VOLUME
86, NUMBER 11 PHYSICAL REVIEW LETTERS 12M
ARCH
2001
Coupling of Two Superconductors through a Ferromagnet: Evidence for a p Junction
V. V. Ryazanov,
1
V. A. Oboznov,
1
A. Yu. Rusanov,
1
A. V. Veretennikov,
1
A. A. Golubov,
2
and J. Aarts
3
1
Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, 142432, Russia
2
University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
3
Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
(
Received 24 August 2000)
We report measurements of the temperature dependence of the critical current, I
c
, in Josephson junc-
tions consisting of conventional superconducting banks of Nb and a weakly ferromagnetic interlayer of a
Cu
x
Ni
12x
alloy, with x around 0.5. With decreasing temperature I
c
generally increases, but for specific
thicknesses of the ferromagnetic interlayer, a maximum is found followed by a strong decrease down to
zero, after which I
c
rises again. Such a sharp cusp can be explained only by assuming that the junction
changes from a 0-phase state at high temperatures to a p phase state at low temperatures.
DOI: 10.1103/PhysRevLett.86.2427 PACS numbers: 74.50.+r, 74.80.Dm
Almost all of the presently known superconductors con-
tain conventional Cooper pairs, two electrons with oppo-
site spin and momentum (1k", 2k#). Such a system is
described by an isotropic excitation gap or an order pa-
rameter. The exceptions are found notably in high T
c
su-
perconductors, and in some organic superconductors and
heavy fermion systems, in which the exact pairing mecha-
nism is not yet fully understood. Still, it is surprising that
of many possible ways to form a pair, so few are actu-
ally realized. For instance, it is not imperative that the net
momentum of the pair is zero. It was predicted long ago
by Larkin and Ovchinnikov [1] and by Fulde and Ferrel
[2] that pairing still can occur when the electron energies
and momenta at the Fermi energy are different for the two
spin directions, for instance as the result of an exchange
field in magnetic superconductors. The “LOFF” state is
qualitatively different from the zero-momentum state: it
is spatially inhomogeneous and the order parameter con-
tains nodes where the phase changes by p. It was never
observed in bulk materials, but below we present evidence
that it can be induced in a weak ferromagnet (F) sand-
wiched between two superconductors (S). Such a SFS
junction can yield a phase shift of p between the super-
conducting banks, as was also predicted [3–5]. The p
state offers new ways for studying the coexistence of su-
perconductivity and magnetism and may also be important
for superconducting electronics, e.g., in quantum comput-
ing: several schemes for the necessary qubits (quantum
two-level systems) rely on phase shifts of p in a super-
conducting network [6,7].
The spatial variation of the superconducting order pa-
rameter in the ferromagnet arises as a response of the
Cooper pair to the energy difference between the two spin
directions. The electron with the energetically favorable
spin increases its momentum by Q ~ E
ex
兾y
F
, where E
ex
is the exchange energy and y
F
is the Fermi velocity, while
the other electron decreases its momentum by Q. Since
the original momentum of each electron can be positive
or negative, the total pair momentum inside the ferromag-
net is 2Q or 22Q. Combination of the two possibilities
leads to an oscillating order parameter c共z兲 in the junction
along the direction normal to the SF interfaces: c共z兲 ~
cos共2Qz兲 [8,9]. The same picture applies in the diffusive
limit. Now the oscillation is superimposed on the decay
of the order parameter due to pair breaking by impuri-
ties in the presence of the exchange field. In the regime
E
ex
¿ k
B
T, the decay length j
F1
is given by 共 ¯hD 兾E
ex
兲
1兾2
,
where D is the electron diffusion coefficient in the fer-
romagnet, while the oscillation period 2pj
F2
is equal
to 2p共 ¯hD兾E
ex
兲
1兾2
. Because of the oscillations, different
signs of the order parameter can occur at the two banks
when the F-layer thickness d
F
is of the order of half a pe-
riod. This is the so-called p-phase state, which competes
for existence with the ordinary 0-phase state. Figure 1a
shows a Ginzburg-Landau free-energy calculation consist-
ing of negative condensation energy and positive gradient
energy for either state in the F layer. The p phase is more
favorable in the range d
F
兾共2pj
F2
兲 between 0.4 and 0.8.
