magneto-transport · spin hall effect (she) spin-orbit coupling: interaction between spin and...

HansHuebl

Magneto-Transport

Walther-Meißner-InstitutBayerischeAkademiederWissenschaften

HansHuebl

Surfthe Wave&Pumpthe Charge

Walther-Meißner-InstitutBayerischeAkademiederWissenschaften

Electronics

Intel4004CPU

Fairchildintegrated circuit

FirstTransistor

electronics:onlychargedegreeoffreedom

Spintronics /Spincurrents

Intel4004CPU

Fairchildintegrated circuit

FirstTransistor

Spin(elec)tronics:(only)spindegreeoffreedom

IBMGermanyÊverspin

Outline

5

VISHE

purespin currentsspin Halleffect

„simple“spin current circuitsspin pumping

spin Hallmagnetoresistance

Chargetransport inmagnetic fields- Halleffect,magnetoresistance

Literature: O‘Handley,ModernMagnetic Materials(2014)

Halleffectandmagneto-resistance

7

“normalmetal”:nolong-rangemagneticordermobilecarriers


8

“normalmetal”:nolong-rangemagneticordermobilecarriers


9

“normalmetal”:nolong-rangemagneticordermobilecarrierswithequaldensityofmobilespinupandspindowncarriers


10

“normalmetal”:nolong-rangemagneticordermobilecarrierswithequaldensityofmobilespinupandspindowncarriers

OrdinaryHalleffect

11

magneticfieldBexertsaLorentzforce…

OrdinaryHalleffect

12

boundarycondition1:opencircuitconditionalongy:Jc,y=0chargeaccumulationsteadystate:“Lorentzforce

compensatedbyHallelectricfield”

OrdinaryHalleffect

13

Þ foropentransverseBC,thelongitudinalresistanceisindependentofB!Ex

Ey

𝐸" = 𝐸%&'( = 𝜌*𝐽,

𝐸- = 𝐸./%%= 𝐸01/'2= 𝜌./%%𝐽,

Ordinary Halleffect

14

boundarycondition2:Ey=0shortcircuitconditiontransversecurrentflow

𝐸" = 𝐸%&'( ≈ 𝜌* 1 + 𝜃./%%7 𝐽,

𝜃./%% =𝜌./%%𝜌*

=𝑅.𝐵𝜌*

Þ Halleffectimpactslongitudinalresistance

Spincurrents- SpinHallphysics

Literature: Tserkovnyak,Rev.of Mod.Phys.77,1375(2005)Sinova,Rev.of Mod.Phys.87,1213(2015)M.Wu&A.Hoffmann(eds.),Recent Advances inMagnetic Insulators - From Spintronics toMicrowave Applications (Elsevier,2014)

Mott’stwocurrentmodel(twospinchannelmodel)

16

purechargecurrent

-Jc =J↑ + J↓ 𝐉s =ℏ 7⁄C (J↑- J↓)

purespincurrent

parallelmotionof and¯ electrons

anti-parallelmotionof and¯ electrons

SpinHalleffect (SHE)

spin-orbitcoupling:interactionbetweenspinandchargemotion…spin-orientationdependentscattering(skew/side-jump/intrinsic(Berryphase)mechanisms)

…actslikeaspin-orientationdependentHallmagneticfieldÞ scattered left,¯ scattered right

𝐉𝐬 = 𝛼FG ℏ2𝑒 𝐉𝐜×𝐬

JsspinHallangleaSHE=sS/sCparameterizesJC« JSconversionefficiency

SpinHalleffect:chargecurrentinducestransversespincurrent

SpinHalleffect (SHE)andinversespin Halleffect (ISHE)

18


SpinHalleffect(SHE)

𝐉𝐜 = 𝛼FG 2𝑒ℏ 𝐉𝐬×𝐬

inversespinHalleffect(ISHE)

-Jc

spin-orbitcoupling:interactionbetweenspinandchargemotion…spin-orientationdependentscattering(skew/side-jump/intrinsic(Berryphase)mechanisms)

…actslikeaspin-orientationdependentHallmagneticfieldÞ scattered left,¯ scattered right

SpinHalleffect &boundary conditions

19

SpinHalleffect:chargecurrentinducestransversespincurrentviaSOC


Js


spinboundarycondition1:openspincircuitalongy:Js,y=0spinaccumulationsteadystate:“spindependentscattering

compensatedbyspinchemicalpotential”


Direct spin Halleffect inGaAs

21

Kerrmicroscopy(„spin imaging“)

Katoetal.,Science306, 1910(2004).

