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
122121212121 ;,;;,; ttssrrFttssrrF
Fermions require:
F is odd in time:
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 3HeSr2RuO4
l=2 high-Tc X
= allowed if correlation function is odd under time-reversal (or odd in frequency)
Allowed Cooper pair symmetries
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)
Allowed Cooper pair symmetries
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)
S/F/S junctions with a weak F: Pd88Ni12 alloy
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)
S/F/S junctions with a weak F: Pd88Ni12 alloy
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!
S/F/S junctions with a weak F: Pd88Ni12 alloy
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)
S/F/S junction with a strong F: Co
)/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
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)
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
Khaire, Khasawneh, Pratt, & Birge, Phys. Rev. Lett. 104, 137002 (2010)
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
Khaire, Khasawneh, Pratt, & Birge, Phys. Rev. Lett. 104, 137002 (2010)
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
Mechanism for generating triplet
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
Mechanism for generating triplet
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