Gross R., Sidorenko A., Tagirov L. Nanoscale Devices

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Depairing Currents in Bilayers of Nb/Pd

A. Yu. Rusanov

, J. Aarts

, M. Aprili

Kamerlingh Onnes Laboratory, Leiden University, the Netherlands

Univ Paris 11, CSNSM, CNRS, Orsay, France

Abstract: In superconductor/ferromagnet (S/F) hybrids the order parameter

induced in the F-layer due to the proximity effect is spatially

inhomogeneous. This could result in the nonmonotonic behavior of

the critical temperature T

and the depairing current density J

as a

function of the thickness of the ferromagnet d

. Specifically T

)

and J

) may demonstrate a minimum around λ

/4, where λ

the period of the spatial oscillation of the order parameter Ψ(x) in

the F-layer. We experimentally studied the superconducting

properties of Nb/Pd

0.89

0.11

bilayers structured in 15 µm long strips

of different width. Close to 1/4 of the period of Ψ(x), J

) shows a

minimum, in contrast to the behavior of T

) where a minimum is

absent. We argue that this difference is caused by the higher

sensitivity of the depairing current to the order parameter changes in

comparison with T

Keywords: proximity

effect, SF hybrids, spintronics, inhomogeneous

superconductivity

Introduction

The proximity effect between a superconductor (S) and a ferromagnet (F) is

in the focus of intensive studies. It is now known that the spatially

inhomogeneous superconducting order parameter

Ψ(x) induced inside the F-

layer in S/F hybrid structures can manifest itself in a number of different

ways [1-3]. Among them, one of the interesting phenomena is the non-

monotonous behavior of the critical temperature T

of S/F multilayers [4]

and

bilayers [5] as a function of the thickness of the ferromagnet d

. In

189

R. Gross et al. (eds.), Nanoscale Devices - Fundamentals and Applications, 189–196.

190 A. Yu. Rusanov, J. Aarts, M. Aprili

bilayers in particular, this effect is difficult to observe [6-8], probably

because it is strongly dependent on the interface transparency [5]. Since T

is basically determined by the largest amplitude of

Ψ(x) in the S-part of the

bilayer, it quickly regains the bulk value. On the other hand, the depairing

current J

of the system should be more sensitive to the average of Ψ(x)

over the S-layer, and therefore also more sensitive to the lowered Ψ(x) close

to the interface [9]. Here we present a first set of measurements of both

) and J

) on bilayers of Nb/Pd

, indicating such a difference in

behavior.

Experimental Details

Bilayers of type s/S/F/N were fabricated by e-gun evaporation in the

system described in Refs. [2, 3]. Here, s denotes the substrate consisting of

a Si waver covered with 50 nm SiO, S is a Niobium layer with a thickness

of 13 nm, F is a layer of Pd

with a thickness varying between 0 nm

and 12 nm, and N is a thin (5 nm) Ag protection layer. The Ni-

concentration of the PdNi layers was analyzed by Rutherford

Backscattering

and determined to be 11 – 12 %. For the depairing current

350 400 450 500 550 600 650

0.0

0.2

0.4

0.6

0.8

1.0

V [au]

I [

2.220

2.222

2.224

2.226

2.228

2.230

2.232

2.234

2.236

2.238

2.240

[

]

Fig. 1. Typical dependence of voltage V (open squares) and temperature T (open

circles) on current I. The measurement was performed on a 1.6 µm wide

Nb/Pd

experiments, samples were structured in the shape of 3 µm wide bridges by

e-beam lithography and Ar-ion etching. All samples were liquid-nitrogen

cooled during etching in order to avoid undesirable diffusion of materials.

bridge of sample 12 (see Table 1).

Depairing Currents in Bilayers of Nb/Pd

191

The structure included the current and voltage leads. In all cases, the

distance between the voltage leads was about 15 ± 0.1 µm, while the actual

width of the bridge turned out to depend on the details of the lithography

process and varied between 1.5 µm and 3.5 µm.

Since the width is a crucial parameter, it was determined for each sample

separately. The width of the transition from the normal to the

superconducting state was about 0.5 K, which is somewhat wider than in

the case of single superconductors. Measurements in the normal state

yielded an average value of the specific resistance ρ

for the Pd

films

of about 35 µΩ·cm and ρ

for the Nb films of about 7.5 µΩcm. The relevant

experimental parameters are given in Table 1. Measurements of the

depairing current were performed by a pulsed current method as described

in ref. [10]. For temperatures close to T

a small onset of voltage was

observed in all samples, probably because of vortex motion. In order to

make certain that this effect has no influence on the determination of I

, the

temperature was monitored during every current pulse. Measurable

differences were found only very close to I

, as shown in the Fig. 1. Hence

we can conclude that a short current pulse in a combination with a long

pause does not cause sample heating and keeps the system in temperature

equilibrium until the dissipation related to the normal state occurs.

