Josephson tunnel junctions with ferromagnetic interlayerJosephson tunnel junct ons w th ferromagnet c nterlayer
Seminar des Walther-Meissner-InstitutsSeminar des Walther-Meissner-InstitutsFriday, 01/19/2007
M WeidesM. WeidesInstitute for Electronic Materials, Institute for Solid State Research, Research Centre Juelich
d2 0 JJπ JJ
d
0-π JJ
1
d1
Cooperation withCooperation with
H. Kohlstedt and R. WaserI tit t f El t i M t i l I tit t f S lid St t R h R h C t J li hInstitute for Electronic Materials, Institute for Solid State Research, Research Centre Juelich
E. Goldobin, D. Doenitz, M. Kemmler, D. Kölle and R. KleinerUniversität Tübingen, Physikalisches Institut - Experimentalphysik II
A. Buzdin Institut Universitare de France and Condensed Matter Theory Group, CPMOH
University Bordeaux 1, UMR 5798, CNRS, F-33405 Talence Cedex, France
V. Oboznov and V.V. RyazanovInstitute for Solid State Physics, Chernogolovka, Russia
K. Madek, S. Beutner, G. Wild, Ch. Probst, A. Marx and R. GrossWalther-Meissner-Institut, Bayerische Akademie der Wissenschaften, Garching, Germany
2
OutlineOutline
i. Theory: Coupling of Josephson junctions ith f ti i t lwith ferromagnetic interlayer
ii Experiment:ii. Experiment:a) Planar 0, π SIFS Josephson junctionsb) St d (0 0 0 ) SIFS J hb) Stepped (0-0, 0-π, π-π) SIFS Josephson junctions
iii. Outlook
3
Coupling of superconducting wavefunctionsCoupling of superconducting wavefunctions
SIS-type junction|Ψ( )|x
|Ψ |1 |Ψ |2
S-wave superconductorCooper pairs e↑+e↓ | |1 | |2
Θ2Θ1
Cooper pairs e +eBosonic system
xsuperconductor superconductorweak linkPhase difference jj
First Josephson equation
4
SIS Josephson Tunnel JunctionsSIS Josephson Tunnel Junctions•High quality Nb/Al2O3/Nb junctions •Josephson penetration length
•Critical current density jc=0.004-4 kA/cm²
•Oxidation for 30 min in various p(O2)
10
10 )) 0.015 mbar, 4 kA/cm2
2
1
10
50 mbar
0.015 mbar4 kA/cm2
0.45 mbar2y
j c (kA
/cm
²
j (kA
/cm
²
kneeregion
x1x1000
x5
0.45 mbar, 720 A/cm2 50 mbar UV, 4.5 A/cm2
0 01
0.15
216 A/cm2720 A/cm2
UV light+50 mbarrren
t den
sity
nt d
ensi
ty
jcregion x5
1E-3
0.01
0
UV light 50 mbar4.5 A/cm2
criti
cal c
ur
curr
en
5
0.01 0.1 1 10 1000 1 2 3voltage (mV) O2 pressure (mbar)
Vg
Proximity effect in SN and SFProximity effect in SN and SFBudzin et al., JETP 35Demler et at., PRB 55
order parameter Ψ
/( ) Nx ξ−Ψ ΨRe{ (x)}Ψ ξN
0/( ) Nxex ξΨ = Ψ
xsuperconductor normal metalsuperconductor normal metal
EexRe{ (x)}Ψ ξF1
Eex: exchange energy,magnetization in plane
1 20
/ /( ) F Fx ixex eξ ξ− −Ψ = Ψx
Re{ (x)}Ψ0π
ξF1 magnetization in plane
osc 22 Fλ πξ=superconductor magnetic metalξF2
63d magnets: ξF2<1 nm diluted magnets: CuNi, PdNi, PdFe
ξF2
