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

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Realization of an N-Shaped IVC of Nanoscale Metallic Junctions 167

0 50 100

100

150

051015

Voltage (mV)

I (mA)

T=1K

T=8K

=10 µΩcm

(

µΩ

cm)

T (K)

Fig. 3. Measured (solid) and calculated (dashed) I(V) curves at two temperatures.

The inset shows

(T) of the bulk compound [9]. After [10]

shown in Fig. 4. Indeed, the calculated I(V) curves in Fig. 5(a) are N-shaped

up to room temperature. Even enhancing disorder by increasing the residual

resistivity up to

= 1000 µΩcm as in Fig. 5(b) does not suppress

completely the maximum in I(V) at low temperatures.

0 100 200 300 400

ρ (

Ω

cm)

T (K)

=342K

B=6T

Fig. 4. Resistivity

(T) of La

0.75

0.25

MnO

at zero (upper curve) and B = 6 T

magnetic field according to [18].

168 Yu. G. Naidyuk, K. Gloos, I. K. Yanson

Fig. 5. (a) I(V) calculated for d = 100 nm at the indicated temperatures, (b) the

same calculation of I(V) for different residual resistances at T = 4 K.

On the other hand, the position of the current maxima shifts to the higher

voltages with increasing temperature (or with the residual resistivity

increase), contrary to what has to be expected for a simple

antiferromagnetic transition. Thus it would be very interesting to measure

I(V) characteristic or voltage dependent resistance for point contacts with

0 20 40 60 80 100 120

(b)

I (mA)

T=4K

100K

200K

300K

add

(a)

1000

V (mV)

T=4K

200

add

=0 µΩ

Realization of an N-Shaped IVC of Nanoscale Metallic Junctions 169

rare-earth manganite compounds experimentally and make a comparison

with the analogous calculations in the thermal regime.

Acknowledgments

The partial support of the complex program "Nanosystems, nanomaterials

and nanotechnologies" of the National Academy of Sciences of Ukraine

and Project Φ1-19 of the National Academy of Sciences of Ukraine are

acknowledged.

