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

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Proximity Effect and Interface Transparency in

Nb-based S/N and S/F Layered Structures

C. Attanasio

Dipartimento di Fisica “E.R. Caianiello” and INFM-Laboratorio Regionale

Supermat, Università degli Studi di Salerno, I-84081 Baronissi (Sa), Italy

Abstract: The interface transparency T has been investigated for different S/N

and S/F layered structures realized by sputtering and by Molecular

Beam Epitaxy (MBE). We have chosen Nb as a superconductor (S),

Cu, Ag and Pd as a normal metal (N) and PdNi and Fe as

ferromagnetic materials (F). The obtained result for T do not seem

strongly influenced by fabrication methods but more by intrinsic

factors related to the microscopic properties of the two materials.

Keywords: proximity effect, transparency, heterostructures

Introduction

The proximity effect between a superconductor (S) and another material

(M) has been object of study since the early sixties [1], but only recently an

important parameter, the interface transparency T, has been added to the

description of this coupling mechanism [2-7]. The quantity T takes into

account all the effects that cause electrons to be reflected rather than

transmitted at the interfaces, with the consequence that the proximity effect

results somehow screened. In principle T can depend on both extrinsic and

intrinsic factors such as, for example, interface imperfections, fabrication

methods, Fermi velocities and band-structure mismatches [4]. When the

non-superconducting material M is magnetic the situation is even more

difficult because of the additional splitting of the spin sub-bands and the

spin-dependent impurity scattering [8]. For these reasons the study of the

interface transparency turns to be important from a theoretical point of

241

R. Gross et al. (eds.), Nanoscale Devices - Fundamentals and Applications, 241–249.

242 C. Attanasio

view because it is related to the microscopic properties of the metals. In

addition it is also important from a practical point of view because having

high quality interfaces it is essential for superconducting devices in which

the working mechanism is based on coupling between different materials

[9].

In this paper we analyze the topic of the interface transparency T when

Nb is placed into a contact with a normal metal N and with a magnetic

material F. For N we have chosen Cu, Ag and Pd while for F we have

chosen PdNi, which is a weak ferromagnet, and Fe. To investigate the

effect of the fabrication method on T some samples have been prepared by

sputtering and others by Molecular Beam Epitaxy (MBE). What essentially

emerges from this study is that the obtained values for T do not seem

strongly dependent from the fabrication methods but more from intrinsic

properties of the constituent metals.

High quality multilayers were grown by MBE and by a dual-source

magnetically enhanced dc triode sputtering system on Si(100) substrates

kept at room temperature. By using suitable shutters, more than one sample

has been fabricated in the same deposition run in order to obtain the same

deposition conditions for all the samples of the series: we prepared eight

samples in the sputtering and four in the MBE chamber. Nb/Cu systems

have been prepared both by sputtering and by MBE while Nb/Ag has been

fabricated by MBE [7] and Nb/Pd by sputtering [5]. In the case of S/F

systems we have prepared Nb/PdNi by sputtering and Nb/Fe by MBE.

The superconducting properties, that is the transition temperature T

and

the upper critical magnetic fields were resistively measured using a

standard dc four-probe technique. In the case of Nb/Cu system to better

study the effect on T of the deposition technique a detailed structural

characterization have been realized by performing low-angle and high-

Samples Preparation

angle X-ray reflectivity measurements [7].

Proximity Effect and Interface Transparency 243

The S/N Case

Theoretical background

The starting point for a complete description of proximity effect in S/N

multilayers, valid for arbitrary transparency, was given by Kupriyanov and

Lukichev [2] in the framework of Usadel equations (dirty limit). In

particular, the model we used to describe the dependence of the critical

temperature versus the S layer thickness, T

), for N/S/N trilayers is based

on the Werthamer approximation, valid for not too low temperatures,

provided the boundary transparency is sufficiently small [3]. In this limit

the system of algebraic equations to determine T

is:



Ω

Ω=





(1a)

ln ,

22 2

CS CS CS

CCCb

TTT

 

Ω



Ψ+ −Ψ = >>

 





 

(1b)

with the identification of the Abrikosov-Gorkov pair-breaking parameter

()

(

)

1SS

/2/

ccb

TT d

ρπ π γγ ξ

=Ω=

, where

()x

is the digamma

function and T

is the bulk critical temperature of the S layer. These

equations contain two parameters

and

defined as

nn nn

γγ

ξρξ

==,

(2)

where

and

are the superconducting and the normal coherence length,

and

are the low-temperature resistivities of S and N, respectively,

while R

is the normal-state boundary resistance times its area. The

parameter

is a measure of the strength of the proximity effect between

the S and N metals. The parameter

, instead, describes the effect of the

boundary transparency T, to which is roughly related by

(3)

244 C. Attanasio

While

was determined experimentally by measuring

and

(or T) can’t be determined experimentally, because R

is difficult to

measure, so it is extracted by a fitting procedure.

