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