lecture iii: spin-triplet supercurrent in ferromagnetic josephson...

Lecture III: Spin-triplet supercurrent in ferromagnetic Josephson junctions

Norman Birge*, Michigan State University

* Work supported by DOE BES

Autumn College on Non-Equilibrium Quantum SystemsMay 2-13, 2011

Buenos Aires, Argentina

Collaborators: Trupti Khaire, Mazin Khasawneh, Caroline KloseHamood Arham, Kurt Boden, William P. Pratt, Jr.

Prologue: Fermion pairing

• Condensed Matter Physics– superconductivity & superfluidity (3He)

• Nuclear Physics– nucleon pairing (even-odd energy differences)

• Astrophysics– superfluidity in neutron stars

• Atomics Physics– BEC to BCS crossover in cold atomic gases

(see lectures by Christophe Salomon)

Prologue:What we remember from quantum mechanics

A convenient basis:

21212211 ,,,;, ssrrsrsr

Wavefunction for two identical fermions (Spin-Statistics Thm or Pauli Exclusion)

11222211 ,;,,;, srsrsrsr

Two possibilities:

2112 ,, rrrr SS1. and 2112 ,, ssss AA

2112 ,, rrrr AA2. and 2112 ,, ssss SS

,, ,21,m

llnln YrRrr

2112 ,, ssss AA

2112 ,, ssss SS

Example: two electrons in free space: 21 rrr

even l

odd l 2112 ,, rrrr AA

2112 ,, rrrr SS

Spatial state is eigenstate of orbital L2:

Spin state is eigenstate of total spin S2: 21 SSS

s=1 (triplet)

s=0 (singlet)

Prologue:What we remember from quantum mechanics

210s

211s

Allowed Cooper pair symmetries

s=0 s=1

l=0(s-wave)

BCS X

l=1(p-wave)

X superfluid 3HeSr2RuO4

l=2(d-wave)

high-Tc X

11222211 ,;,,;, srsrsrsr

Proposal by Berezinskii (1974):

What does this mean?

121212212121 ;,;;,; ttssrrFttssrrF


Fermions require:

F is odd in time:

F is even under exchange of space and spin:


F(r1,r2,s1,s2,t1,t2 ) “anomalous Green’s function” = pair correlation function


s=0 s=1

l=0 BCS X

l=1 X superfluid 3HeSr2RuO4

l=2 high-Tc X

= allowed if correlation function is odd under time-reversal (or odd in frequency)


s=0 s=1

l=0 BCS X

l=1 X superfluid 3HeSr2RuO4

l=2 high-Tc X

= allowed if correlation function is odd under time-reversal (or odd in frequency)

Berezinski model for 3He (1974)

Balatsky & Abrahams (‘92)


s=0 s=1

l=0 BCS S/F

l=1 S/F superfluid 3HeSr2RuO4

l=2 high-Tc S/F

especially interesting

Bergeret, Volkov & Efetov, PRL 90, 117006 (2003); RMP 77, 1321 (2005)

Outline

• Proximity effect in S/N and S/F systems• Prediction: Spin-triplet pair correlations• Our search: S/F/S Josephson junctions

– PdNi – a weak ferromagnet– Co/Ru/Co – a synthetic antiferromagnet– Combining the best of both materials

• Conclusions and Future Prospects

k

E

-kF-kF kF kF

k

E

kF-kF

Andreev Reflection: N/S vs. F/S

S/N S/F

FexFF vEQkk 2

ex

FF E

D

ex

FF E

vQ2

1 ballistic

diffusive

Tkvv

B

FFN 2

TkDD

B

NNN 2

ballistic

diffusive

Coherence time between electron and hole: 2

S N/F

D = diffusion constant

2Eex

Proximity effect: S/N vs. S/F

)/exp()( 0 Nxx )/exp()/cos()( 0 FF xxx

nmfewED

ex

FF ~

N F

x

mfewTk

D

B

NN 2

How to detect the oscillating pair correlation function?

Kontos, Aprili, Lesueur, Grison, PRL 86, 304 (2001)

1. Measure tunneling density of states in S/F/I/N structure, as function of dF

S F I N

dF

How to detect the oscillating pair correlation function?

2. Measure critical current of S/F/S Josephson junction, as function of dF

Ryazanov et al., PRL 86, 2427 (2001); 96, 197003 (2006).

