A diamond in the rough?€¦ · A diamond in the rough? S. Hacohen-Gourgy N. Antler,...

A diamond in the rough?

S. Hacohen-GourgyN. Antler,

Eli-Levenson-Falk, I. Siddiqi

Quantum'Nanoelectronics'LaboratoryPhysics'Department

University'of'California'at'Berkeley

Outline

• Single Spin Logic• Architecture• The major problems• Alternate solutions

• Diamond NV centers• Single NVs• Small ensembles

• Nanobridge SQUID Magnetometer

For Internal E3S Use OnlyThese Slides May Contain Prepublication Data and/or Confidential Information.

Single Spin Logic

• A spin represent a binary 0 or 1

• Global B field defines the quantization axis

• Nearest neighbor interaction exists

• Control of spins creates excited state -> Thermal relaxationis the computation result

• Interaction and layout define the computation

Bglobal

Energy splitting


Single Spin Logic

• All hardware “collective computation” scheme

• Very fast

• Minimum Energy , p is the error rate

• Application specificEmin = kT ln(1/p)


Single Spin Logic

• Universal Single Spin Logic Computation

Unidirectional spin wireNAND Gate

Images adapted from:S. Bandyopadhyay, ISRN materials research 2012 697056 (2012)

1.

2.


• Energy Dissipation of switching1. Internal dissipation ~10s-100s of kT

2. Dissipation in switching circuit

• Wires

• Spin torque

• Spin Hall

• Strain induced using Multiferroics

• Fast laser pulses

• Low write speed ~ns

Single Spin Logic


Single Spin Logic

• Readout

• NV diamond magnetometers

• Magnetic Resonance Force Microscopy (MRFM)

• Spin to charge conversion-QD

• Superconducting Quantum Interference Device (SQUID)

• Readout time ~1sec for 1μB

Image adapted from:P. Maletinsky Nat. Nano. 7, 320 (2012)


Single Spin Logic

• Operation temperature and magnetic field (in thermal equilibrium)

2J = gµBB = kT ln(1/p)

• Possible solutions

• Nanomagnetic logic (NML)

• Single Spin Logic Out of Thermodynamic Equilibrium

• Work at low temp

• High magnetic fields


Single Spin Logic Out of Thermodynamic Equilibrium

• Operation out of thermal equilibrium

• Energy levels are spaced closer than kT

• Random noise events have a long time scale

• Thermalization has a long time scale

500 Nikonov, Bourianoff, and Gargini

x

yz

Bclock

x

yz

Bmeas

spin splitting

x

yz

Bmeas

spin splitting

x

yz

x

yz

Fig. 2. a Spin state in computing a) clocking; (b) setting the initialvalue; (c) switching; (d) read-out; (e) before the next clocking.

Bclock

x

yz

Bclock

x

yz

x

yz

Fig. 2. Continued.

This is done by applying a weaker “setting” mag-netic field along the y-axis for a definite duration(Fig. 2b). This field causes precession of spin by 90degrees from the x-axis to the z-axis, as explainedabove.

c) Computing is envisioned as the switching ofthe spin state depending on the input magnetic field.It is performed by applying a similarly weaker “com-puting” magnetic field along the y-axis for a defi-nite duration (Fig. 2c). This field causes precessionof spin by 180 degrees. The direction of spin remainsclose to the z-axis.

d) One can read-out the spin after any numberof switching cycles. For theoretical simplicity, we en-vision the read-out with the magnetic force micro-scope (MFM) (Fig. 2d).

e) During computing, the magnitude of the spinis being damped by spin relaxation. Since the exter-nal magnetic field is relatively small in stages (b)–(d), the relaxation time is much longer than theswitching time. Therefore, it is possible to performmany (ideally thousands) of switching cycles beforethe spin magnitude is degraded (see Fig. 2e). Afterthat, a refresh of the spin magnitude is needed withthe aid of the “clocking” field. The spin output statesneed to be read-out just before clocking and storedin memory. They are then needed as inputs in thenext clocking cycle. We return to stage (a).

A more practical variation of this spintronics elementis one of multiple quantum dots with a single elec-tron in each, (see Fig. 3). In this case, the comput-ing is done via interaction of spins of single electronswith the spins of neighboring confined electrons (dueto the exchange part of the Coulomb force), and notwith the magnetic fields acting individually on eachsingle electron. Initial setting of spins is performedby injecting spin current from ferromagnetic con-tacts attached to a few input quantum dots. The dotsare formed into geometry patterns which implementlogic gates (AND, OR, etc.) [14] or majority gates[15]. The read-out is performed by passing current

500

Nik

onov

,Bou

rian

off,

and

Gar

gini

xyz

Bcl

ock

xyz

Bm

eas

spin

split

ting

xyz

Bm

eas

spin

split

ting

xyz

xyz

Fig.