Results And Discussion

different temperatures for the sample with d

= 3.5 nm. All show an almost

instantaneous jump of the voltage to the value corresponding to the normal

state of the sample, which is identified as J

. Fig. 2b shows the compilation

of all values of J

as function of reduced temperature t = T/T

for bilayers

of Nb/Pd

with a different thickness d

. Below t = 0.8, the samples

with 5.6 nm and 9.5 nm of Pd

show a sudden upturn, and differ

significantly from other samples in the set. Possibly, the Nb thickness for

those two is slightly higher than for the other samples.

In order to account for small sample-to-sample variations, all values for

were first normalized by determining the slope S = ∆J

/∆t near t = 1.

An average slope S

was defined by the samples with equal slope (3.5 nm,

5.6 nm, 9.5 nm; black dotted line in Fig. 1b). Values for J

(t) were then

normalized according to J

nor

(t) = c

nor

(t), with c

nor

= S

/ S. The

correspondent normalization values c

nor

for each J

curve are presented in

Table 1.

Figure 2a shows a set of typical current (I) - voltage (V) characteristics at

192 A. Yu. Rusanov, J. Aarts, M. Aprili

0 50 100 150 200 250 300 350

0.0

0.5

1.0

1.5

2.0

Voltage [V]

I [

T=4.29K

T=3.84K

T=3.48K

T=3.17K

T=2.0K

T=1.86K

s/Nb/PdNi

= 3.5 nm

0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

, [nm]

3,5;

5,0;

5,6;

6,4;

6,6;

6,8;

8,0;

8,2;

9,5;

9,9;

11,1;

[10

A/m

]

Fig. 2

(a). Current (I) - Voltage (V) characteristics for a Nb/Pd

bilayer with

= 3.5 nm taken at different temperatures. (b). Experimental values for the

depairing current density J

(t) as a function of reduced temperature t for

Nb/Pd

bilayers with different Pd

thickness d

. The black dashed line

indicates the average slope near t = 1 used for calculation of normalization values,

see text.

Depairing Currents in Bilayers of Nb/Pd

193

Table 1. Experimental values of the critical temperature T

determined by the

onset of Ohmic behavior in J

(t), the critical temperature T

determined using a

resistance criterion (20% resistance drop), bridgewidth w , the sample resistance R

at T = 10 K, the Pd

thickness d

, and the normalization constant c

nor

for the

Sample

[K]

[µm]

[Ω]

[nm]

nor

1 7.46 7.46 1.6 122.7 0.0 1

2 4.40 4.7 1.5 130.3 3.5 1

3 4.20 4.5 1.7 46.2 5.0 0.76

4 4.50 4.65 3.4 55.8 5.6 1

5 4.10 4.50 1.7 67.4 6.4 1.8

6 4.20 4.00 2.8 33.4 6.6 1.8

7 4.00 4.28 3.2 38.1 6.8 1.5

8 4.30 4.10 1.6 44.5 8.0 1.5

9 4.35 4.70 1.6 72.8 8.2 1.4

10 4.35 4.60 2.3 49.6 9.5 1

11 4.25 4.30 2.5 34.0 9.9 1.2

12 4.00 4.00 1.6 54.0 11.1 0.9

The normalized values of J

nor

at t = 0.5 together with T

as function of

are plotted in Fig. 3. It is useful to note that T

) is quite featureless and

in particular does not show a dip (although it would have been useful to

have one more sample at smaller thickness). Looking at J

nor

(t = 0.5), and

disregarding the two samples with deviating behavior of J

(t) (the samples

with d

= 5.6 nm and 9.5 nm are indicated as black solid squares in Fig. 3)

the asymptotic value for J

nor

is 2.0 ± 0.4×10

A/m

. However, the

correspondent J

nor

values at d

= 3.5 nm and 5 nm are 0.5×10

A/m

and

0.8×10

A/m

, significantly lower that the asymptotic value. It appears

therefore that J

nor

(t = 0.5) shows a dip in the region of d

around 40 nm,

where T

) flattens.