Weak F: Cu48Ni52 alloy

Robinson, Piano, Burnell, Bell, Blamire, PRL 97, 177003 (2005)

Strong F: Co

0.0 1.0 2.0 3.0 4.0 5.0

dCo (nm)

I cRN

(mV)

0-state: Is = Ic sin( 2- 1)-state: Is = Ic sin( 2- 1+ ) S F S

dF

Prediction: long-range spin-triplet pair correlations induced by noncollinear magnetization

ex

FSF E

DTk

D

B

FTF 2

TF

SF

Singlet Triplet

Bergeret, Volkov & Efetov, Phys. Rev. B 64, 134506 (2001); PRL 90, 117006 (2003)

Kadrigrobov, Shekhter & Jonson, Europhys. Lett. 54, 394 (2001)

S F

S F2F1

Features of odd-frequency, spin-triplet pair correlations

• s=1: pairs not subject to Eexlong-range penetration in F

l=0: insensitive to disorder

Bergeret, Volkov & Efetov, Rev. Mod. Phys. 77, 1321 (2005)

s=0 s=1

l=0 BCS S/F

l=1 S/F Sr2RuO4

l=2 high-Tc S/F

Possible observation of triplet:

Keizer, Goennenwein, Klapwijk, Miao, Xiao, Gupta, Nature 439, 825 (2006)

0.3 – 1 m

Long-range propagation of supercurrent,

but large sample-to-sample variations in Ic.

Reproduced last year by J. Aarts

CrO2 is a “half metal”

k

E

EF

Our approach:Systematic study of S/F/S junctions:

sfTFF

SF ld

S F S

dF

suppress singlet

triplet limited by spin-flip scattering

ex

FSF E

DTk

D

B

FTF 2

Signature of spin-triplet:

Log(Ic)

dF

singlet:

triplet:

S F S

dF

homogeneous Minhomogeneous M

SF

Fc

dI exp

TF

Fc

dI exp

1. Sputter S/F/S2. Pattern pillars with photolithography

Nb

Nb bottom contact

F

Au

Tri-‐layer photoresist

Si Substrate

Sample Fabrication

10 – 40 m

Nb

Nb bottom contact

F

Au

Si Substrate

Si Ox

1. Sputter S/F/S2. Pattern pillars with photolithography3. Ion mill4. Deposit SiOx

Sample Fabrication

10 – 40 m

Nb bottom contact

F

Au

Si Substrate

Si Ox

1. Sputter S/F/S2. Pattern pillars with photolithography3. Ion mill4. Deposit SiOx

Nb top contact

1. Sputter S/F/S2. Pattern pillars with photolithography3. Ion mill4. Deposit SiOx5. Liftoff6. Deposit top Nb contact

Sample Fabrication

10 – 40 m

Measurement

-0.2 -0.1 0.0 0.1 0.2

-5

0

5

V (n

V)I (mA)

Ic-Ic

Low sample resistance (7 – 100

Measure with SQUID-based current comparator circuit

I-V characteristic of overdampedJosephson junctions

Measure at T = 4.2 K in “quick-dipper” cryostat in helium storage dewar

Ic critical current

supercurrent

S/F/S junctions with a weak F: Pd88Ni12 alloy

Each point represents average over 2 - 4 junctions on same substrate

30 40 50 60 70 80 90 100

103

104

105

106

107

108

J c (A

/m2 )

dPdNi (nm)

Nb (S)

PdNi (F)

Nb (S)

(previous work on PdNi Josephson junctions had dPdNi < 15 nm)

T.S. Khaire, W.P. Pratt, and N.O. Birge, Phys. Rev. B 79, 094523 (2009)

Each point represents average over 2 - 4 junctions on same substrate

Periodic minima in Jc

30 40 50 60 70 80 90 100

103

104

105

106

107

108

J c (A

/m2 )

dPdNi (nm)


Nb (S)

PdNi (F)

Nb (S)

)/cos()/exp( 21 FFc xxI

1 = 7.7 ± 0.5 nm 2 = 4.4 ± 0.1 nm

30 40 50 60 70 80 90 100

103

104

105

106

107

108

J c (A

/m2 )

dPdNi (nm)


Nb (S)

PdNi (F)

Nb (S)

T.S. Khaire, W.P. Pratt, and N.O. Birge, Phys. Rev. B 79, 094523 (2009)

30 40 50 60 70 80 90 100

103

104

105

106

107

108

J c (A

/m2 )

dPdNi (nm)

No sign of spin-triplet supercurrent!


Nb (S)

PdNi (F)

Nb (S)

Why don’t we see spin-triplet supercurrent in S/F/S Josephson junctions with PdNi?