[ ]sJJ ´= CSHES 2e!a

-Jc

Js

Ä

4GaAsSHE 102 -´@a

ÄÄÄÄ

iSHE inMetallicF/NNanostructures

22

( )SFSHSHESHE /exp la LR -µD

4

C

SHESHE 101 -´@=

ssaAluminium:

Valenzuela&Tinkham,Nature442,176(2006).

detection ofdiffusive spin currentviainversespin Halleffect

Js

-Jc,ISHE

JsAl

FM1

LSH

Gold: aSHE=0.0016Platinum: aSHE=0.013…0.11 (0.16)Bi,Bi/Ag,Ta : aSHE=0.1…0.3

Valenzuela&Tinkham,Nature442,176(2006).Mosendz etal., Phys.Rev.Lett.104,046601(2010).Liuetal., Science 336,555(2012).Niimi etal., Phys.Rev.Lett.109,156602(2012).…andmanymore…M.Wu& A.Hoffmann(eds.),RecentAdvancesinMagneticInsulators- FromSpintronics toMicrowaveApplications(Elsevier,2014)

[ ]sJJ ´= sSHEISHEc

2!ea

-Jc,drive


23Þ spinHalleffectimpactslongitudinalresistance(=SMR)!

𝐸" ≈ 𝜌* 1 + 𝛼L.7 𝐽,

spinboundarycondition2:shortspincircuitalongy:µs,y=0transversespincurrentflow

wrap-up:

𝑗N = 𝑗N↑ + 𝑗N↓ ≠ 0

𝑗Q = Rℏ/7C 𝑗N↑+ Tℏ/7

C 𝑗N↓ = 0

𝑗N = 𝑗N↑ + 𝑗N↓ = 0

𝑗Q = Rℏ/7C 𝑗N↑+ Tℏ/7

C 𝑗N↓ ≠ 0

purecharge current purespin current

SHE:𝑗N → 𝑗Q

ISHE:𝑗Q → 𝑗N

Chargevs.SpinCurrents

24

Outline

25

VISHE




Coherent magnetizationdynamics- (Anti-)ferromagnetic Resonance- Spinpumping (damping)- Spinpumping (electrically detected)

Literature: Vonsovskii,Ferromagnetic Resonance (1964)Tserkovnyak,Rev.of Mod.Phys.77,1375(2005)Sinova,Rev.of Mod.Phys.87,1213(2015)M.Wu&A.Hoffmann(eds.),Recent Advances inMagnetic Insulators - From Spintronics toMicrowave Applications (Elsevier,2014)

Heff

Coherent magnetization dynamics

27

F

M

ferromagnet (F)withmacroscopicmomentM

M

!+++++=

RFexchangeanistropydemag.

0eff

HHHHHH

Heff

Magnetization dynamics

28

M

Heff

29

ttdd

¶¶

´+´=MMHMM aµg eff0

driveoutofequilibrium,e.g.withmicrowaveradiation


Landau-Lifshitz equation(LL)

Heff

30

driveoutofequilibrium,e.g.withmicrowaveradiation


Gilbertdamping

ttdd

¶¶

´+´=MMHMM aµg eff0

Gilbertdamping

Resonance Frequency

example:no anisotropy,external magnetic field only

𝐇WXX = 𝐇WY0

Resonance Frequency: Effects of Anisotropy

example:easyplaneanisotropy,calculate resonance frequencies

𝜃

Hext

resonator-based CWFMR

x xxx

xx

e1 h1 TE

resonatordimensions=n lMW /2resonatordeterminesMWfrequencyresonatorqualityQ>1000

® experiments@fixedMWfrequency® e1 andh1 spatiallyseparated

Bruker biospin

( )...100 ++´=¶¶ hHMM µgt

H0

FMRsignal® FMRresonancecondition:2pnMW =g Bres® realandimaginarypartofRFsusceptibility