Figure 1b shows the behavior of c共z兲 in the F layer below
and above d
F,cr
. The crossover from the 0 phase to the p
phase state should manifest itself in an anomalous thick-
ness dependence both of the superconducting transition
temperature T
c
of the junction [10,11] and of the critical
current I
c
[4]. Experiments on T
c
共d
F
兲 have been per-
formed in systems such as Nb兾Gd [12], Nb兾Fe [13], V兾Fe
[14], and Pb兾Fe [15] but the results are not conclusive.
Especially, it was shown that also in bilayer systems (no
coupling) T
c
共d
F
兲 can behave in an anomalous fashion [15].
Our approach is to induce the crossover as a function
of temperature, not of thickness, and to use a unique sig-
nature of the junction I
c
: according to the Josephson re-
lation I
s
苷 I
c
sin共f兲, with f the phase difference across
the junction, biasing with f 苷 p should lead to a nega-
tive current response upon a small increase of the phase.
In other words, I
c
becomes negative. A change of state
from 0 to p will lead to a zero crossing of I
c
, and if only
the absolute value of the current is measured, a sharp cusp
will be observed. The condition for having the temperature
as a parameter is k
B
T 艐 E
ex
. The exchange field and the
temperature then are equally important and the behavior of
0031-9007兾01兾86(11)兾2427(4)$15.00 © 2001 The American Physical Society 2427
VOLUME
86, NUMBER 11 PHYSICAL REVIEW LETTERS 12M
ARCH
2001
FIG. 1. (a) Calculations of the Ginzburg-Landau (GL) free
energy in the F layer for the 0- and p-phase states. (b) The
spatial distribution of the order parameter in the F layer of the
SFS junction calculated for various ratios of d
F
兾共2pj
F2
兲: for
d
F
兾共2pj
F2
兲 苷 1兾共2p兲 and 1 the lowest energy corresponds to
the 0 phase, while for d
F
兾共2pj
F2
兲 苷 1兾2 and 3兾2 the p phase
is energetically favorable. Shown for comparison is the 0 phase
for d
F
兾共2pj
F2
兲 苷 1兾2 (dotted line), which has higher energy
than the p phase.
the order parameter should be written as
c共z兲 ~ e
2z兾j
F
~ e
2z兾j
F1
e
2iz兾j
F2
, (1)
with j
F
given by
j
F
苷
s
¯hD
2共pk
B
T 1 iE
ex
兲
, (2)
which yields for j
F1
and j
F2
:
j
F1,2
苷
s
¯hD
关E
2
ex
1 共pk
B
T兲
2
兴
1兾2
6 k
B
T
. (3)
This reverts to j
F1
苷 j
F2
for E
ex
¿ k
B
T as discussed
above, and encountered with classical ferromagnets (Fe,
Co, Ni) with E
ex
of the order of 1 eV. In the case k
B
T 艐
E
ex
the decay length j
F1
increases with decreasing tem-
perature whereas j
F2
decreases. This is how varying
the temperature provides the possibility to cross from a
0-phase to a p-phase state [16]. Moreover, a small value
for E
ex
ensures a large decay length j
F1
, making Josephson
SFS sandwiches with homogeneous and continuous ferro-
magnetic interlayers possible.