In the free electron model it is possible to express the interface transparency

in terms of the Fermi velocities by [4]

[]

(4)

where v

N,S

are the projections of the Fermi velocities of N and S metals on

the direction perpendicular to the interface.

Discussion

Two different samples typology have been prepared: N/S/N and S/N/S

trilayers. The first, with external layers of normal metal with constant

thickness, d

, and an internal layer of superconducting material with

variable thickness, d

, were used to determine the dependence of T

on d

The others, with external layers of superconducting metal with constant d

and an internal layer of normal material with variable d

were instead used

to estimate the normal coherence length [5,7]. N/S/N trilayers were also

used to determine the Ginzburg-Landau coherence length at zero

temperature,

(0)

, from the slope S= - dH

/dT|

T=Tc

of the upper

perpendicular magnetic field close to the critical temperature.

is, in fact,

related to

(0)

by the relation

= 2 (0)

. What we found is that in all

our systems

(0)

typically decreases when increasing d

until a saturation

value. So for samples with thicker Nb interlayer the perpendicular H

(T)

reflects the properties of the single Nb film [5,7].

To determine

by S/N/S trilayers we should consider that, if two S

layers are separated by a thin N layer, the decay of the superconducting

order parameter from both sides overlaps. By increasing the thickness of the

N layer the S layers become more and more decoupled until no overlap is

left. For this reason the behavior of the T

) curve will go from a

maximum value (related to the critical temperature of the S layer with

thickness

equal to 2d

) to a limiting value (related to the critical

temperature of the S layer with thickness equal to d

). The thickness for

which the minimum is reached is called decoupling thickness and can be

associated with approximately twice the coherence length (d

≈2

)

Proximity Effect and Interface Transparency 245

[4, 5, 7]. Finally the S and N resistivities

and

have been measured on

samples deliberately fabricated [5, 7].

All the above values have been used to reproduce the T

) for all the

sets of fabricated trilayers using equations (1) with T (given by equation

(3)) as the only fitting parameter. In Table 1 are reported all the measured

quantities for all the systems together with the values obtained from the

fitting procedure for the interface transparency. In the last column are

reported the theoretical results for T obtained using equation (4) with the

following values for the Fermi energies: v

= 2.73 × 10

cm s

-1

[10], v

1.57 × 10

cm s

-1

[11], v

= 1.39 × 10

cm s

-1

[11] and v

= 2.00 × 10

-1

s [12]. What we see is that we obtained the higher value for T in tha case

of Nb/Pd system for which the values of the Fermi energies are very

similar. In addition, in the case of Nb/Cu and Nb/Ag we got very similar

values for T as well as for the case of MBE and sputtered Nb/Cu samples in

spite of their different interface quality [5,7].

Table 1. Measured values of the electrical resistivities and of the coherence lengths

of the N and S materials and of the bulk critical temperature. T is the transparency

of the systems obtained by fitting the experimental data of the T

) curves. T

theo

has been calculated from equation (4). The first (second) line in the table refers to

Samples

(

Ω

cm)

(

Ω

cm)

(Å)

(Å) T

(K) T T

theo

Nb/Cu

1.3 3.6 260 64 9.2 0.30 0.50

Nb/Cu

1.8 4.6 170 67 8.8 0.26 0.50

Nb/Ag 4.0 7.3 190 54 9.2 0.33 0.55

Nb/Pd 5.0 2.5 60 64 8.8 0.46 0.98

The S/F Case

Theoretical background

The

experimental investigation of S/F systems, that is the study of

interplay of two competing phenomena the superconductivity and the

ferromagnetism, started almost forty years ago [13]. More recently the

improvement of the deposition techniques has made possible to prepare

very

thin high-quality ferromagnetic layers and a rich variety of

MBE (sputtering) prepared Nb/Cu trilayers.

246 C. Attanasio

phenomena have been predicted [14-16], such as, for example, the non-

monotonic behavior of the superconducting critical temperature T

in S/F

layered structures as a function of the F layer thickness, d

[14, 17, 18]. In

general the presence of an exchange field E

in F cause an energy shift

between the quasiparticles of the pair entering the ferromagnet and this

results in the creation of non-zero momentum Cooper pairs [19]. This

implies that the superconducting order parameter does not simply decay in

the ferromagnetic material, as happens for normal metals, but also oscillates

over a length scale given by

, the coherence length in F, which, in the

dirty limit, is given by

= (hD

)

1/2

, where D

is the diffusion

coefficient [19]. In the case of S/F systems where F is a strong ferromagnet

(Fe, Co, Ni) the exchange energy is typically of the order of 1 eV, resulting

in a coherence length

of few Angstroms. In the case of the so-called

weak ferromagnets (CuNi [20], PdNi [15, 21]), E

is in the meV range

leading to a

of the order of hundred of Angstroms.

