Leçon #3: Systèmes S/F

Norman Birge

Michigan State University

Résumé: Systèmes S/F

• L’histoire ancienne: Meservey & Tedrow • La réflection d’Andréev croisée • La réflection d’Andréev à l’interface S/F (en

présence de l’énergie d’échange) • L’éffet de proximite dans les systèmes S/F

• Tc des multicouches • Densité d’états • Jonctions Josephson: junctions “”

• Corrélations induit du type “spin-triplet” • Jonctions Josephson • Tc des multicouches

Spin-dependent tunneling: S/F Tedrow & Meservey, PRL 26, 192 (1971); Meservey & Tedrow, PRB 7, 318 (1973)

S/I/N tunnel junction Split quasiparticle density of states with B field

S/I/F tunnel junction with B field

Spin-dependent tunneling S/F Tedrow & Meservey, PRL 26, 192 (1971); Meservey & Tedrow, PRB 7, 318 (1973)

Spin imbalance in a superconductor Quay, Chevallier, Bena, Aprili, Nature Phys. 9, 84 (2014).

Crossed Andreev Reflection (CAR) Deutscher & Feinbert, Appl. Phys. Lett. 76, 487 (2000)

The reflected hole goes into a different wire! The two wires must touch S within a distance S

Experiments on Crossed Andreev Reflection (CAR) - 1 Beckmann, Weber & von Löhneysen, PRL 93, 197003 (2004).

Experiments on Crossed Andreev Reflection (CAR) - 2 Russo, Kroug, Klapwijk & Morpurgo, PRL 95, 1027002 (2005).

Experiments on Crossed Andreev Reflection (CAR) - 3 Hermann, Portier, Roche, Levi-Yeyati, Kontos & Strunk, PRL 104, 026801 (2010).

Andreev Reflection at an S/F interface and the superconducting proximity effect in F. Go to whiteboard!

Buzdin, Bulaevskii & Panyukov, JETP Lett. 35, 178 – 180 (1982). Demler, Arnold & Beasley, PRB 55, 15174 (1997)

k

E

-kF

-kF

kF

kF

Proximity effect: “leakage of Cooper pairs”

from S to F

FexFF vEQkk 2

ex

FF

E

D

ex

FF

E

vQ

2

1 ballistic

diffusive

ballistic

diffusive D = diffusion

constant

2Eex

Tk

vv

B

FFN

2

Tk

DD

B

NNN

2

S F

Compare with “normal metal

coherence length:

Pair correlations oscillate in F with

wavevector Q. Length scale of

oscillations is very short due to large Eex.

Proximity effect: S/N vs. S/F

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

nmfewE

D

ex

FF

~

NF

x

mfewTk

D

B

NN

2

How can we detect the oscillating correlation function?

How to detect the oscillating pair correlation function?

Jiang, Davidovic, Reich, Chien, PRL 74, 314 (1995).

1. Measure Tc of S/F bilayers as a function of dF

S F

dF

Problem: interpretation controversial due to magnetic dead layers.

How to detect the oscillating pair correlation function?

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

2. 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?

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

Ryazanov et al., PRL 86, 2427 (2001).

Weak F: Cu48Ni52 alloy, vary T

Kontos, Aprili … 89, 137007 (2002)

Weak F: Pd88Ni12, vary dF

0-state: Is = Ic sin(f2-f1) -state: Is = Ic sin(f2-f1+) S F S

dF

How to detect the oscillating pair correlation function?

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

Oboznov et al., PRL 96, 197003 (2006).

More 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 cR

N (

mV

)

0-state: Is = Ic sin(f2-f1) -state: Is = Ic sin(f2-f1+) S F S

dF

2001 Prediction: spin-triplet pair correlations

i) are long-ranged in F

ex

FS

FE

D

Tk

D

B

FT

F

2

T

F

S

F

Singlet Triplet

Bergeret, Volkov & Efetov, PRL 86, 4096 (2001); PRL 90, 117006 (2003)

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

S F

S F2 F1

k

E

-kF

-kF

kFkF

or

ii) can be induced by noncollinear magnetization

S/F/S Josephson junction can carry

spin-triplet supercurrent

Bergeret, Volkov & Efetov, PRL 86, 4096 (2001)