Oscillating order parameter Ψ in F-layerOscillating order parameter Ψ in F layerExchange interaction in FMe↑ and e↓ different densit of states
EδN
E
e↑ and e↓ : different density of states
(↑↓- ↓↑) Cooper pair aquires
Eex
EF
EF
(↑↓ ↓↑) Cooper pair aquiresfinite center of mass momentuminside magnet 2Eex k -qF k +qF
k(a) (b) kF2q=2Eex/vFℏ qF(a) (b) F
superconductor ferromagnet
Phase of the pair wave function
2q 2Eex/vFℏ
0
Δϕ= 2qxPhase of the pair wave function
k0
k0
-kF kF -k +qF k +qF
Demler et al., PRB 55 (1997)
7
Josephson junctions - Current-phase relationJosephson junctions Current phase relationsupercurrent IS energy EJ
I 2E0 JJ π JJ Ic 2EJ
EJϕ
0 JJ π JJ
-Ic
EJ-2π 2π-π πϕ
0-JJ (SFS) dF≪ ξF2
c
-π 2π-2π π
π-JJ (SFS) dF≈½ξF2
8
Determination of π coupling in SFS-JJsDetermination of π coupling in SFS JJs
Nb IJ=|Ic|sin(ϕ+π)=-|Ic|sin(ϕ)Ni60Cu40
Nb
NbdF
J | c| (ϕ ) | c| (ϕ)
IJ ∼ |Ψ|2
1.61.0
Nb d0-π= d0-π(ξF2), ξF2= ξF2(T)
1.0
1.2
1.4
0 6
0.8
I c [a.
U.]
I c/I c0
I c/I c0Ic(dF)0
Ic(H)Ic(T) 0-0 0-π
0.4
0.6
0.8
0 2
0.4
0.6
ππ
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0 1 2 3 4 50.0
0.2
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
0
dF T/Tc H [Φ
0]
9
Kontos et al., PRL 89 (2002) V. Ryazanov et al., PRL 86, (2001) Bauer et al., PRL 92 (2004)
Status in 2003: π coupled SFS/SIFS
Nb
Status in 2003: π coupled SFS/SIFS
Nb •High critical current• Thick Al2O3 barrier
Pd88Ni12
Al2O3NiCu
•High critical current•Low resistance
• jc(π)=10 mA/cm²• λJ=3.7 mm
NbV. Ryazanov et al., PRL 86 (2001)H. Sellier et al., PRB 68 (2003) T. Kontos et al., PRL 89 (2002)
Nb • A=1 mm², ( )
Wanted:
•Strongly underdamped (βc≫1) →Al2O3-layer•Small size →thin Al2O3•high IcR product in π state
10•Small junction to junction deviation
OutlineOutline
i. Theory: Coupling of Josephson junctions ith f ti i t lwith ferromagnetic interlayer
ii Experiment:ii. Experiment:a) Planar 0, π SIFS Josephson junctionsb) St d (0 0 0 ) SIFS J hb) Stepped (0-0, 0-π, π-π) SIFS Josephson junctions
iii. Outlook
11
Sputter machineSputter machineUnivex 450B LeyboldCl S
deposition byCluster System
p yAr-ion plasma in DC field
Momentum transfer fromMomentum transfer fromAr+ to target atom
Computer-controlled4-inch capable
12
Fabrication of junctionsFabrication of junctions(b) Ion beam etching(a) Multilayer deposition
NiCu 15 to 1 nm
Nb 40 nm
Al-Al O 5 nm2 3
Cu 2 nm
NiCu 15 to 1 nm
Nb 120 nm(d) Wiring deposition(c) Niobium anodization
--
++
13Weides et al., Physica C 437-438, 349 (2006)
Ni60Cu40 alloyNi60Cu40 alloy
Onset of ferromagnetism in NixCu1-x at x≈47%
Ryazanov: Ni53Cu47• kBT ≈ Eex
Ni l t i h FMSellier: Ni48Cu52• Ni cluster, inhomogeneous FM• strong Cooper pair breaking
Ni60Cu40
T 225 K age
(a.U
.)