RFsu

sceptib

ilityc

Bext – Bres (T)

Imc

Recµ0DH(FMRlinewidth)

( )...1ext0 ++´=¶¶ hHMM µgt

Hext

M MHext

M

(akaM

Wabsorption)

BroadbandFMR

sample

IMWh1

coplanarwaveguide(CPW)

10mm

Broadbandmagnetic resonance setup

2cm

Vector NetworkAnalyzer

1

221 V

VS =

SpectraVector NetworkAnalyzer

V FMI

1

221 V

VS =

𝑆7[ = 𝑆7[* 1 − 𝑖𝜔𝜇*1

16𝑤𝑍*𝛿𝑙𝜒"" Shaw,Appl.Phys.Lett.105,062406(2014)

Quantitativeanalysisà mag.hf-susceptibility

Antiferromagnets

=

antiferromagnetic below TN ,Néel Temperature

antiferromagnet

two compensating sublattices

Hagiwara et.al.,J.Phys.:Condens.Matter 8(1996)7349–7354

H⊥H||

common antiferromagnets:• Cr• NiO• Fe2O3• MnF2

The Spin Flop Transition

Hext Hext>Hc

magnetic easyaxis

gain inZeemanenergy >loss inanisotropy energy

𝐻h = (𝐻j7+2𝐻j𝐻k)[/7

Antiferromagnetic Resonance

Keffer and Kittel, Physical Review 85, 329 (1952)

simultaneous precession of magnetisation of both sublattices

two sublatticesÞ two resonance

frequencies

Hext

effective field:

𝐇Cmm,o = 𝜆𝐌r + 𝐇C"s + 𝐇o

𝐇Cmm,r = 𝜆𝐌o + 𝐇C"s + 𝐇o

Ma

Mb

very higheffective fields,lM>100TpossibleÞ highfrequencies

MnF2: A prototypical antiferromagnet

miniSMPconnector

MnF2 crystal

coplanar waveguide:center line

andground plane

http://wwwchem.uwimona.edu.jm:1104/courses/mnf2J.html

Only easyaxis anisotropy

TN=67K

Bexchange=52T

Banisoptropy =0.8T Mn2+

F-

Hagiwara et.al.,J.Phys.:Condens.Matter 8(1996)7349–7354

Hext>Hc

spinflo

p MnF2

Bext

c-axis (easy)

q

I.S.Ja

cobs,J.A

ppl.Ph

ys.32,S61

(196

1).

Simulated Resonance Frequency

Antiferromagnetic resonance MnF2

F/N+microwave photons =spin battery

resonantly driven magnetization inFrelaxesviathe emission ofaspin currentinto the adjacent Nlayer

spin pumping

Tserkovnyak,Phys.Rev.Lett.88,117601(2002).Brataas,Phys.Rev.B66,060404(2002).Tserkovnyak,Phys.Rev.B66,224403(2002).

suggested by Tserkovnyak,Brataas &Bauer,PRL(2002)

44

÷øö

çèæ ´==

dtdG

AmmIJ r

SS 4p

!

hpga

FsatSP

14 tM

Gr!

=inF:additionaldamping

inN:DCspincurrent Q= 2

MWcircS sin

2 rGJ n!

andACspincurrent…see

Gr:spinmixingconductance,units1/m2

nMW

D.Weietal.,NatureComm.5,1(2014)



spin pumping



45

÷øö

çèæ ´==

dtdG

AmmIJ r

SS 4p

!

hpga

FsatSP

14 tM

Gr!



MWcircS sin

2 rGJ n!



nMW


Spinpumpingasadampingmechanism

Pysat,Py

Au/PyPt/PySP

41

MtGr p

hgaaa!

=

-=

Gr =2.5´ 1019 m-2

M.Wu& A.Hoffmann(eds.),RecentAdvancesinMagneticInsulators- FromSpintronics toMicrowaveApplications(Elsevier,2014)

Au/Py

Pt/Py

dampingduetoSP



spin pumping



47

÷øö

çèæ ´==

dtdG

AmmIJ r

SS 4p

!

hpga

FsatSP

14 tM

Gr!