2.a

Spin

stat

ein

com

putin

ga)

cloc

king

;(b)

sett

ing

the

initi

alva

lue;

(c)

switc

hing

;(d)

read

-out

;(e)

befo

reth

ene

xtcl

ocki

ng.

Bcl

ock

xyz

Bcl

ock

xyz

xyz

Fig.

2.C

ontin

ued.

Thi

sis

done

byap

plyi

nga

wea

ker

“set

ting”

mag

-ne

ticfie

ldal

ong

the

y-ax

isfo

ra

defin

itedu

ratio

n(F

ig.2

b).T

his

field

caus

espr

eces

sion

ofsp

inby

90de

gree

sfr

omth

ex-

axis

toth

ez-

axis

,as

expl

aine

dab

ove. c)

Com

putin

gis

envi

sion

edas

the

switc

hing

ofth

esp

inst

ate

depe

ndin

gon

the

inpu

tmag

netic

field

.It

ispe

rfor

med

byap

plyi

nga

sim

ilarl

yw

eake

r“co

m-

putin

g”m

agne

ticfie

ldal

ong

the

y-ax

isfo

ra

defi-

nite

dura

tion

(Fig

.2c)

.Thi

sfie

ldca

uses

prec

essi

onof

spin

by18

0de

gree

s.T

hedi

rect

ion

ofsp

inre

mai

nscl

ose

toth

ez-

axis

.d)

One

can

read

-out

the

spin

afte

ran

ynu

mbe

rof

switc

hing

cycl

es.F

orth

eore

tical

sim

plic

ity,w

een

-vi

sion

the

read

-out

with

the

mag

netic

forc

em

icro

-sc

ope

(MFM

)(F

ig.2

d).

e)D

urin

gco

mpu

ting,

the

mag

nitu

deof

the

spin

isbe

ing

dam

ped

bysp

inre

laxa

tion.

Sinc

eth

eex

ter-

nal

mag

netic

field

isre

lativ

ely

smal

lin

stag

es(b

)–(d

),th

ere

laxa

tion

time

ism

uch

long

erth

anth

esw

itchi

ngtim

e.T

here

fore

,it

ispo

ssib

leto

perf

orm

man

y(i

deal

lyth

ousa

nds)

ofsw

itchi

ngcy

cles

befo

reth

esp

inm

agni

tude

isde

grad

ed(s

eeFi

g.2e

).A

fter

that

,are

fres

hof

the

spin

mag

nitu

deis

need

edw

ithth

eai

dof

the

“clo

ckin

g”fie

ld.T

hesp

inou

tput

stat

esne

edto

bere

ad-o

utju

stbe

fore

cloc

king

and

stor

edin

mem

ory.

The

yar

eth

enne

eded

asin

puts

inth

ene

xtcl

ocki

ngcy

cle.

We

retu

rnto

stag

e(a

).

Am

ore

prac

tical

vari

atio

nof

this

spin

tron

icse

lem

ent

ison

eof

mul

tiple

quan

tum

dots

with

asi

ngle

elec

-tr

onin

each

,(s

eeFi

g.3)

.In

this

case

,th

eco

mpu

t-in

gis

done

via

inte

ract

ion

ofsp

ins

ofsi

ngle

elec

tron

sw

ithth

esp

ins

ofne

ighb

orin

gco

nfine

del

ectr

ons

(due

toth

eex

chan

gepa

rtof

the

Cou

lom

bfo

rce)

,and

not

with

the

mag

netic

field

sac

ting

indi

vidu

ally

onea

chsi

ngle

elec

tron

.In

itial

sett

ing

ofsp

ins

ispe

rfor

med

byin

ject

ing

spin

curr

ent

from

ferr

omag

netic

con-

tact

sat

tach

edto

afe

win

putq

uant

umdo

ts.T

hedo

tsar

efo

rmed

into

geom

etry

patt

erns

whi

chim

plem

ent

logi

cga

tes

(AN

D,

OR

,et

c.)

