Interplay of Magnetic and Superconducting Proximity effect in F/S hybrid structures
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Interplay of Magnetic and Superconducting Proximity effect in F/S hybrid structures. Thierry Champel. Institut f ü r Theoretische Festk ö rperphysik. Collaborators:. Tomas L ö fwander. Matthias Eschrig. Grenoble 16/03/2006. PLAN. S/F PROXIMITY EFFECT. Characteristic features. Motivation.

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Interplay of Magnetic and Superconducting Proximity effect in F/S hybrid structures

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Interplay of magnetic and superconducting proximity effect in f s hybrid structures

Interplay of Magnetic and Superconducting Proximity effect in F/S hybrid structures

Thierry Champel

Institut für Theoretische Festkörperphysik

Collaborators:

Tomas Löfwander

Matthias Eschrig

Grenoble 16/03/2006


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

PLAN

S/F PROXIMITY EFFECT

Characteristic features

Motivation

RESULTS

Study of triplet correlations within:

1/

S/F bilayer with a rotating exchange field

2/

F/S/F trilayer with noncollinear moments

3/

F/S/F/S/F pentalayer with noncollinear moments


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

SUPERCONDUCTOR/FERROMAGNET HYBRID NANOSTRUCTURES

CONTEXT: SPINTRONICS

S

F

Systems under study:

Singlet Cooper pairing

Zeeman splitting

Possibility for a new physics with interesting applications


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

S/F PROXIMITY EFFECT

Proximity effect: Penetration of

Pairing correlations into non-

superconducting areas

nanoscale

if J=0

In F: center of mass momentum

of Cooper pair: 2q

fS

Spatial modulation of the pair amplitude in F

change of sign = influence on jC in Josephson junctions

leakage of pairs = influence on TC

Dependence on impurities, interface quality, domain state of F, ...


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

Some characteristic features


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

S/F PROXIMITY EFFECT : SOME CHARACTERISTIC FEATURES

Nonmonotonic behavior of Tc(df)

S

F

Transparency

-

dF

+

Th:

Buzdin et al. (1991)

for recent th. developments see e.g. Fominov et al., PRB 2002

Superconducting switch

Tagirov, PRL 1999

Buzdin et al., EPL 1999

Th:

F

F

S

or

dS

dF

dF


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

S/F PROXIMITY EFFECT : SOME CHARACTERISTIC FEATURES

p-junctions

S

F

S

2dF

Th:

Buzdin et al. (1982)

  • Ryazanov et al, PRL (2001)

  • Kontos et al, PRL (2002)

  • Guichard et al, PRL (2003)

  • Bauer et al, PRL (2004)

Exp:

From Ryazanov et al. (2005)

Taken in Buzdin, RMP 77, 935 (2005)

Critical current Ic of Cu0.47Ni0.53 junctions as a function of the F layer thickness


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

MOTIVATION : ROLE OF INHOMOGENEITY OF EXCHANGE FIELD?

Theoretical motivation

  • S/F wire with a local inhomogeneity of J

Bergeret et al., PRL 2001

  • F/S/F trilayer with noncollinear F moments

Volkov et al., PRL 2003

As a result of inhomogeneity:

Production of triplet components which penetrate far in F

QUESTIONS:

Why do we have triplet correlations?

Under which conditions are long-range triplet components produced?

Signatures and consequences on physical quantities?


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

Triplet correlations


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

S/F PROXIMITY EFFECT : THEORETICAL ASPECTS

METHODS

Quasi-classical equations of superconductivity for the Nambu-Gorkov

Green functions

Quasi-classical approximation

+ consideration of the diffusive limit

main difficulties:

System of coupled nonlinear differential eqs.

Coupling with the self-consistent gap eq.

Inhomogeneous superconductivity


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

S/F PROXIMITY EFFECT : COEXISTENCE OF SINGLET/TRIPLET CORRELATIONS

Pair states

Order parameter:

triplet

triplet vector

singlet

Linearized Usadel equation within this basis

  • Coexistence of singlet/triplet correlations

  • Role of inhomogeneity of J

T. C. and M. Eschrig, PRB 71, 220506(R) (2005)

T. C. and M. Eschrig, PRB 72, 054523 (2005)


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

S/F PROXIMITY EFFECT : COEXISTENCE OF SINGLET/TRIPLET CORRELATIONS

Sup.