MWcircS sin

2 rGJ n!



nMW


Spinpumping with spin current detection

magnetization precession

FMR

inversespin Halleffect

DCcharge current Jc

DCspin current

microwave +DCmagnetic field

DCvoltage drop V

spin pumping

opencircuit

( ) Q= ¯ 2MWS sinRe

2gJ n!

( )[ ]sJeJ ˆ2 SSHISHEC ´=

!"

!a

Tserkovnyak etal.,Phys.Rev.Lett.88,117601(2002).Saitoh etal.,Appl.Phys.Lett.88,182509(2006)

Measurementsetupsampleholder

shielding

wires

fusedsilicatube

sample

5mm

TypicalsampledimensionsL´W´ t=3mm´ 1mm´ (10nm/10nm)

Ni/Pt

FMR

(arb

.u.)

T=290K

f=0°

0 50 100 150 200 250 300 350

-4

-2

0

2

4

V DC (µ

V)

µ0H (mT)

Ni/Pt

7nmPt10nmNi

Ni/Pt

FMR

(arb

.u.)

T=290K

f=180°

0 50 100 150 200 250 300 350

-4

-2

0

2

4

V DC (µ

V)

µ0H (mT)

FMR

(arb

.u.)

T=290K

f=0°

0 50 100 150 200 250 300 350

-4

-2

0

2

4

V DC (µ

V)

µ0H (mT)

Ni/Pt Ni/Pt

7nmPt10nmNi

Ni/Pt

FMR

(arb

.u.)

T=290K

f=180°

0 50 100 150 200 250 300 350

-4

-2

0

2

4

V DC (µ

V)

µ0H (mT)

FMR

(arb

.u.)

T=290K

f=90°

450 500 550 600 650 700 750

-4

-2

0

2

4

V DC (µ

V)µ0H (mT)

FMR

(arb

.u.)

T=290K

f=0°

0 50 100 150 200 250 300 350

-4

-2

0

2

4

V DC (µ

V)

µ0H (mT)

Ni/Pt Ni/Pt Ni/Pt

7nmPt10nmNi

0 100 200 300-0.3-0.2-0.10.00.10.20.3

100 200 300-0.8

-0.4

0.0

0.4

0.8

0 150 300-4

-2

0

2

4

0 50 100-40

-20

0

20

40

0 25 50 75-40

-20

0

20

40

25 50 75 100-80

-40

0

40

80

100 200 300-6-4-20246

125 250 375-15-10-505

1015

Fe3O4 (i)(111)

FMR

Hres

290K

V DC (µ

V)

µ0H (mT)

(j)

(k) Fe3O4(100)

Hres

290K

(l)

µ0H (mT)

(arb

.u.)

(arb

.u.)

FMR

(a) Ni

0°180° Hres

290K

µ0H (mT)

VD

C (µ

V)

(b)

Co(e)

Hres

290K

µ0H (mT)

(f)

2Co FeSi(g)

Hres

290K

µ0H (mT)

(h)

(c) Fe

Hres

290K

µ0H (mT)

(d)

75nmDMS(m)

Hres

10K

µ0H (mT)

(n)

200nmDMS(o)

Hres

10K

(p)

µ0H (mT)

Differentmaterials

works formany differentF/platinumbilayers

samesign ofVDCfor f=0°for allbilayers

notMWrectification[MW-inducedJc(t)´m(t)® VDC]butspin pumping!Similar spin-mixingconductance for allsystems

Czeschka,Phys.Rev.Lett 107,046601(2011)

AFMRvs EDspin pumping MnF2

Ross, J. Appl. Phys., 118 233907 (2015)

Spinpumping inMnF2

Mainspin pumpingsignal notduetospin pumping

Smalldifference signalindicates spin currentinjected into Pt

difference signal under field inversion

Ross, J. Appl. Phys., 118 233907 (2015)

SpinHallmagnetoresistance- SpinHallmagnetoresistance

Literature: Sinova,Rev.of Mod.Phys.87,1213(2015)Nakayama,Phys.Rev.Lett.110,206601(2013)Althammer,Phys.Rev.B 87,224401(2013)Chen,Phys.Rev.B87,144411(2013)Vlietstra Phys.Rev.B87,184421(2013)....