In order to understand these data, we analyze the behavior of T

) by

using the proximity effect model for S/F bilayers as developed by Fominov

et al. [5]. In this model, the parameters used are the following. Firstly there

are what can be called the diffusion lengths

= (ħD

/(2πk

))

1/2

and

= (ħD

/(2πk

))

1/2

, with D

S,F

the different confusion constants.

(t) curves plotted in Fig. 1b.

194 A. Yu. Rusanov, J. Aarts, M. Aprili

0 20 40 60 80 100 120

[10

A/m

]

[A]

t = 0.5

0 20 40 60 80 100 120

T [K]

Fig. 3. Depairing current density J

nor

(open squares) at t = 0.5 and critical

temperature T

(open circles) of Nb/PdNi bilayers as a function of ferromagnet

thickness d

. Black solid squares indicate the samples with the deviating values of

. The black solid line shows the fitted T

) curve. Dashed lines are guides to

Of course,

is nothing else than the superconducting coherence length,

and related to the Ginzburg-Landau coherence length by

= 2

(0)/π. It

can be directly determined by the temperature dependence of the upper

critical field, and for our Nb films we use

= 8 nm. Note that

is not

exactly the same as what is often called the coherence length in the

ferromagnet. It does not contain the exchange energy E

, which in the

model is a separate parameter, and therefore does not by itself set the scale

for the oscillations of the order parameter. We estimate its value from a

Fermi velocity v

for PdNi of 2×10

m/s [11] and a mean free path ℓ

mfp

the order of the film thickness, around 4 nm. Together with T

= 7.5 K this

yields D

= 2.7×10

-4

/s and

= 6.6 nm. The other parameters are the

specific resistances

S,F

, given before, the bulk transition temperature T

and the interface transparency parameter

the eye.

Depairing Currents in Bilayers of Nb/Pd

195

The free parameters are therefore E

and

, and we find a good fit for

the values

= 0.45 and E

= 150 K. The fit is shown in Fig. 3. Note that it

shows a very slight minimum around 4 nm, emphasizing that the minimum

is almost absent even for modest values of

From the value for E

we can make the following estimate. Since

>> k

T, the characteristic oscillation length for the inhomogeneous

order parameter in the F-layer can be written as

= 2π

= 2π(ħD

)

1/2

It follows that

≈ 25 nm, and

≈ 3.9 nm. From this, a possible minimum

in T

) could be expected around 0.7

/4 [5], which is around d

4.3 nm. The value for

can also be compared to the data of Josephson

junctions of Nb/Pd

/I/Nb (with I an insulator), where the 0-π transition

should be found at 3λ

/8 = 9 nm. The actual transition is found around

7 nm [3], a little bit lower, but still in a reasonable agreement. We conclude

therefore that the dip in the behavior of J

) at low temperatures is due to

the presence of an inhomogeneous order parameter in the F-layer, which is

sensed by J

but not by T

Conclusion

We measured T

) on Nb/Pd

0.81

0.11

bilayers together with the depairing

current. Close to 1/4 of the period of Ψ(x) in the F-layer J

) shows a

clear minimum, in contrast to the absence of the correspondent effect in

). We believe, that this difference is caused by a higher sensitivity of

the depairing current to the order parameter changes than T

. While the

critical temperature senses only the highest value of the ∆ in S, depairing

currents are more localized tools and shows the complete behavior of the

superconducting order parameter ∆(x) across the whole superconductor.

Acknowledgments

This work is part of the research program of the ‘Stichting voor

Fundamenteel Onderzoek der Materie (FOM)’, which is financially

supported by the ‘Nederlandse Organisatie voor Wetenschappelijk

Onderzoek (NWO)’. Support of the ESF program ‘Pi-shift’ is gratefully

acknowledged, as well as discussions with A. A. Golubov and

Ya. V. Fominov, who also allowed the use of his computer code.

196 A. Yu. Rusanov, J. Aarts, M. Aprili

References

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3. Kontos T, Aprili M, Lesueur J, Genet F, Stephanidis B, Boursier R (2002).