5 nm Ni60Cu40T=10 K
• TC = 225 K• dead magnetic layer ≈ 1-3 nm• ρ (10 K) = 53 97 μΩ cm
-6 -4 -2 0 2 4 6s
Hal
l vol
ta
• ρNiCu(10 K) = 53.97 μΩ cm• matom = 0.15 μB
• Ms= 123 emu Anom
alou
14
Ms 123 emu-100 -80 -60 -40 -20 0 20 40 60 80 100
Magnetic field H (mT)
Improved SINFS junctionsImproved SINFS junctionsCu layer improves uniformity of NiCu
01234
(a)
mA)
SIFS dF=2 nm
0 2
0.3
-100 -80 -60 -40 -20 0 20 40 60 80 100
ent I
c (m
SIFS dF=4 nm
Al Al O
Nb
Ni60Cu40
1.2
-140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 140
0.2
al c
urre
(b)
Nb
Nb
Al-Al O2 3
0.6
0.8
1.0
criti
ca SINFS dF=4.7 nm
Al-Al O2 3
Cu
Ni60Cu40
-600 -400 -200 0 200 400 6000.0
0.2
0.4
(c)Nb
15Weides et al., Physica C 437-438, 349 (2006)
magnetic field (μT)
Low variation of parametersLow variation of parameters20
SIFS F-layer : 3 3 nm
10
15SIFS, F layer : 3.3 nm
Ic=14.30 mA δIc=2%R 26 97 mΩ δR 0 5%m
A)
5
16-600 -400 -200 0 200 400 600
Rn=26.97 mΩ δRn=0.5%
rren
t I (m
magnetic field ( T)
-5
0
10121416
bias
cur magnetic field (μT)
ent I
c (mA)
15
-10
468
10b
ritic
al c
urre
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6-20
-1502 cr
16Weides et al., Physica C 437-438, 349 (2006)
voltage (mV)
Thickness induced 0 to π transition101
SIFS sample @4.2K(mA)
Thickness induced 0 to π transition
100thin Al2O3 barrier
thick A l2O
3 barrier
urre
nt I c (
Ni60Cu40
NbdF
10-1 ξF1
= 0.78 nmξF2= 1.35 nmritic
al c
uNi60Cu40
Al2O3
dFCu
10-2dd ea d= 3.09 nm
0 coupling π coupling
cr
Nb
3.0 3 .5 4.0 4.5 5.0 5. 5 6.0 6.5 7.0 7.5 8.0
thickness of the F-layer dF (nm)
Ic(dF)∼(γB2)-1 e-dF/ξF1 |cos(-dF/ξF2)|damping phase modulationtransparency
F
17Weides et al., Appl. Phys. Lett. 89, 122511 (2006)
Temperature dependences of IVC in π stateTemperature dependences of IVC in π state600
14 19 KSIS at 4 2 K)
200
4000
A)
4.19 K3.15 K
2.61 K2.40 K
SIS at 4.2 K
curre
nt (m
A)0 -3 -2 -1 0 1 2 3
-1
400
(mA
) SIFS
curre
nt (μ
A
SIFS JJvoltage (mV)
2.11 K
-400
-200
0
200
ritic
al c
urre
nt
bias
c SIFS JJπ coupled
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6-600
-0.4 0.0 0.4cr
magnetic field (mT)
π JJ (dF =5.87 nm) @ 2.1 K:
voltage (mV)
18
jc=5 A/cm² βc=700 λJ=170 μm V=IcR≈400 μVWeides et al., Appl. Phys. Lett. 89, 122511 (2006)
Temperature induced 0 to π transition
400
500 π
μA)
Temperature induced 0 to π transition
1015
300
400
π
0
0curr
ent I
c (μ
510 π 0
dF= 5.11 nm 0 JJ
criti
cal
2.5
T [K] Vc=50nV
3.58 3.44 3.393 29
010
100 dF= 5.20 nm 0 or π JJ
dF= 5.87 nm π JJ
Cum
ber
met
er β
c
1.5
2.0
rren
t Ic (μ
A)
