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

Thierry ChampelThierry Champel

Collaborators:

Tomas Löfwander

Matthias Eschrig

Institut für Theoretische Festkörperphysik

Grenoble 16/03/2006

PLANPLAN

S/F PROXIMITY EFFECTS/F PROXIMITY EFFECT

RESULTSRESULTS

Characteristic features

Motivation

S/F bilayer with a rotating exchange field

F/S/F trilayer with noncollinear moments

1/

2/

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

Study of triplet correlations within:

SUPERCONDUCTOR/FERROMAGNET HYBRID NANOSTRUCTURESSUPERCONDUCTOR/FERROMAGNET HYBRID NANOSTRUCTURES

Systems under study: FS

Singlet Cooper pairing

Zeeman splitting

CONTEXT: SPINTRONICS

Possibility for a new physics with interesting applications

S/F PROXIMITY EFFECTS/F PROXIMITY EFFECT

Proximity effect: Penetration ofPairing correlations into non-superconducting areas

In F: center of mass momentum of Cooper pair: 2q

Spatial modulation of the pair amplitude in F

if J=0

fS

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

leakage of pairs = influence on TC

change of sign = influence on jC in Josephson junctions

nanoscale

Some characteristic

features

S/F PROXIMITY EFFECT : SOME CHARACTERISTIC FEATURESS/F PROXIMITY EFFECT : SOME CHARACTERISTIC FEATURES

Tagirov, PRL 1999

Buzdin et al., EPL 1999

Nonmonotonic behavior of Tc(df)

Superconducting switch

Transparency

+

-

FS

dF

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

Th: Buzdin et al. (1991)

FS

dF

F

dFdS

or

Th:

S/F PROXIMITY EFFECT : SOME CHARACTERISTIC FEATURESS/F PROXIMITY EFFECT : SOME CHARACTERISTIC FEATURES

•Ryazanov et al, PRL (2001)• Kontos et al, PRL (2002)• Guichard et al, PRL (2003)• Bauer et al, PRL (2004)

junctions

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

From Ryazanov et al. (2005)Taken in Buzdin, RMP 77, 935 (2005)

F SS

2dF

Th: Buzdin et al. (1982)

Exp:

MOTIVATION : ROLE OF INHOMOGENEITY OF EXCHANGE FIELD?MOTIVATION : ROLE OF INHOMOGENEITY OF EXCHANGE FIELD?

Theoretical motivation

• S/F wire with a local inhomogeneity of J

• F/S/F trilayer with noncollinear F moments

Bergeret et al., PRL 2001

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?

Triplet correlations

S/F PROXIMITY EFFECT : THEORETICAL ASPECTSS/F PROXIMITY EFFECT : THEORETICAL ASPECTS

Quasi-classical approximation

METHODSMETHODS Quasi-classical equations of superconductivity for the Nambu-GorkovGreen functions

main difficulties:main difficulties:

System of coupled nonlinear differential eqs.Coupling with the self-consistent gap eq. Inhomogeneous superconductivityInhomogeneous superconductivity

+ consideration of the diffusive limit

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

Pair states

singlettriplet

Order parameter:

triplet vector

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)

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

Sup. Fer.

S=1

S=0

S=0, Sz=0

Sz=+1

Sz=-1Energy of pair states:

FS

Picture for a fixed exchange field

Singlet component:

Correlator:

Pauli principle:

Order parameter:

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

Triplet vector:

Symmetry Properties of triplet correlations

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

PECULIARITY OF THE DIFFUSIVE LIMIT

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

Spin structure of the Green function g

Normalization condition

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

local density of states

spin magnetization

• Spin-dependent local DOS• Spin magnetization

• Superconductivity dependent on moment orientation

Physical consequencesPhysical consequencesof the presence of of the presence of triplet correlations:triplet correlations:

TRIPLET CORRELATIONS IN S/F HYBRID STRUCTURESTRIPLET CORRELATIONS IN S/F HYBRID STRUCTURES

To resume:

Signatures at the quantitative level on physical quantities?

S/F bilayerwith spiral

magnetic order

EFFECT OF INHOMOGENEITY OF EXCHANGE FIELD: STUDY OF A S/F BILAYEREFFECT 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)

• Enhancement of Tc with Q

TC

EFFECT OF INHOMOGENEITY OF EXCHANGE FIELD : MAGNETIC SPIRAL ORDEREFFECT OF INHOMOGENEITY OF EXCHANGE FIELD : MAGNETIC SPIRAL ORDER

superconducting switch operated by controlling the domain state in F

jC

TC

Destruction of π phase by inhomogeneity

S/F/S junctions

unpublished (2006)

F/S/F trilayerwith noncollinear

moments

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

Spatial dependence of the induced magnetization

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

or

xF

FS

collinear moments

M

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

Spatial dependences of:

the induced local magnetizationthe pair correlations

(a)-(c): projections

(b)-(d): angles relative to z-axis

x

F FS

y

z

perpendicular moments

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

M

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

angle relative to z-axis for B

B applied in yz plane

norm. state

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

Integrated magnetization : screening effect

sup. state

x

F FS

y

z

Changes in torque between normal and superconducting states

F/S/F/S/F pentalayer

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

SWITCHING BETWEEN THE 0 AND SWITCHING BETWEEN THE 0 AND ππ STATES IN F-S-F-S-F PENTALAYERSSTATES IN F-S-F-S-F PENTALAYERS

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

switching region

π state

0 state

TC

CONCLUSIONCONCLUSION

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

• F/S/F trilayer

Superconducting switch controlled by domain state

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?