The theoretical prediction of the T

) behavior has been done first in the

limit of high transparency [22] and then considering the possibility of finite

T [23] in the case of strong ferromagnet, where the exchange energy is very

large. Recently the theory has been extended to the case of S/F bilayers in a

more general case [24] which also applies for the weak ferromagnets for

which, again, d

is large with respect the interatomic distance.

Discussion

Two different sets of samples have been fabricated: F/S and S/F bilayers,

using for the ferromagnetic material PdNi

(with Ni percentage equal to 10)

and Fe. The first set, consisting of an F layer with constant thickness, d

and a Nb layer with variable thickness, d

, were used to determine the

dependence

of T

on d

and to estimate the interface transparency of the

S/F barrier. The other, with constant d

and variable d

were instead used to

estimate the coherence length in F and, consequently, the value of the

exchange energy E

. The S and F resistivities,

and

, have been

measured on samples deliberately fabricated.

The Nb coherence length was determined through the dirty limit

expression

= (hD

)

1/2

. Here D

is the Nb diffusion coefficient

which is related to the low temperature resistivity

via the electronic

Proximity Effect and Interface Transparency 247

mean free path [25]. All these values have been used to reproduce the T

)

for all the sets of fabricated bilayers using the Fominov theory in the case

of Nb/PdNi and the Tagirov calculations for Nb/Fe, leaving

as the only

fitting parameter. In Table 2 are reported all the measured quantities for all

the systems together with the values obtained from the fitting procedure for

the parameter

. We see that in the case of Nb/PdNi we got a value which

is much smaller of that obtained for the case of Nb/Fe as well as for other

S/F systems reported in the literature [4, 18, 26]. In addition the value of

is of the same order of what reported for the case of Nb/CuNi (for which

= 0.3) [24] but a bit higher probably due to the slightly higher value of

(or smaller

) found in our Nb/PdNi system.

Table 2. Values of the electrical resistivities and of the coherence lengths of the F

and S materials and of the bulk critical temperature. The parameter

has been

c s

Samples

(

Ω

cm)

(

Ω

cm)

(Å)

(Å) T

(K)

Nb/PdNi 24 6 20 80 9.0 0.7

Nb/Fe 7.5 3.6 7 64 9.1 45

Conclusion

In conclusion, we have experimentally studied the interface transparency in

Nb-based S/N and S/F layered structures. The obtained results seem more

influenced by the intrinsic properties of the two metals more than by the

fabrication methods. In the S/N case, as expected by simply theoretical

arguments, we get higher transparency for the Nb/Pd system. In the S/F

case Nb/PdNi shows a relatively high transparency with respect to the case

of combining a superconductor with strong ferromagnets, confirming the

fact that ferromagnetic alloys are could be of great interest in the physics of

S/F contacts.

obtained by fitting the experimental data of the T (d ) curves.

248 C. Attanasio

Acknowledgments

This work has been made possible thanks to the collaboration of Carla

Cirillo, Serghej L. Prischepa, Matteo Salvato and Achille Angrisani

Armenio.

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Proximity Effect and Interface Transparency 249

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Properties of S/N Multilayers with Different

Geometrical Symmetry

S. L. Prischepa

Minsk 220013 Belarus

Abstract: The influence of finite dimensions of superconducting metallic

multilayers on the H-T phase diagram and angular dependences of the

upper critical magnetic field H

is studied. It is established

the H

values and their temperature and angular dependencies. For

multilayers with the symmetry plane in the center of the

superconducting layer and for temperatures close to T

the values of

the parallel critical magnetic fields are larger than for the samples for

which the symmetry plane lies in the middle of the normal layer. This

reveals the characteristic feature of bi-dimensional behavior in the

presence of the S/N interfaces in the system than the temperature

dependencies.

Keywords: S/N multilayer, upper critical magnetic field, proximity effect,

dimensional crossover

Introduction

Superconductivity in type II superconductors first was studied in infinite

samples [1]. Later the peculiarities of superconducting phase nucleation in

homogeneous finite samples of different geometry were discussed. In

particular, the cases of semi-infinite samples [2-4], slabs and thin films [3-

6] were considered.

251

R. Gross et al. (eds.), Nanoscale Devices - Fundamentals and Applications, 251–263.

Belarus State University of Informatics and RadioElectronics, P. Brovka 6,

whole temperature range up to T . The angular dependencies of

experimentally that the geometrical symmetry determines crucially

the upper critical magnetic field seem to be more sensitive to the

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

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