Marco Aprili 1
CSNSM-CNRSBât.108 Université Paris-Sud
91405 ORSAYand
“Pôle Supraconductivité”ESPCI
10, rue Vauquelin75005 Paris
Ferromagnet/Superconductor hybrid systems, proximity effects
Outline
1. Inhomogeneous superconductivity : gain & price of S/F nanostructures
2. Macroscopic and microscopic measurements
3. Josephson coupling in S/F/S (better S/F/I/S)
4. Macroscopic Quantum-Mechanics : π-SQUIDs and π-rings
Below Tc the system condenses in amacroscopic number of Cooper pairs
CoherenceLength: ξο
ξocondensateΨ = iϕe oΨ
Order parameter
PhaseAmplitude
Superconductivity
Cooper pair
+
-+
- x
ψ
D-wave p=0 l=2 θ
Π-wave p?0 l=0
k+∆p -k+∆p
k -k
S-wave p=0 l=0
Cooper Pairs Order parameter
x
ψ
Quantum Mechanics
∆p θ = ∆p x
The Fulde-Ferrell-Larkin-Ovchinnikov state
∆p =
Eex
hvF
Superconductor Superconductor + Ferromagnet
-pF +pF -pF+∆p +pF+∆p
Exchange interactionSinglet state
Fulde and Ferrell PR 135, A550Larkin and Ovchinnikov Sov.Phys. JETP 20, 762
Never found, why ?
1. Sensitivity to disorder : +
-
scattering
<∆>Fermi = 0
2. Phase diagram :
Eex ˜ ∆
usually Eex ˜ 0.1-1 eV∆ ˜ 1 meV
Ferromagnet/Superconductor proximity effect
-pF +pF -pF+∆p +pF+∆p
FerromagnetSuperconductor
Ψ
dF
+
-
+
-
+
Question :
Where’s the gain ?
Why S/F hybrid structures rather thanbulk superconductors ?
Andreev Reflection
-pF
+pF
e-
Superconductor Normal Metal
+pF
e-
No
e-
h+
+pF-pF
e-e-
e-
h+
electron-hole excitation
+pF-pF
Cooper pair
Superconducting Correlation Propagation
S
e-
h+
+E
-E
No condensate ϕ(E,x) = Et/hPhase coherence is lost whenϕ(E,x) ˜ 1 ? ˜ h vF/E
N
e-
h+
+E+Eex
-E-Eex
S F
x ˜ h vF/Eex
As E<<Eex
= ξF
Coherent superposition of ψe and ψh
ψ = ψ e + ψh ∝ cos(E / ThE )
ψ e = e− iEt h × ψ 0 ( x )
ψ h = e iEt h × ψ 0 ( x )
ETh=x/hvF
E ˜ Eex
Answer
1. ξF does not depend on ∆.Superconducting correlations survive in F even if Eex>>∆
Therefore S/F does not require comparable energy scales !!!
2. Only phase coherence is needed.No pairing equation in F.
Therefore oscillations even in the dirty limit !!!
But...Spin must be a good Quantum Number
ψ = ψ e + ψh ∝ cos(E / ThE )ex
e-
h+
+E +Eex
-E-Eex
is lost if Spin-Orbit scattering
-Eex
+Eex
SO scatteringCalculations by Demler et al. PRB 55, 15174
1/τso = 0.9 Eex
1/τso = 0.5 Eex
1/τso = 0.0
Condition : τso vF>ξF
Therefore 1/τso < Eex
The price to pay: Nanostructures !
Eex ˜ 0.1-1 eVξF=hvF/Eex ξF ˜ 0.5-5 nm
ξN=hvF/KBT T ˜ 1 K ξN ˜ 1 µm
Reduced to 0.1-1 nmin the dirty limit
1. Deposition of thin films by e-gun and magnetron sputtering(thickness control down to 0.1 nm)
2. Materials : Nb (high Tc and Hc2, small coherence length)Ferromagnetic materials and alloys : Gd, CuNi and PdNi
Eex ˜ 0.01 eV ξF ˜ 10 nmhomogeneous thin films
NiNi
Indirect exchange
µ ˜ 2.4 µB per NiµNi = 0.6 µB
˜ 15 Å
Itinerant ferromagnetism
PdNi Hallρ = oR B + sR sM
Hallresisitivity
Normal
Rs ˜ ρ2
Anomalous
Ms
-30
-20
-10
0
10
20
30
ρ Hal
l/ρ2
800040000-4000-8000
H(G)
50Å T=1.5K
Ni=2.4%
Ni=5.5%
Ni=7.0%
(Orsay-group)
-150
-100
-50
0
50
100
150
ρ Hal
l/ρ2 (Ω
-1.c
m-1
)
-4000 -2000 0 2000 4000H (G)
Ni =12% 50 Å
T=1.5 K
Hc=1000 G
1.3
1.2
1.1
1.0
0.9
0.8
0.7
RH
all (
Ω)
120100806040200
T (K)
Curie’s Temperature
TCurie
Tc oscillations : Calculations
dM dS
S/F Multilayer
solving the Usadel eqs.