[14]

orm

ajor

ityga

tes

[15]

.T

here

ad-o

utis

perf

orm

edby

pass

ing

curr

ent

500 Nikonov, Bourianoff, and Gargini

x

yz

Bclock

x

yz

Bmeas

spin splitting

x

yz

Bmeas

spin splitting

x

yz

x

yz

Fig. 2. a Spin state in computing a) clocking; (b) setting the initialvalue; (c) switching; (d) read-out; (e) before the next clocking.

Bclock

x

yz

Bclock

x

yz

x

yz

Fig. 2. Continued.

This is done by applying a weaker “setting” mag-netic field along the y-axis for a definite duration(Fig. 2b). This field causes precession of spin by 90degrees from the x-axis to the z-axis, as explainedabove.

c) Computing is envisioned as the switching ofthe spin state depending on the input magnetic field.It is performed by applying a similarly weaker “com-puting” magnetic field along the y-axis for a defi-nite duration (Fig. 2c). This field causes precessionof spin by 180 degrees. The direction of spin remainsclose to the z-axis.

d) One can read-out the spin after any numberof switching cycles. For theoretical simplicity, we en-vision the read-out with the magnetic force micro-scope (MFM) (Fig. 2d).

e) During computing, the magnitude of the spinis being damped by spin relaxation. Since the exter-nal magnetic field is relatively small in stages (b)–(d), the relaxation time is much longer than theswitching time. Therefore, it is possible to performmany (ideally thousands) of switching cycles beforethe spin magnitude is degraded (see Fig. 2e). Afterthat, a refresh of the spin magnitude is needed withthe aid of the “clocking” field. The spin output statesneed to be read-out just before clocking and storedin memory. They are then needed as inputs in thenext clocking cycle. We return to stage (a).

A more practical variation of this spintronics elementis one of multiple quantum dots with a single elec-tron in each, (see Fig. 3). In this case, the comput-ing is done via interaction of spins of single electronswith the spins of neighboring confined electrons (dueto the exchange part of the Coulomb force), and notwith the magnetic fields acting individually on eachsingle electron. Initial setting of spins is performedby injecting spin current from ferromagnetic con-tacts attached to a few input quantum dots. The dotsare formed into geometry patterns which implementlogic gates (AND, OR, etc.) [14] or majority gates[15]. The read-out is performed by passing current

Images adapted from:S. N. Molotkov and S. S. Nazin JETP Lett. 62, 256 (1995)


Diamond NVs

Images adapted from:R. Hanson et. al. Science 320, 352 (2008)E. Rittweger et. al. Nat. Photonics 3, 144 (2009)

• Can be controlled in an out of thermalequilibrium fashion using RFs

• Reset and readout using optics

For Internal E3S Use Only. These Slides May Contain Prepublication Data and/or Confidential Information.

Single Spin Logic With Diamond NVs

• Optically we are addressing an ensemble of ~500nm

Nano antenna figure adapted from:Tao Joon Seok et. al. Nano. Lett. 11, 2606 (2011)



• Optically we are addressing an ensemble of ~500nm

• Do they flip together?

• How strong is the coupling?

• Ensemble dephasing time?


Diamond NVs

Image adapted from:F. Dolde Nat. Phys. 9, 139 (2013)

• Coupling is dipolar - Spin diffusion

• Higher concentration stronger coupling

• How strong can we make without affectingthe dephasing time?

• Dominating T1 process at low temp



• Can spin diffusion be controlled using local fields?

Blocal

Figure adapted from:A. Jarmola PRL 108, 197601 (2012)For Internal E3S Use Only

These Slides May Contain Prepublication Data and/or Confidential Information.

nanobridge SQUID magnetometer



Nanobridge Banks



0 10 20 30 40 50 60 70 8010−2

10−1

100

101

In−Plane Field (mT)

Flux

Noi

se (µ

0/H

z1/2

)

17nΦ0/√Hz30nΦ0/√Hz

51nΦ0/√Hz

361nΦ0/√Hz

42nΦ0/√Hz

45nΦ0/√Hz

225nΦ0/√Hz

2500nΦ0/√Hz

New ground plane design

Linear regime

Paramp regime


Spin interaction in NV ensembles


Summary

• Shown NVs may be a candidate for Spin Logic

• NV room-temperature operation is well established

• Shown our nanobridge magnetometer can measure smallensembles, to study the spin dynamics

• Results will tell us if this is a promising pathway


THE END

A diamond in the rough?€¦ · A diamond in the rough? S. Hacohen-Gourgy N. Antler,...

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