SMRmechanism

YIG M

Pt

SMRmechanism

Pt

YIG

Jc 𝐉𝐬 = 𝛼L.tℏ2𝑒 𝐉𝐜×𝐬

M

SMRmechanism

Pt

YIG

JcJs

s

𝐉𝐬 = 𝛼L.tℏ2𝑒 𝐉𝐜×𝐬

M

SMRmechanism

Pt

YIG

JcJs

s


M

electron spin accumulation inPtwith spin s

SMRmechanism

Pt

YIG

Jc

if 𝜏Lvv ∝ 𝐌× 𝐌×𝐬 isfinite

M

enhanceddissipationinPt→largerPtresistance

→outflowofJs intoYIG

Js,YIG

Js

s


electron spin accumulation inPtwith spin s

SMRmechanism

Pt

YIG

Jc

M

enhanceddissipationinPt→largerPtresistance

→outflowofJs intoYIG

Js

sJc

Js,backJs

s

M

Js,YIG

𝜏Lvv ∝ 𝐌× 𝐌×𝐬 = 0

reduceddissipation→smallerPtresistance

→openboundaryconditionsforJs

if 𝜏Lvv ∝ 𝐌× 𝐌×𝐬 isfinite

SMRmechanism

Pt

YIG

Jc

M

Js

s

Js,YIG

𝑅 = 𝑅* − 𝑅[ 𝐦 y 𝐬 7

= 𝑅* − 𝑅[cos7(𝛼)

JcJs,backJs

s

M

PRL 110,206601(2013)

SpinHallMR(SMR):R smallest forM||s,largerotherwise

SMRmechanism

Pt

YIG

Jc

M

Js

s

Js,YIG

𝑅 = 𝑅* − 𝑅[ 𝐦 y 𝐬 7

= 𝑅* − 𝑅[cos7(𝛼)

JcJs,backJs

s

M

PRL 110,206601(2013)

SpinHallMR(SMR):R smallest forM||s,largerotherwise

64

Measuring resistance

V

I

Rl

RlLeadresistanceinfluences results

R =V

I

Measuring resistance

IRl

Rl

V

Leadresistanceinfluences results

4wire methodprobes device physics

R =V

I

Measuring resistance — switching techniques

IRl

Rl

V

Schreieretal.,Appl.Phys.Lett.103,242404(2013)

Vres(I) =1

2(V (+I)� V (�I))

Vtherm(I) =1

2(V (+I) + V (�I))

Contains allodd terms inI:à resistive effects

Contains alleven terms inI:à thermaleffects

R =V

I

SMRfingerprint

H||j H||t

SpinHallMR(SMR):Rsmallest forM‖s(viz.M‖t) ,largerotherwise

SMRamplitude: Δ𝑅/𝑅 ≅ 4×10T~

Js

Jc

s

H||n H||t H||n H||j

Extraction of spin Hall angle from SMRYIG/Pt@WMI YIG/Pt@IMR

Ptthickness dependenceà spin Hallangleand spin diffusion length inPt

YIG/Pt @Huangetal.,PRL,109,107204(2012)

spinmixingconductance:𝑔↑↓=1x1019 m-2

−𝜌[𝜌*

=𝛼L.7 2𝜆�07 𝜌�0

𝑔↑↓𝑡�0

tanh7 𝑡�02𝜆�0

1 + 2𝜆�0𝜌�0𝑔↑↓coth𝑡�0𝜆�0

SpinHallmagneto-resistance:ü MRin(nonmagnetic)Pt,governed

byM ininsulatingYIGü “simple”measurementofspinHall

transportparametersü electricaldetectionofM inFMI

Acknowledgements“Magnetiker”

SebastianT.B.Goennenwein

RudolfGrossMatthiasAlthammerMathiasWeilerStephanGeprägsKathrinGanzhornStefanKlinglerMatthiasPernpeintnerRichardSchlitzTobiasWimmerSybilleMeyerHannesMaier-FlaigFranzCzeschkaAndreasBrandlmayer

Summary

71

VISHE




magneto-transport · spin hall effect (she) spin-orbit coupling: interaction between spin and...

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