Radovic et al. PRB 44, 759 see also Buzdin et al. Sov. Phys. JETP 74, 124
Tc oscillations : measures
ξF=1.35 nm
BUT
Jiang et al. PRL 74, 314 see also: Strunk et al. PRB 49, 4053Aarts et al. PRB 44, 7745
other pair breaking mechanism ?dead layer ?
+
-
+0-state
π-state -
The superconducting Density of States
1.4
1.2
1.0
0.8
0.6
Ns(E
)
-3 -2 -1 0 1 2 3
Energy/ ∆ s
Eex>>∆S
Kontos, Ph.D Thesis (Orsay)
see also: Guoya Sun et al. PRB 65, 174508Buzdin PRB 62, 11377
TEM
S FI N
Nb Al
Substrate
SiPdNi
Planar Tunnel Junctions
Junction Area
I
V
1
2
A
B
High energy and amplituderesolution
∫Gn
G (E)NPdNi
NPdNi (EF)= [ ?f
?eV- ]
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0-4 -2 0 2 4
Energy(meV)
Nb=500ÅT=350mKTc=8.7K
fit BCS∆ = 1.42 meV
G Gn
BCS Density of States
without PdNi
GAC
VDC
junction
DC + AC
+
-
+
ξF ˜ 50 Å
F
1.010
1.005
1.000
0.995
0.990
0.985
No
rmal
ized
co
nd
uct
ance
4x10-3
20-2-4
Energy(eV)
T=350mK
Ni=10 %
75 Å
50 Å
H=100 Gauss
Tunneling Spectroscopy
Pd1-xNix x ˜ 10% Tc ˜ 100 K Eex ˜ 10 meV
Density of States at Zero Energy
+
1.005
1.000
0.995
0.990
0.985
0.980
0.975
N(0
)
543210
dF/ξF
-
TheoryRinterface ˜ 10-6 Ω
Kontos et al. PRL 86, 304 (2001)
Josephson Coupling
Macroscopically
I = Ic sinθ12?? ? g? ? ? ?? ? ? ? ? ?? ? ? ? ? ? ? ? ?
Current-phase relationship
+E+Eexe-
h+
-E-Eex
Cooper pair transfert
Microscopically
~ Ψ Oscillations
S1F S2
Josephson Coupling
-20
-10
0
10
20
I (m
A)
-3 -2 -1 0 1 2 3V (mV)
x10
SIS
SIFS
I-V characteristics
80
60
40
20
0
IcR
n(µ
V)
180160140120100806040
dF (Å)
experiment at 1.5K
theory
R Interface = 10 -6 Ω
ξF = 46 Å
S F S
I+
V+dF1 dF2
V-
I- Kontos et al. PRL 89, 137007 (2002)
I=Icsin∆θ
0-junction
I=-Icsin∆θ
π-junction
Temperature dependence
V. Ryazanov et al., PRL 86 2427 (2001)
IcRn ˜ 2nV
12
11
10
9
8
7
I c (
µΑ)
4.54.03.53.02.52.01.5
T (K)
IcRn ˜ 5µV
Kontos et al. PRL 89, 137007 (2002)
SFS
SFIS
In collaboration with W. Guichard, O. Bourgeois & P. Gandit, CRTBT-Grenoble
SQUIDIc
F F
Quantum Interference Devices
dF1 dF2
Resine mask
After depositionand lift-off
Linearity :IcL<< Φo
Diffraction
I=2Ic cos (πΦ/Φo+ϕ/2)
0
0
π
Guichard et al. PRL 90, 167001 (2003)
0
π
π
Sponteneous Supercurrents
Free energy: U φ,φext( ) =LI 2
2−
φ0
2πIc cos
2πφ0
φ + ϕ
magnetic term Josephson term
zero ring, φext=0 π ring, φext=0
ϕ=0 zero ringϕ=π π ring
φ=φ ext + LIπ ring
IcL/φ0>>1
Groundstate = +/- Φ0/2
+-
Question :
Can superconductivity be used to change the magnetic order ?
How nano-structures can help on that ?
Heterostructure
.... . . ..Fe < 1%
Nb60nm
Pd6nm
Tc=8.5K
1. Why proximity effect ?
We do not need similar energy scales as in bulk superconductors.∆=1 meV Eex=0.1-1 eV
2. Why dilute alloys ? d>ξF = 2-20nm
d
Idea : χPd is reduced byinduced superconductivity