The junctions we studied consisted of superconduct-
ing Nb (S) banks with an interlayer of a ferromagnetic
Cu
12x
Ni
x
alloy (F). The onset of ferromagnetism is
around x 苷 0.44; above this concentration the Ni mag-
netic moment increases with about 0.01 m
B
兾at. % Ni,
which allows precise tuning of the magnetism. An insulat-
ing SiO layer was used between the top electrode and the
bottom SF sandwich. The window in this layer determined
the junction area of 50 3 50 mm
2
. A schematic sample
cross section is given in Fig. 2 (upper panel). Because of
the low junction resistance R
n
艐 10
25
V the transverse
transport characteristics were measured by a
SQUID pico-
voltmeter with a sensitivity of 10
211
V in the temperature
range of 1.2 to 9 K. Junctions were fabricated with x
between 0.40 and 0.57. Upon crossing to the ferromag-
netic regime the junction critical currents dropped sharply
but the I-V characteristics and magnetic field dependence
I
c
共H兲 (H in the plane of the junction) were still similar to
those for standard SNS junctions (N is a normal metal).
In Fig. 2 (middle panel) I-V data are shown for a junction
with x 苷 0.5, d
F
苷 14 nm at a temperature of 4.2 K.
The voltage onset at I
c
is sharp and well defined. Figure 2
(lower panel) shows that I
c
共H兲 for this junction yields
the classical “Fraunhofer” pattern. The oscillation period
is in reasonable agreement with the cross section of the
junction. Note that the central peak is at zero field, even
though the alloy is ferromagnetic. This signifies that on
average there is no change in the phase difference over
the junction along the different directions in the plane of
the junction, presumably due to a small-scale magnetic
domain structure of the magnetic layer with zero net mag-
netization. The peak was found shifted when the sample
was heated above T
c
(but below the ferromagnetic transi-
tion temperature, T
Curie
) and a small field briefly applied,
leading to a finite magnetization. Sometimes the peak
was found shifted in zero applied field, probably due to
flux trapping in the superconducting banks during cooling
down. This could be remedied by reheating and recooling.
The starting point for all measurements was a central peak
at zero field.
Our main result was obtained for junctions with
Cu
0.48
Ni
0.52
alloys. At this concentration T
Curie
is about
20 to 30 K. The resistivity of such alloys at 10 K is of the
order of 50 mV cm, indicating a mean free path of about
1 nm. The magnetization of the films is in-plane.
SQUID
magnetometry at 10 K on single alloy films of thickness
20 to 100 nm, and on Nb兾alloy兾Nb trilayers with similar
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VOLUME
86, NUMBER 11 PHYSICAL REVIEW LETTERS 12M
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2001
FIG. 2. (Top) Schematic cross section of the sample. (Center)
Typical I-V characteristic. (Bottom) Magnetic field dependence
of the critical current I
c
for the junction with Cu
0.5
Ni
0.5
and
d
F
苷 14 nm.
alloy thickness, showed a small hysteresis loop with a
coercive field of about 8 mT and a saturation moment of
0.07m
B
兾Ni atom. We found no significant difference be-
tween single layers and trilayers, from which we conclude
that also in the junctions the alloy layer is ferromagnetic
and that a supercurrent can be sustained even through a
ferromagnetic layer. Figure 3 shows I
c
共T兲 in zero mag-
netic field for two junctions with d
F
苷 22 nm [17]. The
curve marked (a) shows that I
c
increases with decreasing
temperature, goes through a maximum, returns to zero,
and rises again sharply. For all data points, it was ascer-
tained that the zero-field value was the maximum value for
I
c
. The curve marked (b) shows the same characteristic
behavior although the zero value for I
c
lies at a different
temperature. In this case I
c
共H兲 characteristics were mea-
sured at three different temperatures to ascertain that I
c
FIG. 3. Critical current I
c
as a function of temperature T for
two junctions with Cu
0.48
Ni
0.52
and d
F
苷 22 nm [17]. Inset: I
c
versus magnetic field H for the temperatures around the cross-
over to the p state as indicated on curve b: (1) T 苷 4.19 K,
(2) T 苷 3.45 K, (3) T 苷 2.61 K.
was determined correctly. The data, shown in the inset of
Fig. 3, prove that the I
c
共T兲 oscillations are not associated
with residual magnetic inductance changes which would
change the position of the central peak. It is important to
realize that the phase difference in zero applied field is
uniform in the plane of the junction, either 0 or p. The
Fraunhofer pattern will not shift when the phase turns from
0top, but the zero-field I
c
goes from positive to negative.