Fer.

Energy of pair states:

Sz=-1

S=1

Picture for a fixed exchange field

S=0, Sz=0

S=0

Sz=+1

S

F


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

S/F PROXIMITY EFFECT : COEXISTENCE OF SINGLET/TRIPLET CORRELATIONS

PECULIARITY OF THE DIFFUSIVE LIMIT

Symmetry Properties of triplet correlations

Correlator:

Pauli principle:

Singlet component:

Triplet vector:

So, ft dropped out of the gap equation. But it isn’t zero…

Order parameter:


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

S/F PROXIMITY EFFECT : LOCAL DENSITY OF STATES AND SPIN MAGNETIZATION

Spin structure of the Green function g

Normalization condition

localdensity of states

spin magnetization

T. C. and M. Eschrig, PRB 72, 054523 (2005)


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

TRIPLET CORRELATIONS IN S/F HYBRID STRUCTURES

To resume:

Physical consequences

of the presence of

triplet correlations:

  • Spin-dependent local DOS

  • Spin magnetization

  • Superconductivity dependent on moment orientation

Signatures at the quantitative level on physical quantities?


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

S/F bilayer

with spiral magnetic order


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

EFFECT OF INHOMOGENEITY OF EXCHANGE FIELD: STUDY OF A S/F BILAYER

Within this model, only short-range triplet correlations (SZ=0) are produced

T. C. and M. Eschrig, PRB 71, 220506(R) (2005)

Spatial dependence of pair correlations

Effect of inhomogeneity of J on Tc(df)

TC

  • Enhancement of Tc with Q


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

EFFECT OF INHOMOGENEITY OF EXCHANGE FIELD : MAGNETIC SPIRAL ORDER

TC

superconducting switch operated

by controlling the domain state in F

jC

S/F/S junctions

Destruction of π phase by inhomogeneity

unpublished (2006)


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

F/S/F trilayer

with noncollinear moments


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

STUDY OF A F/S/F TRILAYER : LOCAL INDUCED MAGNETIZATION

collinear moments

Spatial dependence of the

induced magnetization

or

S

M

F

F

x

T. Löfwander, T. C., et al., PRL 95, 187003 (2005)


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

STUDY OF A F/S/F TRILAYER : PAIR CORRELATIONS AND MAGNETIZATION

perpendicular moments

Spatial dependences of:

F

S

F

the pair correlations

the induced local magnetization

z

x

y

M

(a)-(c): projections

(b)-(d): angles relative

to z-axis

T. Löfwander, T. C., et al., PRL (2005)


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

STUDY OF A F/S/F TRILAYER : TOTAL INDUCED MAGNETIZATION AND TORQUE

Integrated magnetization : screening effect

F

F

S

z

x

y

B applied in yz plane

sup. state

Changes in torque between normal and superconducting states

norm. state

angle relative to z-axis for B

T. Löfwander, T. C., et al., PRL (2005)


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

F/S/F/S/F pentalayer


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

SWITCHING BETWEEN THE 0 AND πSTATES IN F-S-F-S-F PENTALAYERS

T. C. et al., unpublished (2006)

TC

Switching between the 0 and π states by controlling the moment orientations in F

π state

0 state

switching region


Interplay of magnetic and superconducting proximity effect in f s hybrid structures

CONCLUSION

The coexistence near the S/F interface of singlet components with triplet

components is the hallmark of the S/F proximity effect

Consequences:

  • Sensitivity of superconductivity on moment direction

  • Spin-dependent density of states

  • Spin magnetization

Concrete examples:

  • S/F bilayer within spiral order model

Superconducting switch controlled by domain state

  • F/S/F trilayer

Torque variation by cooling down the trilayer

  • F/S/F/S/F pentalayer

Switching between the 0 and π states by acting on the

moment orientation

Future directions:

Influence on transport properties?


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