3.29 3.25 3.22 3.19 3.16 3.14 3.12 3.113 1
2.0 2.5 3.0 3.5 4.01M
cCpa
ra
temperature (K)
0.5
1.0
crit
ical
cur3.1
3.09 3.075 3.06 3.04π
19-200 -100 0 100 200
0.0
magnetic field (μT)
Weides et al., Appl. Phys. Lett. 89, 122511 (2006)
Macroscopic quantum tunneling on π coupled junctionMacroscopic quantum tunneling on π coupled junction
SIFS junctions @ 120 mK:j @•thermal to quantum regime transover•photon induced transitions between quantized energy levels
20Madek et al. submitted to PRL
OutlineOutline
i. Theory: Coupling of Josephson junctions ith f ti i t lwith ferromagnetic interlayer
ii Experiment:ii. Experiment:a) Planar 0, π SIFS Josephson junctionsb) St d (0 0 0 ) SIFS J hb) Stepped (0-0, 0-π, π-π) SIFS Josephson junctions
iii. Outlook
21
Fabrication of step in F-layerFabrication of step in F layerresist
SF6
ArNb
CuNi Cu0.6 0.4
Nbd2 Ni Cu0.6 0.4 d1
Nb
π 0ΔdF
Nb
CuAl-Al O2 3
(a) (b) (c)
0.4
0.6
0.8
-50
0
50
100
-0 .5
0. 0
0. 5
1. 0 JJ w ith d1
(shifted along I-axis)
JJ with d2
JJ with d1
JJ ith dbi
as cu
rrent
(mA)
bias
curre
nt (m
A)
Etched and non etched
0 2
0.0
0.2 -1000 -500 0 500 1000-100
-40 -20 0 20 40
-1 .0
curre
nt I c (
mA)
JJ w ith d2
voltage (μV) voltage (μV)
Etched and non-etchedplanar junctions
-0.6
-0.4
-0.2
T=4.2 Kcritic
al
0 coupled JJs without etching
dF=d2=5.05 nm after etching
dF=d1=4.75 nm
22Weides et al., J. Appl. Phys. (2007) [cond-mat/0612164]
-0.4 -0.2 0.0 0.2 0.4-0.8
magnetic field (mT)
SEM and AFM of stepped SIFS stacksSEM and AFM of stepped SIFS stacks
23Weides et al., J. Appl. Phys. (2007) [cond-mat/0612164]
0 π and 0-π JJs fabricated in single process
1
0, π and 0 π JJs fabricated in single process
1 SIFS junction with dF
SIFS junction with dF-Δd
F
mA
)nt
|Ic(d
F)| (m
0.1
π coupling0 couplingcal c
urre
n c
ritic
4.8 5.0 5.2 5.4 5.6 5.8
thickness of F-layer dF (nm)
24Weides et al., Phys. Rev. Lett. 97, 247001 (2006)
Stepped SIFS: 0-0 or 0-π JJs
3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
2 )Stepped SIFS: 0 0 or 0 π JJs
100ξF1=0.78 nmξ =1 35 nm SIFS JJ @ 4.2Kc (
A/cm
2
10
j (d )
jc(d
1) ξ
F2=1.35 nm
ensi
ty j c
1 stepped JJ:0-π phase and
stepped JJ:uniform phase (0-0)
jc(d2)
Δdurre
nt d
0.1
symmetric jc'sand tailored j
c's
ΔdF
ΔdF
0 coupling π couplingritic
al c
u
F
d2
d2 d1d1
p g π coupling
c
thickness of the F-layer d (nm)
25
thickness of the F layer dF
(nm)
Weides et al., J. Appl. Phys. (2007) [cond-mat/0612164]
0-0 JJ with tailored j and centered step in F-layer0 0 JJ with tailored jc and centered step in F layer
0.8
1.0
