Interplay of Magnetic and Superconducting Proximity effect in F/S hybrid structures Thierry Champel...
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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?