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
Thierry Champel
Institut für Theoretische Festkörperphysik
Collaborators:
Tomas Löfwander
Matthias Eschrig
Grenoble 16/03/2006
PLAN in F/S hybrid structures
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
SUPERCONDUCTOR/FERROMAGNET HYBRID NANOSTRUCTURES in F/S hybrid structures
CONTEXT: SPINTRONICS
S
F
Systems under study:
Singlet Cooper pairing
Zeeman splitting
Possibility for a new physics with interesting applications
S/F PROXIMITY EFFECT in F/S hybrid structures
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, ...
Some characteristic features in F/S hybrid structures
S/F PROXIMITY EFFECT : SOME CHARACTERISTIC FEATURES in F/S hybrid structures
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
S/F PROXIMITY EFFECT : SOME CHARACTERISTIC FEATURES in F/S hybrid structures
pjunctions
S
F
S
2dF
Th:
Buzdin et al. (1982)
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
MOTIVATION : ROLE OF INHOMOGENEITY OF EXCHANGE FIELD? in F/S hybrid structures
Theoretical motivation
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 longrange triplet components produced?
Signatures and consequences on physical quantities?
Triplet correlations in F/S hybrid structures
S/F PROXIMITY EFFECT : THEORETICAL ASPECTS in F/S hybrid structures
METHODS
Quasiclassical equations of superconductivity for the NambuGorkov
Green functions
Quasiclassical approximation
+ consideration of the diffusive limit
main difficulties:
System of coupled nonlinear differential eqs.
Coupling with the selfconsistent gap eq.
Inhomogeneous superconductivity
S/F PROXIMITY EFFECT : COEXISTENCE OF SINGLET/TRIPLET CORRELATIONS
Pair states
Order parameter:
triplet
triplet vector
singlet
Linearized Usadel equation within this basis
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 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
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:
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)
TRIPLET CORRELATIONS IN S/F HYBRID STRUCTURES MAGNETIZATION
To resume:
Physical consequences
of the presence of
triplet correlations:
Signatures at the quantitative level on physical quantities?
S/F bilayer MAGNETIZATION
with spiral magnetic order
EFFECT OF INHOMOGENEITY OF EXCHANGE FIELD: STUDY OF A S/F BILAYER
Within this model, only shortrange 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
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)
F/S/F trilayer ORDER
with noncollinear moments
STUDY OF A F/S/F TRILAYER : LOCAL INDUCED MAGNETIZATION ORDER
collinear moments
Spatial dependence of the
induced magnetization
or
S
M
F
F
x
T. Löfwander, T. C., et al., PRL 95, 187003 (2005)
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 zaxis
T. Löfwander, T. C., et al., PRL (2005)
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 zaxis for B
T. Löfwander, T. C., et al., PRL (2005)
F/S/F/S/F pentalayer TORQUE
SWITCHING BETWEEN THE 0 AND TORQUEπSTATES IN FSFSF 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
CONCLUSION TORQUE
The coexistence near the S/F interface of singlet components with triplet
components is the hallmark of the S/F proximity effect
Consequences:
Concrete examples:
Superconducting switch controlled by domain state
Torque variation by cooling down the trilayer
Switching between the 0 and π states by acting on the
moment orientation
Future directions:
Influence on transport properties?