Nonuniform superconductivity in superconductorferromagnet nanostructures

1
Non-uniform superconductivity in
superconductor/ferromagnet nanostructures

• A. Buzdin
• Institut Universitaire de France, Paris
• and Condensed Matter Theory Group, University of
  Bordeaux

in collaboration with M. Daumens, J. Cayssol, S.
Tollis University of Bordeaux A. Koshelev,
Argonne National Laboratory
2
Antagonism of magnetism (ferromagnetism) and
superconductivity

• Orbital effect (Lorentz force)

B
p
FL
FL
-p

• Paramagnetic effect (singlet pair)

µBH?Tc
Sz1/2
Sz-1/2
3
Superconducting order parameter behavior in
ferromagnet

• Standard Ginzburg-Landau functional

The minimum energy corresponds to ?const
The coefficients of GL functional are functions
of internal exchange field!
Modified Ginzburg-Landau functional
The non-uniform state ?exp(iqr) will correspond
to minimum energy and higher transition
temperature
4
F
q
q0
?exp(iqr) - Fulde-Ferrell-Larkin-Ovchinnikov
state (1964)

• Proximity effect in ferromagnet ?

In the usual case (normal metal)
5
In ferromagnet ( in presence of exchange field)
the equation for superconducting order parameter
is different
Its solution corresponds to the order parameter
which decays with oscillations!
?exp-(q1 iq2 )x
?
Order parameter changes its sign!
x
6
Remarkable effects come from the possible shift
of sign of the wave function in the ferromagnet,
allowing the possibility of a  p-coupling 
between the two superconductors (p-phase
difference instead of the usual zero-phase
difference)
? phase  
 0 phase
F
S
S/F bilayer
7
The oscillations of the critical temperature as a
function of the thickness of the ferromagnetic
layer in S/F multilayers has been predicted by
Buzdin and Kuprianov, JETPL, 1990 and observed
on experiment by Jiang et al. PRL, 1995, in
Nb/Gd multilayers
8
S-F-S Josephson junction in the clean limit
(Buzdin, Bulaevskii and Panjukov, JETP Lett. 81)
Damping oscillating dependence of the critical
current Ic as the function of the parameter ?hdF
/vF has been predicted. h- exchange field in the
ferromagnet, dF - its thickness
S
S
F
Ic
?
9
The oscillations of the critical current as a
function of temperature (for different thickness
of the ferromagnet) in S/F/S trilayers have been
observed on experiment by Ryazanov et al 2000 PRL
F
and as a function of a ferromagnetic
layer thickness by Kontos et al 2002 PRL
10
Critical current density vs. F-layer thickness
(Ryazanov et al. 2005)
IcIc0exp(-dF/?F1) cos (dF /?F2) sin (dF /?F2)
dFgtgt ?F1
?F2 gt?F1
dF,?1 (3/4)??F2(3/8)?ex
0-state
?-state
dF,?2 (7/4)??F2(7/8)?ex
0
Nb-Cu0.47Ni0.53-Nb
0-state
?-state
IIcsin?

IIcsin(? ?) - Icsin(?)
11
In the clean limit (h?gtgt1), we find oscillations
of period vf/h, oscillating like sin(x)/x2
Density of states 
T/Tc variation
12
Density of states measured by Kontos et al (PRL
2001) on Nb/PdNi bilayers
13
Atomic layer S-F systems
(Andreev et al, PRB 1991, Houzet et al, PRB 2001,
Europhys. Lett. 2002)
Magnetic layered superconductors like RuSr2GdCu2O8
F
exchange field h
BCS coupling
 0 
S
F
 p 
S
t
F
 0 
S
Also even for the quite small exchange field
(hgtTc) the p-phase must appear.
14
Hamiltonian of the system
BCS coupling
Exchange field
It is possible to obtain the exact solution of
this model and to find all Green functions.
15
T/Tco
1
0-phase
p-phase
h/Tco
2
The limit tltltTco
Ic
p-phase
0-phase
h/Tco
16
Superconducting multilayered systems
(Buzdin, Cayssol and Tollis, to be published, PRL
2005 )
layered superconductors with a structure like
high-Tc
Zeeman effect, i.e. the exchange field µBH
BCS coupling
 0 
S
t1
 p 
S
t2ltltt1
BCS coupling
 0 
S
t1
 p 
S
At low temperature the paramagnetic limit may be
strongly exceed µBHt1. p-phase with FFLO
modulation in plane.
17
The mechanism of the p -junction realization due
to the tunneling through thin ferromagnetic
layer(Buzdin, 2003)
d/2
-d/2
The large and small
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At T0, and ?Bgtgth/Tc
F(x)
19

• How the transition from 0- to p state occurs?

J(f)Icsinf Icgt0 in the 0- state and
Iclt0 in the p state
J(f)I1sinf I2sin2f
Energy E(f)(F0/2pc)-I1cosf (I2/2)sin2f
E
I2gt0
IcI2
f
p
0
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J(f)I2sin2f
The realization of the equilibrium phase
difference 0ltf0ltp
I2lt0
E
f
p
0
21
Grain boundaries in YBaCuO

• (Manhnhart, van-Harlingen et al. 1995-1996)

YBaCuO-Nb Josephson junctions of zig-zag geometry
(Hilgenkamp, Smilde et al. 2002)
Possibility to fabricate different alternating 0-
and p- junctions
S
YBaCuO
0
F
p
S
0
Nb
p
0
Arbitrary equilibrium phase difference f-
junction (Buzdin, Koshelev, 2003)
Nb
p
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• We will study the properties of long Josephson
  junctions with lengths
• d0 of 0-junctions and dp of p-junctions in the
  limit d0 , dp ltlt?J,
• ?J is the Josephson length of individual junction
  (for simplicity we assume that it is the same for
  0- and p-junctions)

f(x)
p
p
p
0
0
0
dp
d0
The energy per period of our system is
x is the coordinate along the zig-zag boundary
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The current-phase relation for f - junction
The current-phase relation is quite peculiar, the
current has two maxima and two minima at
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New kinds of solitons in f - junctions
Besides 2p degeneracy, there is f0 degeneracy!
New solitons - f0 ?f0 or f0 ? 2p -f0,
The flux of the first type of solitons is F0(f0
/p).
The flux of the second type of solitons is
F0((p-f0) /p).
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Conclusions

• The p-junction realization in S/F/S structures is
  quite a general phenomenon, and it exists even
  for thin F-layers (dlt?f), in the case of low
  interface transparency.
• New non-uniform superconducting phases in
  superconducting layered structures with
  alternating electron transfer integrals
• Transition to the f- junction state can be
  observed by decreasing the temperature from Tc.

For review see - A. Buzdin, Rev. Mod. Phys.
(July 2005)