symmetric stepped JJj2/j
1
shifted by 10% along I-axis
I max
0.2
0.4
0.6
0 80.6
0.40.2
0.0
criti
cal c
urre
nt I c/I Simulated Ic(H) pattern
0 1 2 3 4 5 6 7 8 9 100.0
1.00.8c
magnetic f ield h
0.6
0.8calculated
d1=4.68 nm, d2=4.98 nm d1=4.68 nm, d2=4.92 nmd =4 72 nm d =4 92 nmA)
stepped JJ with different jc(dF)100x100 μm2
centered step in F-layermeasured
0.4
d1=4.72 nm, d2=4.92 nm
T=4.2 K
curre
nt I c (
mA measured
Measured Ic(H) pattern
0 0
0.2
criti
cal
26Weides et al., J. Appl. Phys. (2007) [cond-mat/0612164]
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.80.0
magnetic field (mT)
0-π coupled Josephson junctions0 π coupled Josephson junctionsNb/Al2O3/Nb with current injectorsYBCO-Nb ramp zigzags
π0
π0π 0
(a) (b)Goldobin et al., Phys. Rev. Lett. 92 (2004)
Hil k l N 422 (2003)Hilgenkamp et al., Nature 422 (2003)
SFS/SIFS-like structures
0 4
0.5
/I c0d2
0 π
0.2
0.3
0.4
I (d )criti
cal c
urre
nt I c/
273 4 5 6 7 80.0
0.1
d1
Ic(d2)
d2
Ic(d1)
F-layer thickness dF (nm)
d1Weides et al.,Phys. Rev. Lett. 97 (2006)
0-π JJs: fractional flux (Semifluxons)0 π JJs: fractional flux (Semifluxons)sin( ) ( ) ( ) ( )xx tt t x xxx h x xφ φ φ αφ γ θ− − = − + +Perturbed sine-Gordon equation with 0-π phase boundaryGoldobin et al., Phys. Rev. B 66 (2002)
2π
πθ=πθ=0
φ(x)
hase
μ(x
) fie
ld μ
x(x)
π
2π
θ=πθ=0Φ(x,t)=μ(x,t)+θ(x)
-4 -2 0 2 4
π
0
00
0
θ πθ 0
j ti di t (λ )
phas
e m
agne
tic p
hm
agne
tic f π
Φ=±½Φ0
FLAT PHASE STATE: Energetically unfavorable SEMIFLUXON: formed at boundary (pinned)
-4 -2 0 2 400 junction coordinate (λJ)m
π0 π0 0γ γ
28
Fractional flux in 0-π SIFS junctionFractional flux in 0 π SIFS junction200
A] T=4.0K 0 JJ
0 or π
0 π100
150
, I0-
πc
(H) [
μA π JJ 0-π JJ
0-π
0
50
0 c(H),
Iπ c(H),
jc(0)=jc(π)≈2 A/cm2150
200 T=2.65K
curre
nts
I0 c
λJ=260 μm
A=330x33 μm250
100
crit
ical
c
μ
-150 -100 -50 0 50 100 1500
magnetic field (μT)
29
g (μ )
Weides et al., Phys. Rev. Lett. 97, 247001 (2006)Effective length of 0-π JJ: ℓ≈1.3λJ
Magnetic field of spontaneous fractional fluxMagnetic field of spontaneous fractional flux1.5
"semifluxon" in JJsemif luxon in JJ
1.0
semifluxon in JJwith L=1.3λ
J
semif luxon in JJwith L→ ∞
j ( ) j ( )0
S
F
0.5 z
x
x
jc( )π jc( )0FS
0.0
d 1d 2
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-0.5
coordinate x/λ (norm units)coordinate x/λJ
(norm. units)
Short 0-π JJ: |Φ|= Φ0 ℓ2/8π
30
| | 0
Spontaneous flux in ground state: ±Φ=13%·Φ0/2Weides et al., Phys. Rev. Lett. 97, 247001 (2006)
OutlineOutline
i. Theory: Coupling of Josephson junctions ith f ti i t lwith ferromagnetic interlayer