• Not enough non-collinear magnetization• Magnetic inhomogeneity on wrong length scale• Too much spin-flip and/or spin-orbit scattering

How to measure the spin memory length using Giant Magnetoresistance (GMR)

P state

AP state

Permalloy = Ni0.84Fe0.16

Pd0.88Ni0.12

RP < RAP

Cu

Albert Fert & Peter Grunberg 2007 Nobel Prize

Jack Bass & Bill Pratt

Dependence of GMR signal on dPdNi

dPdNi dPy

Fix dPy, vary dPdNi

PdNiPdNiPdNi dRA*

sfPdNiPdNiPdNi lRA

*

If dPdNi < lsfPdNi

If dPdNi > lsfPdNi

0 1 2 3

dPdNi

Raw GMR signal

P state

AP statedPdNi = 12 nm

-80 -40 0 40 80

10.05

10.10

10.15

R (n

)

H (Oe)

GMR signal vs. dPdNi

0 5 10 15 200.00

0.05

0.10

0.15

0.20

AR

(fm

2 )

dPdNi (nm)

Fit to Valet-Fert theory

Result: lsf PdNi = 2.8 ± 0.5 nmH.Z. Arham, T.S. Khaire, R. Loloee, W. P. Pratt, Jr., and N.O.B., Phys. Rev. B 80, 174515 (2009)

0 5 10 15 200.00

0.05

0.10

0.15

0.20

AR

(fm

2 )

dPdNi (nm)

Fit with lsf PdNi

Pd1-xNix magnetic characterization

-4000 -2000 0 2000 4000-150

-100

-50

0

50

100

150

M (e

mu/

cm3 )

Field (Oe)

PdNi alloy has out-of-plane magnetic anisotropy!!(violates assumptions about P and AP states in GMR experiment)

H out-of-plane

H in-plane

0 50 100 150 200 250 3000

20

40

60

80

100

120

140

160

M (e

mu/

cm3 )

Temperature (K)

Alternate “spoiler” spin valve geometry

dPdNi

PdNi

Why don’t we see spin-triplet supercurrent in S/F/S Josephson junctions with PdNi?

• Not enough non-collinear magnetization• Magnetic inhomogeneity on wrong length scale• Too much spin-flip and/or spin-orbit scattering

Try a different approach:Use a strong F with long spin-memory length: Co

Aside: Characterization of Josephson Junctions by the Fraunhofer pattern

“I never believe anybody’s Josephson junction data unless they show me a Fraunhofer pattern.” -- Dale van Harlingen

2R

2L+ d

NHext

o

oCC

JII

)(2)0()(

1

where RdH NLext 2)2(

L= London

penetration

length

/o

I c(

) / I c

(0)

Airy diffraction pattern for a circular junction

Large-area Nb/Co/Nb junctions

-20 -10 0 10 200.00

0.02

0.04

0.06

I c (m

A)

H (Oe)

Nb/Co/Nb, dCo = 5 nm, 2R = 40 m

2R

2L+ d

FHext

Random Fraunhofer pattern due to complex domain configuration

Trick: achieve flux cancellation with Co/Ru/Co synthetic antiferromagnet

H.A.M. vandenBerg et al., J. Mag. Magn. Mat. 165, 524 (1997).

Nb

CoRuCo

Nb

Co/Ru/Co synthetic antiferromagnet restores Fraunhofer pattern!

-20 -10 0 10 200.00

0.04

0.08

0.12

0.16

0.20

I c(m

A)

H (Oe)

dCo = 13 nmw = 20 m

-20 -10 0 10 200.00

0.02

0.04

0.06

I c (m

A)

H (Oe)

dCo = 5 nm

w = 40 m

with Ru without Ru

S/F/S junction with a strong F: Co

0 5 10 15 20 25

104

105

106

107

108

J c (A

/m2 )

dCo (nm)

Nb

CoRuCo

Nb

Cu

Cu

M.A. Khasawneh, W.P. Pratt, and N.O. Birge, Phys. Rev. B 80, 020506(R) (2009)


)/exp( 1Fc xI 1 = 2.4 ± 0.1 nm

0 5 10 15 20 25

104

105

106

107

108

J c (A

/m2 )

dCo (nm)

1 = 3.0 nm (Robinson et al. found for dCo = 1 – 5 nm)

No oscillations of Ic: phase shifts cancel in two F layersBlanter & Hekking, PRB 69, 024525 (2004); Crouzy et al., PRB 75, 054503 (2007).