In a current-driven experiment, this leads to the sharp cusp
observed in I
c
共T兲. The p state can also be demonstrated
by the thickness dependence of the effect. Shown in
Fig. 4a is a series of measurements for junctions of differ-
ent thicknesses in the range 23 to 27 nm. At 23 nm only
positive curvature is visible, an inflection point is observed
for 25 nm, a maximum for 26 nm, and the full cusp now
at 27 nm. Figure 4b shows a set of calculations based on
the formalism of the quasiclassical Usadel equations [18],
with reasonable parameters for E
ex
and d
F
兾j
ⴱ
, where
j
ⴱ
苷 关 ¯hD 兾共2pk
B
T
c
兲兴
1兾2
. They qualitatively demonstrate
how the crossover moves into the measurement window
upon increasing the F-layer thickness. Quantitatively, the
thickness dependence in the calculations is much weaker
than in the experiments. Parameters such as the spin flip
scattering length probably also play a role. Still, the ap-
pearance of the crossover is mimicked correctly. If we
estimate it around d
F
兾2pj
F2
艐 0.4
0.5, it follows that
j
F2
艐 10 nm, as expected for the low magnetic moment
and justifying the assumption of dirty limit conditions.
A final remark concerns qualitative and quantitative re-
producibility. Qualitatively, the cusps can be observed for
certain thickness intervals in all sample batches with fer-
romagnetic layers which are presently fabricated, both for
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86, NUMBER 11 PHYSICAL REVIEW LETTERS 12M
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2001
FIG. 4. (a) Critical current I
c
as a function of temperature
for Cu
0.48
Ni
0.52
junctions with different F-layer thicknesses be-
tween 23 and 27 nm as indicated. (b) Model calculations of the
temperature dependence of the critical current in a SFS junc-
tion for E
ex
苷 0.8pT
c
and various ratios of d
F
兾2pj
ⴱ
, where
j
ⴱ
苷
p
¯hD兾共2pk
B
T
c
兲.
concentrations of 52 at. % Ni (with T
Curie
about 20– 30 K)
and 57 at. % Ni (with T
Curie
around 100 K). Moreover, for
higher Ni concentration the crossovers are at lower thick-
ness, reflecting the decrease in j
F1,F2
. Quantitatively, there
are still variations in the values of thickness interval and
crossover temperatures, and in the magnitude of the criti-
cal current for different batches, even with the same nomi-
nal F-layer content. Typical batch-to-batch variations are
demonstrated in the differences between Figs. 3 and 4. We
believe this is due to small variations in the magnetic prop-
erties of the F layers. In single films, T
Curie
shows a spread
of about 10 K; the weak magnetism is apparently sensitive
to the details of the preparation procedure.
We thank M. Feigelman for helpful discussion and ad-
vice, and N. S. Stepakov for assistance during the experi-
ment. This work was supported by Grant No. 047-005-001
from the Netherlands Organization for Scientific Research
(NWO), INTAS-RFBR Grant No. N11459 and RFBR
Grant No. N98-02-17045.
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[17] It was actually the same junction, but removed after the first
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2430
![FIG. 3. Critical current Ic as a function of temperature T for two junctions with Cu0.48Ni0.52 and dF 22 nm [17]. Inset: Ic versus magnetic field H for the temperatures around the crossover to the p state as indicated on curve b: (1) T 4.19 K, (2) T 3.45 K, (3) T 2.61 K.](/figures/fig-3-critical-current-ic-as-a-function-of-temperature-t-for-3e5nraz1.webp)