Phys Rev Lett 89:137007

4. Radović Z, Ledvij M, Dobrosavljević-Grujić L, Buzdin AI, Clem JR (1991).

Phys Rev B 4:759

5. Fominov YaV, Chtchelkatchev NM, Golubov AA (2002). Phys Rev B

66:014507

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Goryunov YuV, Garifullin IA, Khaliullin GG (1998). Phys Rev B 57:5071

7. Ryazanov VV, Oboznov VA, Prokof’ev AS, Dubonos SV (2003). JETP Lett

77:43

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M, Klimm S, Horn S, Tagirov LR, Tidecks R (2003). Ann Phys 12:37

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11. Dumoulin L, Nedellec P, Chaikin PM (1981). Phys Rev Lett 47:208

Superconductor-Ferromagnet Heterostructures

1 1 2

Université Bordeaux I , CPMOH, 33400 Talence Cedex, France

Commissariat à l'Énergie Atomique, DSM, Département de Recherche

Fondamentale sur la Matière Condensée, SPSMS, F-38054 Grenoble,

France

Abstract: We provide a general description of superconductor/ferromagnet

structures and study the evolution of the critical temperature, critical

current and magnetization variation with the thickness of the

ferromagnetic layer. Special attention is given to the influence of the

magnetic scattering on the properties of such hybrid systems.

Keywords: magnetism, superconductivity, magnetic impurities

Introduction

Ferromagnetism and singlet superconductivity are two antagonistic

orderings. Indeed, a magnetic field can destroy conventional

superconductivity via the orbital effect and via the paramagnetic effect and

therefore, they usually try to avoid each other. The competition between

these two orderings has always been a subject of great interest for both

theoretical and experimental physics. The question of their coexistence was

first addressed by Ginzburg as soon as 1956 [1]. In fact, it was

demonstrated later that a modulated magnetic structure

(cryptoferromagnetic state [2]) appears instead of ferromagnetism in a

singlet superconductor. As a review of the problem of singlet

superconductivity and magnetism coexistence, see [3]. Moreover, Larkin

and Ovchinnikov, and Fulde and Ferrell demonstrated in 1964 that the

superconductivity of a pure ferromagnetic superconductor may be non

uniform

at low temperature ([4] and [5]). It is unfortunately not easy to

197

R. Gross et al. (eds.), Nanoscale Devices - Fundamentals and Applications, 197–224.

A. I. Buzdin , M. Fauré , M. Houzet

198 A. I. Buzdin, M. Fauré, M. Houzet

verify this prediction on experiment because of the incompatibility of

ferromagnetism and superconductivity in bulk materials.

However, their interplay may be studied when the two orderings are

spatially separated, which is obtained in artificially made

superconductor/ferromagnet (S/F) structures. These hybrid systems give us

the unique possibility to study the properties of superconducting electrons

under the influence of a huge exchange field acting on the electron spins. In

such systems, Cooper pairs can penetrate into the F layer and induce

superconductivity there, which is the so called proximity effect. In addition,

it is possible to study the interplay between superconductivity and

magnetism in a controlled manner, since varying the layer thicknesses

changes the relative strength of the two competing phenomena.

Note that almost all the interesting effects related to superconductivity

and magnetism interplay in S/F structures occur at a nanoscopic scale. The

observation of these effects became possible only a few years ago thanks to

recent progress in the preparation of high-quality hybrid layers.

The most striking feature of S/F systems is the highly non monotonic

behavior of the critical temperature

T and the critical current

I with the

thickness of the ferromagnetic layer. In S/F/S junctions and S/F multilayers,

this is related to 0-

transitions, which are studied in the present work.

Another interesting manifestation of the proximity effect is the variation of

the magnetization in both types of layers.

A general review of S/F structures was reported in [6]; see also [7]. Here,

we would like to concentrate on the influence of magnetic scattering on the

properties of S/F systems. Although the oscillatory behavior of

T and

is well known, a noticeable difference between theoretical calculations and

experimental results still exists. It could be understood by the introduction

of an additional scattering mechanism in theoretical descriptions. Indeed,

magnetic impurities, spin-wave or non stoichiometric lattices can play an

important role as the spin-flip process has dramatic consequences on

superconductivity (on the contrary of non magnetic impurities which have

very little impact). More precisely, the pair-breaking effect induced by

magnetic impurities leads to the decrease of the decay length of

T and

and to the increase of the oscillations period. Note that the question of the

spin flip scattering was firstly addressed by Tagirov [8], while Demler et al.

studied the spin-orbit scattering role [9].

In the present work, we study the critical temperature and current as well

as magnetization in S/F bilayers and multilayers in the framework of the

Usadel equations and report on the spin-flip scattering influence.

Gross R., Sidorenko A., Tagirov L. Nanoscale Devices - Fundamentals and Applications

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