Nb

CoRuCo

Nb

Cu

Cu


0 5 10 15 20 25

104

105

106

107

108

J c (A

/m2 )

dCo (nm)

No sign of spin-triplet supercurrent!M.A. Khasawneh, W.P. Pratt, and N.O. Birge, Phys. Rev. B 80, 020506(R) (2009)

Nb

CoRuCo

Nb

Cu

Cu

Why don’t we see spin-triplet supercurrent in S/F/S Josephson junctions with Co/Ru/Co?

• Not enough non-collinear magnetization• Magnetic inhomogeneity on wrong length scale• Too much spin-flip scattering at Co/Ru interface

Measure spin-flip scattering at Co/Ru interface using GMR

Co domain structure

Neighboring domains have mostly anti-parallel magnetization

Not much non-collinear M

Domains are large ~ 3 m

Borchers et al., PRL 82, 2796 (1999).SEMPA = scanning electron microscopy

with polarization analysis

Why haven’t we seen spin-triplet correlations?

• PdNi– Spin memory length too short– Bad for propagation of triplet– Good for generation of triplet

• Co/Ru/Co– Not enough magnetic inhomogeneity– Bad for generation of triplet– Good for propagation of triplet

New Idea: combine best of two materials

Nb

Nb

Co

CoRu

X

X

Create triplet Propagate triplet

CuCu

CuCu

X = PdNi or CuNi alloy(Cu buffer layers magnetically isolate X from Co)

0 5 10 15 20 25 30

0.1

1

10

100

1000

DCo (nm)

I cRN (

nV)

Finally, the triplet appears!

with X = PdNi, dX = 4 nm

without X

Khaire, Khasawneh, Pratt, & Birge, Phys. Rev. Lett. 104, 137002 (2010)

Nb

X

CoRuCo

X

Nb

CuCu

CuCu

0 5 10 15 20 25 30

0.1

1

10

100

1000

DCo (nm)

I cRN (

nV)

Finally, the triplet appears!

with X = CuNi, dX = 3 nm

Fix DCo = 20 nm and vary dX


with X = PdNi, dX = 4 nm

without X

Nb

X

CoRuCo

X

Nb

CuCu

CuCu

0 2 4 6 8 10

0.1

1

10

100

dX (nm)

I cRN (

nV)

Control amplitude of triplet with dX

X = CuNi

X = PdNi


Nb

X

CoRuCo

X

Nb

CuCu

CuCu

0 10 20 30 40 50

0.1

1

10

100

1000

I CRN (

nV)

DCo (nm)

What happens with thicker Co layers?

poor Fraunhofer patterns –(Co/Ru/Co AF coupling not as effective)

Khasawneh, Khaire, Klose, Pratt, & Birge, Supercon. Sci. & Tech. 24, 024005 (2011).

B. Cooper pairs feel non-collinear M between X and Co layers.

Nb Cu X Cu Co

Mechanism for generating triplet

Nb Cu X Cu Co

A. Cooper pairs feel non-collinear M between X-layer domains

ss

Pure Ni works well for X layer (no need for inhomogeneous X layer)

0 2 4 6 8 10

0.1

1

10

100

I CR N

(nV)

dx (nm)

Ni

CuNi

PdNi

Khasawneh, Khaire, Klose, Pratt, & Birge, Supercon. Sci. & Tech. 24, 024005 (2011).

B. Cooper pairs feel non-collinear M between X and Co layers.

Nb Cu X Cu Co


Nb Cu X Cu Co

A. Cooper pairs feel non-collinear M between X-layer domains

ss

M. Houzet and A. I. Buzdin, PRB 76, 060504R 2007

F’ and F” are not required to be inhomogeneous

S N F’ N F N F N F” N S

Nb Cu X Cu Co Co Cu X Cu Nb

Ru

X = PdNi, CuNi, or Ni


Microscopic mechanism for triplet generation(from discussion with M. Eschrig)

S 210,0

z

S F1QxQx

QxiQx

ee

z

iQxiQx

sin0,1cos0,0

sincos2

12

1

S F1 F2

FF kkQ

1,10,1

1,1

0,12

1z

long-range triplet components

short-range triplet component

k

E

-kF-kF kF kF

M. Houzet and A. I. Buzdin, PRB 76, 060504R 2007

Triplet contribution to the critical current is observed only for dX (0.5–2.5) F.

