dc 0i

dc 10i A

Mu

lti A

pe

rtu

red

De

vice

(M

AD

)

A magnetic shift register from Gschwind: Design of Digital Computers, 1967

This three-coil device behaves like a common-base transistor amplifier

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

Coupled Nanomagnets as Coupled Nanomagnets as CircuitsCircuits

inzH

ini

yH

pumpi

outzH

outi

Right neighbor(Equivalent circuit)

Left neighbor(Equivalent circuit)

Magnetic field-coupling is an idea Magnetic field-coupling is an idea

worth pursuing…worth pursuing…

Low dissipation, robust operation, high Low dissipation, robust operation, high

integration density and reasonably integration density and reasonably

high speedhigh speed

As they are active devices, there is no As they are active devices, there is no

intrinsic limit to their scalabilityintrinsic limit to their scalability

Field-coupling is functionally equivalent Field-coupling is functionally equivalent

to electrically interconected device to electrically interconected device

architecturesarchitectures

1cm

1.0μm

ConclusionsConclusions

Our Group Our Group

Prof. Wolfgang Porod

Prof. Paolo Lugli

Prof. Arpad Csurgay

(Circuit modeling)

Prof. Gary H. Bernstein

(Experiments)

Prof. Vitali Metlushko

(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