Houzet & Buzdin, PRB 76, 060504(R) (2007):

Non-collinear magnetizations convert pairs

from spin-singlet to spin-triplet dF

Log(Ic)

dF

singlet

triplet

Tk

D

B

FT

F

2

ex

FS

FE

D

Signature of spin-triplet supercurrent:

1. Sputter S/F/S

2. Pattern pillars with photolithography

Nb

Nb bottom contact

F

Au

Image reversal photoresist

Si Substrate

Sample Fabrication

10 – 40 m

Nb

Nb bottom contact

F

Au

Si Substrate

Si Ox

1. Sputter S/F/S

2. Pattern pillars with photolithography

3. Ion mill

4. Deposit SiOx

Sample Fabrication

10 – 40 m

Nb bottom contact

F

Au

Si Substrate

Si Ox

1. Sputter S/F/S

2. Pattern pillars with photolithography

3. Ion mill

4. Deposit SiOx

Nb top contact

1. Sputter S/F/S

2. Pattern pillars with photolithography

3. Ion mill

4. Deposit SiOx

5. Liftoff

6. Deposit top Nb contact

Sample Fabrication

10 – 40 m

Measurement

Low sample resistance ( 100 W)

Measure with SQUID-based

current comparator circuit

Ic critical current

-0.2 -0.1 0.0 0.1 0.2

-5

0

5

V (

nV

)

I (mA)

Ic -Ic

supercurrent

Measure at T = 4.2 K in “quick-dipper”

cryostat in helium storage dewar

I-V characteristic of overdamped

Josephson junction

Problem: Large-area S/F/S junctions with strong

ferromagnets distorted Fraunhofer patterns

-20 -10 0 10 200.00

0.02

0.04

0.06

I c (

mA

)

H (Oe)

dCo = 5 nm, 2R = 40 m

2R

2L + dF Hext

Random Fraunhofer pattern due

to complex domain configuration

Nb

Co

Nb

Solution: Co/Ru/Co synthetic antiferromagnet

cancels flux and 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 nm

w = 20 m

-20 -10 0 10 200.00

0.02

0.04

0.06

I c (

mA

)

H (Oe)

dCo = 5 nm

w = 40 m

0 5 10 15 20 25 30

0.1

1

10

100

1000

DCo

(nm)

I cR

N (

nV

)

How to generate spin-triplet supercurrent

with F, F = PdNi,

d = 4 nm

without F,F

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

Nb

F

Co

Ru

Co

F

Nb

Cu

Cu

Cu

Cu

Fix DCo = 20 nm and vary dF’

Control amplitude of triplet with dF’, dF’’

0 2 4 6 8 10

0.1

1

10

100

I C

RN

(n

V)

dF' (nm)

Ni

CuNi

PdNi

Khasawneh, Khaire, Klose, Pratt & NOB, Supercond. Sci. Technol. 24, 024005 (2011).

Nb

F’’

Co

Ru

Co

F’

Nb

Cu

Cu

Cu

Cu

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

S )

2

10,0

S F1

)

) ) ) )

) )QxQx

QxiQx

ee

zz

iQxiQx

sin0,1cos0,0

sincos2

1

2

1

S F1 F2

FF kkQ

) )

)

1,1

2

sin0,1cos1,1

2

sin0,1

z

long-range triplet

components in F2

short-range triplet

component

k

E

-kF

-kF

kF

kF

rotate basis:

1,1

1,1

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)ξF

Optimization of triplet generation

0 2 4 6 8 10

0.1

1

10

100

I CR

N (

nV

)dx (nm)

Ni

PdNi

CuNi

CuNi

F

PdNi

F

Ni

F

CuNi

ex

PdNi

ex

Ni

ex EEE

Fxe

/increase ~ sin2(Qx); decrease ~

Earlier 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 in 2010 by J. Aarts:

M. S. Anwar et al., Phys. Rev. B 82, 100501 (2010)

CrO2 is a “half metal”

k

E

EF

Spin-triplet supercurrents observed by others in 2010

1. Robinson et al., Science 329, 59 (2010)

2. Sprungmann et al., PRB 82, 060505 (2010)

Heusler alloy Cu2MnAl

Spin-triplet supercurrents observed by others in 2010

3. Anwar et al., PRB 82, 100501 (2010)

4. Wang et al., Nature Phys. 6, 389 (2010)

Log(Ic)

dF

singlet:

triplet:

homogeneous M

inhomogeneous M

First step toward control of supercurrent:

magnetize the samples (Expect Ic to drop by reducing non-collinear magnetization?)