ii Experiment:ii. Experiment:a) Planar 0, π SIFS Josephson junctionsb) St d (0 0 0 ) SIFS J hb) Stepped (0-0, 0-π, π-π) SIFS Josephson junctions
iii. Outlook
31
OutlookOutlook• Material Science: π SIFS junctions with F=Co, Fe, Ni,... possible? • Study of dynamics (spin waves & ac supercurrent)• Study of dynamics (spin waves & ac-supercurrent)• 0-π JJs in various geometries
Short to Long JJ limit, annular JJ, multiple 0-π steps ...g• Readout of fractional vortex by SQUID, LTSEM ...• Macroscopic quantum tunneling in π and 0-π JJs• Qubit based on π or 0-π JJs (flux/phase qubits)
"thanks for your0.4
0.6
0 coupling π coupling
t Ic (
mA
)
0 JJ π JJ 0-π JJthanks for your
attendance"4 5 5 0 5 5 6 0 6 5
0.0
0.2
d2d1
criti
cal c
urre
n
32
4.5 5.0 5.5 6.0 6.5
thickness dF (nm)
Etching of junction-SIMSEtching of junction SIMS
1000010000 Al
1000Ni
coun
t
100Nb
artic
le c
100CuPa
00:00 01:00 02:00 03:00 04:00 05:0010
33Etching time (min:sec)
Fabrication of wedge-shaped F-layerFabrication of wedge shaped F layer
Nb 40 nm 0 3 Ni60Cu40 sputter rate at 50 W/s)
NiCu 15 to 1 nm
Nb 40 nm
0.2
0.3 60 40 p
r-rat
e(n
m/
Al 4 nmAl O 1 nm2 3
0.1sput
ter
Nb 120 nm
0 20 40 60 80 1000.0
distance alongwedge(mm)4 inch, 100 mm
distance alongwedge(mm)
(a) SIFS cross section (b) NiCu sputter rate
34
SIFS junctions with FM in clean limitSIFS junctions with FM in clean limitF. Born et al. (cond-mat/0604277)similar reports by Robinson et al.Dirty limit: ℓ ≪ ξF1on SFS JJs (condmat/ 0606067)Clean limit: ℓ ≫ ξF1
Promising magnets:Promising magnets:Co, Ni, Fe, NiAl, CoFe etc.
0 630
35
300
350
)SFS33 Ni3Al
Nb/Al-Al2O3/Ni3Al/Nb (SIFS)Nb/Al-Al2O3/Cu/Ni3+δAl/Nb (SINFS)
0.2
0.4
0.6
20
25
30
200
250
300
dens
ity j c (A
/cm
2
tIc (
mA
)
3 5.87 nm 7.45 nm 8.74 nm
A=330*33 μm2
-900 -880 -860 -840 -820 -800 -780 -7600.0
10
15
100
150
criti
cal c
uren
t d
criti
cal c
uren
t
jc=100 A/cm2
λJ=36 μm
35-1000 -900 -800 -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900 10000
5
0
50
magnetic field (μT)
Possible applicationsPossible applications
π shifter in Rapid Single Flux Quantum (SFQ ) logics• π shifter in Rapid Single Flux Quantum (SFQ ) logics• Memory (readout and changing of the state using SFQ
logic)logic)• Qubit: semifluxon (or two) in the quantum limit
– advantages: like spin but big and pinned.– Coupling: no problem
• Study of fractional quantization, including “heavy” vortices, non-symmetric vortices
• Study of heavily degenerated frustrated system, Ising-like model
36