Ferromagnet/Superconductor hybrid systems, proximity effects Marco - - PowerPoint PPT Presentation
Ferromagnet/Superconductor hybrid systems, proximity effects Marco Aprili 1 CSNSM-CNRS Bt.108 Universit Paris-Sud 91405 ORSAY and Ple Supraconductivit ESPCI 10, rue Vauquelin 75005 Paris Outline 1. Inhomogeneous
Marco Aprili 1
CSNSM-CNRS Bât.108 Université Paris-Sud 91405 ORSAY and “Pôle Supraconductivité” ESPCI 10, rue Vauquelin 75005 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 a macroscopic number of Cooper pairs Coherence Length: ξο ξo
condensate Ψ
= iϕ
e
Order parameter
Phase Amplitude Superconductivity
Cooper pair
+
ψ D-wave p=0 l=2 θ Π-wave p?0 l=0 k+∆p
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+∆p
Exchange interaction
Singlet state
Fulde and Ferrell PR 135, A550 Larkin and Ovchinnikov Sov.Phys. JETP 20, 762
Never found, why ?
+
<∆>Fermi = 0
Eex ˜ ∆
usually Eex ˜ 0.1-1 eV ∆ ˜ 1 meV
Ferromagnet/Superconductor proximity effect
+pF
+pF+∆p Ferromagnet Superconductor
Ψ dF
+
Question : Where’s the gain ? Why S/F hybrid structures rather than bulk superconductors ?
Andreev Reflection
+pF
e-
Superconductor Normal Metal +pF
e- No e- h+
+pF
e- e- e- h+
electron-hole excitation +pF
Cooper pair
Superconducting Correlation Propagation S
e- h+ +E
No condensate ϕ(E,x) = Et/h Phase coherence is lost when ϕ(E,x) ˜ 1 ? ˜ h vF/E
N
e- h+ +E+Eex
S F
x ˜ h vF/Eex As E<<Eex = ξF Coherent superposition of ψe and ψh
ψ = ψe + ψh ∝ cos(E /
Th
E
)
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 = ψe + ψh ∝ cos(E /
Th
E
)
ex
e- h+
+E +Eex
is lost if Spin-Orbit scattering
+Eex
SO scattering
Calculations 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 eV ξF=hvF/Eex ξF ˜ 0.5-5 nm ξN=hvF/KBT T ˜ 1 K ξN ˜ 1 µm Reduced to 0.1-1 nm in 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 nm homogeneous thin films
Ni Ni Indirect exchange
µ ˜ 2.4 µB per Ni µNi = 0.6 µB
˜ 15 Å
Itinerant ferromagnetism
PdNi
Hall ρ
=
s R s M
Hall resisitivity Normal Rs ˜ ρ2 Anomalous
Ms
10 20 30
ρHall/ρ
2
8000 4000
H(G)
50Å
T=1.5K Ni=2.4% Ni=5.5% Ni=7.0%
(Orsay-group)
50 100 150
ρHall/ρ2(Ω-1 .cm -1 )
2000 4000
H (G)
Ni =12% 50 Å T=1.5 K H
c=1000 G
1.3 1.2 1.1 1.0 0.9 0.8 0.7
RHall ( Ω)
120 100 80 60 40 20
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, 4053 Aarts et al. PRB 44, 7745
dead layer ?
+
0-state π-state
1.4 1.2 1.0 0.8 0.6
Ns(E)
1 2 3
Energy/ ∆ s
Eex>>∆S Kontos, Ph.D Thesis (Orsay) see also: Guoya Sun et al. PRB 65, 174508 Buzdin PRB 62, 11377
TEM S FI N Nb Al
Substrate
Si
PdNi
Planar Tunnel Junctions
Junction Area
I V 1 2 A B
High energy and amplitude resolution
Gn G (E) NPdNi NPdNi (EF)
=
[
?f ?eV
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
2 4
Energy(meV) Nb=500Å T=350mK Tc=8.7K
fit BCS ∆ = 1.42 meV
G G
n
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
Normalized conductance
4x10
2
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) 5 4 3 2 1 dF/ξF
Rinterface ˜ 10-6 Ω
Kontos et al. PRL 86, 304 (2001)
Josephson Coupling
Macroscopically
I = Ic sinθ12? ? g? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Current-phase relationship
+E+Eex e- h+
Cooper pair transfert Microscopically
~ Ψ Oscillations S1 F S2
Josephson Coupling
10 20
I (mA)
1 2 3
V (mV)
x10
SIS SIFS
I-V characteristics
80 60 40 20
IcRn(µV)
180 160 140 120 100 80 60 40
dF (Å) experiment at 1.5K theory R
Interface = 10
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
IcRn ˜ 2nV
12 11 10 9 8 7
I c ( µΑ)
4.5 4.0 3.5 3.0 2.5 2.0 1.5
T (K)
IcRn ˜ 5µV
Kontos et al. PRL 89, 137007 (2002)
SFS SFIS
In collaboration with W. Guichard, O. Bourgeois & P. Gandit, CRTBT-Grenoble
SQUID Ic F F Quantum Interference Devices dF1 dF2
Resine mask After deposition and lift-off
Linearity :IcL<< Φo Diffraction I=2Ic cos (πΦ/Φo+ϕ/2) π
Guichard et al. PRL 90, 167001 (2003)
π π
Sponteneous Supercurrents
Free energy:
U φ,φext
( ) = LI 2
2 − φ0 2π Ic cos 2π φ0 φ + ϕ
magnetic term Josephson term
zero ring, φext=0 π ring, φext=0 ϕ=0 zero ring ϕ=π π ring
φ=φext +LI
π 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% Nb
60nm
Pd
6nm
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
d
Idea : χPd is reduced by induced superconductivity