Optimization of triplet generation

0 2 4 6 8 10

0.1

1

10

100

I CR N

(nV)

dx (nm)

Ni

PdNi

CuNi

CuNiF

PdNiF

NiF

CuNiex

PdNiex

Niex EEE

Log(Ic)

dF

singlet:

triplet:

homogeneous M

inhomogeneous M

Does triplet disappear after we magnetize the samples?(makes M more homogeneous)

Does triplet disappear after we magnetize the samples?

0 1000 2000 3000 4000

100

1000

I cRN

(nV)

Happlied (Oe)

X = Ni

dX = 1 nm

Why does Ic increase?

No!!!unpublished

data

Nb

Nb

Cu

Cu

CoCo

Cu

Cu

Ni

Ni

MNi MCo

S F1 F2M tilted by spin-triplets

maximized for= 90

H = 0 H largeH

H = 0

-

sin

cos

sin

0,1 z

Co/Ru/Co undergoes “spin-flop” transition

• Tunneling – Energy dependence of triplet pair correlations– Independent signature of odd-frequency triplet– No need for Ru layer

• Lateral geometry– Longer distances in F– Measure proximity effect & Josephson effect

Future Experiments

Nb

PdNi

Co

Nb

PdNi

Co

Normal metaloxide tunnel barrier

0.2 -- 1 m

Cu

Summary• New type of Fermion pairing occurs in S/F systems: odd-

frequency, spin-triplet, s-wave. – Triplet long-range penetration in F– S-wave insensitive to disorder

• S/F/S Josephson junctions with PdNi and Co: clear signature of spin-triplet supercurrent– Separately optimize generation and propagation

• Stay tuned for future results!

Nb

X

CoRuCo

X

Nb

CuCu

CuCu

For a general introduction to this subject, read “Spin-Polarized Supercurrents for Spintronics“ by Matthias Eschrig in Physics Today, January 2011:

See also the “News & Views” commentary by TeunKlapwijk, “Magnetic nanostructures: Supercurrentsin ferromagnets” in Nature Physics 6, 329 (2010).

References

Lecture III: Spin-triplet supercurrent in ferromagnetic Josephson junctionsSlide Number 2Prologue: Fermion pairingPrologue:��What we remember from quantum mechanicsPrologue:��What we remember from quantum mechanicsAllowed Cooper pair symmetriesProposal by Berezinskii (1974):Allowed Cooper pair symmetriesAllowed Cooper pair symmetriesAllowed Cooper pair symmetriesOutlineAndreev Reflection: N/S vs. F/SProximity effect: S/N vs. S/F Slide Number 14Slide Number 15Prediction: long-range spin-triplet pair correlations induced by noncollinear magnetizationFeatures of odd-frequency, spin-triplet �pair correlationsPossible observation of triplet:Our approach:�Systematic study of S/F/S junctions: Signature of spin-triplet:Slide Number 21Slide Number 22Slide Number 23MeasurementS/F/S junctions with a weak F: Pd88Ni12 alloySlide Number 26Slide Number 27Slide Number 28Why don’t we see spin-triplet supercurrent in S/F/S Josephson junctions with PdNi?How to measure the spin memory length using Giant Magnetoresistance (GMR)Dependence of GMR signal on dPdNiRaw GMR signalGMR signal vs. dPdNiFit to Valet-Fert theoryPd1-xNix magnetic characterizationAlternate “spoiler” spin valve geometryWhy don’t we see spin-triplet supercurrent in S/F/S Josephson junctions with PdNi?Aside: Characterization of Josephson Junctions by the Fraunhofer patternLarge-area Nb/Co/Nb junctionsTrick: achieve flux cancellation with Co/Ru/Co synthetic antiferromagnet Co/Ru/Co synthetic antiferromagnet restores Fraunhofer pattern!S/F/S junction with a strong F: CoS/F/S junction with a strong F: CoS/F/S junction with a strong F: CoWhy don’t we see spin-triplet supercurrent in S/F/S Josephson junctions with Co/Ru/Co?Co domain structureWhy haven’t we seen spin-triplet correlations?New Idea: combine best of two materialsFinally, the triplet appears!Finally, the triplet appears!Control amplitude of triplet with dXSlide Number 52Slide Number 53Pure Ni works well for X layer (no need for inhomogeneous X layer)Slide Number 55Slide Number 56Microscopic mechanism for triplet generation�(from discussion with M. Eschrig)Slide Number 58Slide Number 59Does triplet disappear after we magnetize the samples?Slide Number 61Future ExperimentsSummarySlide Number 64

lecture iii: spin-triplet supercurrent in ferromagnetic josephson...

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