Nb

F’’

Co

Ru

Co

F’

Nb

Cu

Cu

Cu

Cu

Ic increases!

0 1000 2000 3000 4000

100

1000

I cR

N (

nV

)

Happlied (Oe)

F = F = Ni

dNi = 1 nm

Why does Ic increase?

Klose et al., Phys.Rev. Lett. 108, 127002 (2012)

Magnetizing field

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

Spin-flop transition optimizes 90 angle between MCo and MNi

and aligns Ni magnetizations

Magnetic configuration confirmed at NIST by SEMPA (McMorran & Unguris) and

PNR (Ginley & Borchers); see Klose et al., Phys.Rev. Lett. 108, 127002 (2012)

Other probes of spin-triplet correlations:

Tc of S/F/F’ trilayers

Singh, Voltan, Lahabi, Aarts,

PRX 5, 021019 (2015).

Next step: Full control of spin-triplet supercurrent

0-junction 0-junction -junction

F

Cu

Cu

Co

Ru

Co

Cu

F Cu

F

Cu

Cu

Co

Ru

Co

Cu

F Cu

F

Cu

Cu

Co

Ru

Co

Cu

F Cu

Ic = 0

• Hard F ferromagnet in bottom layer maintains its magnetization.

• Soft F ferromagnetic top layer drives the state of the junction.

• Use shape anisotropy to help control F’’ magnetization.

• Requires single-domain magnet(s) e-beam lithography

Summary

• Experimental observation of long-range

supercurrent in S/F/S Josephson junctions:

– requires three F layers

– Possibility to control supercurrent with magnetic state

• New type of Fermion pairing occurs in S/F

systems: odd-frequency, spin-triplet, s-wave.

• Further reading: see article by Matthias Eschrig in

Physics Today, January 2011.

Collaborators MSU:

Trupti Khaire, Mazin Khasawneh, Caroline Klose, Reza Loloee, Kurt Boden,

Hamood Arham, Yixing Wang, Eric Gingrich, Simon Diesch, Bethany Niedzielski,

William Martinez, Joseph Glick, Alex Cramer, William P. Pratt, Jr.

NIST: Julie Borchers, John Unguris, Ben McMorran

For memory applications: Northrop Grumman and ASU

spring 2010 summer 2013

Postlude:

What we were taught in quantum mechanics

A convenient basis (for systems with translational and rotational symmetry):

) ) )21212211 ,,,;, ssrrsrsr

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

) )11222211 ,;,,;, srsrsrsr

Two possibilities:

) )2112 ,, rrrr SS

1. even l, and s=0 (singlet) ) )2112 ,, ssss AA

) )2112 ,, rrrr AA

2. odd l, and s=1 (triplet) ) )2112 ,, ssss SS

) ) )f ,, 21,21,

m

llnln YrrRrr

) )

2

11sS ) )

2

10sA

Allowed Cooper pair symmetries

s=0 s=1

l=0

(s-wave)

BCS X

l=1

(p-wave)

X superfluid 3He

Sr2RuO4

l=2

(d-wave)

high-Tc X

) )11222211 ,;,,;, srsrsrsr

Proposal by Berezinskii (1974):

What does this mean?

) )121212212121 ;,;;,; ttssrrFttssrrF

) )122121212121 ;,;;,; ttssrrFttssrrF

Fermions require:

If F is odd in time:

then F is even

under exchange of

space and spin:

) )211212212121 ;,;;,; ttssrrFttssrrF

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

Allowed Cooper pair symmetries

s=0 s=1

l=0 BCS X

l=1 X superfluid 3He

Sr2RuO4

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)

Allowed Cooper pair symmetries

s=0 s=1

l=0 BCS S/F

l=1 S/F superfluid 3He

Sr2RuO4

l=2 high-Tc S/F

This talk

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

Eschrig & Lofwander, Nature Phys. 4, 138 (2008).