References

1. Naidyuk YuG, Yanson IK (2004) Point-contact spectroscopy. Springer Series

in Solid-State Sciences. Vol. 145 Springer, New York

2. Jansen AGM, van Gelder AP, Wyder P (1980). J Phys C 13:6073

3. Yanson IK (1983). Sov J Low Temp Phys 9:343

4. Yanson IK, Shklyarevskii OI (1986). Sov J Low Temp Phys 12:509

5. Duif A, Jansen AGM, Wyder P (1989). J Phys: Condens Matter 1:3157

6. Moreland J, Clark AF, Soulen Jr RJ, Smith JL (1994). Physica B 194-196:1727

7. Naidyuk YuG, Gloos K, Menovsky AA (1997). J Phys: Condens Matter 9:6279

8. Gloos K, Anders FB, Assmus W, Buschinger B, Geibel C, Kim JS, Menovsky

AA, Mueller-Reisener R, Nuettgens S, Schank C, Stewart GR, Naidyuk YuG

(1998). J Low Temp Phys 110:873

9. Geibel C, Schank C, Thies S, Kitazawa H, Bredl CD, Böohm A, Rau M,

Grauel A, Caspary R, Helfrich R, Ahlheim U, Weber G, Steglich F (1991). Z

Phys B 84:1

10. Naidyuk YuG, Gloos K, Yanson IK, Sato NK (2004). J Phys: Condens Matter

16:3433

11. Kohlrausch N (1900). Ann Physik (Leipzig) 1:132

12. Verkin BI, Yanson IK, Kulik IO, Shklyarevskii OI, Lysykh AA, Naidyuk YuG

(1979). Solid State Commun 30:215

13. Verkin BI, Yanson IK, Kulik IO, Shklyarevskii OI, Lysykh AA, Naidyuk YuG

(1980). Izv Akad Nauk SSSR Ser Fiz 44:1330

14. Kulik IO (1984). Phys Lett 106 A:187

15. Kulik IO (1992). Sov J Low Temp Phys 18:302

16. Esaki L (1992). In: Lundquist Stig (ed) Nobel lectures in Physics 1971-1980.

World Scientific Publishing Company; (1974) Science 183:1149

17. Price PJ (1992). In: Moss TS, Landsberg PT (eds) Handbook on

Semiconductors. Elsevier Science Publishers B.V., Amsterdam Volume I

Chapter 12

170 Yu. G. Naidyuk, K. Gloos, I. K. Yanson

18. Mitra J, Raychaudhuri AK, Gayathri N, Mukovskii YaM (2002). Phys Rev B

65:140406

19. Rao CNR, Raveau B (eds) (1998) CMR, Charge Ordering and Related

Properties of Manganese Oxides. World Scientific, Singapore

20. Tokura Y (ed) (2000) Colossal Magneto-Resistance Oxides. Gordon and

Breach Sciences, Netherlands

PI-SHIFT EFFECT AND

FERROMAGNET/SUPERCONDUCTOR

NANOSCALE DEVICES

Josephson Effect in Composite Junctions with

Ferromagnetic Materials

M.Yu. Kupriyanov

, A.A. Golubov

, M. Siegel

D.V.Skobeltsyn Institute of Nuclear Physics, Moscow State University,

Moscow, Russia

Faculty of Science and Technology, University of Twente, The

Netherlands,

Institute for Micro and Nanoelectronic Systems, Karlsruhe University,

Germany

Abstract: The proximity effect in the system consisting of a superconducting

electrode S with ferromagnetic F and normal N layers on the top of it,

is studied theoretically in the framework of the Usadel equations. The

results are applied for the calculation of the electronic density of

states and the Josephson current in a S(F/N)I(F/N)S tunnel junction.

Keywords: proximity effect, Josephson π contacts

Introduction

In the past few years there was a noticeable interest in "Unconventional

Josephson

Junctions" (UJJ). Contrary to already well known

"Conventional Josephson Junctions" (CJJ) or 0-Josephson junctions, the

current phase relationship

)(

I in UJJ may have negative critical current

(the

so-called π- junctions) or even cross the

-axis at a position in

between

=0 and

= π (see [1] for a recent review). SFS π- junctions

were first realized by Ryazanov et. al. [2]. The existence of UJJ opens the

way for fabrication of Josephson structures with engineered properties [3]

putting together UJJ and CJJ into a discrete analogue of a Josephson

173

R. Gross et al. (eds.), Nanoscale Devices - Fundamentals and Applications, 173–187.

174 M.Yu. Kupriyanov, A.A. Golubov, M. Siegel

junction (DJJ). By changing the shape of )(

I of individual junctions in

the DJJ it is possible to engineer a junction with desired properties. Even

the Josephson structures composed from arrays of 0- and π-junctions

possess extraordinary characteristics [4-15]. In particular, the existence of

Josephson vortices with unconventional shape of magnetic field distribution

was predicted in these structures [7-15]. There is also a possibility of

realization of Josephson structures, where the average phase difference

the ground state may have any value in the interval between 0 and π [7-9]

(so called "

-junctions"[15]).

In the developed theoretical models [10-15] it was supposed that both ϕ

and its first derivative are continuous at the boundaries between 0- and π-

segments inside a DJJ. This suggestion is not obvious since the transition

from 0- and π-segments should be supplemented by a redistribution of a

local current near the segment interfaces. In the present work we attack this

problem by studying the generic building block of these structures, namely

the S(FN)I(FN)S structure presented in Fig.1. In the framework of the

Usadel equations [16] we start with the examination of the proximity effect

in the S(FN) system and get the analytical solutions describing the

oscillatory behavior of superconducting correlations induced into thin

ferromagnetic film. These solutions have been used for calculations of the

density of states in the S(F/N) proximity system and the lateral spatial

variations of the critical current density in the S(FN)I(FN)S Josephson

junction. Based on these results we derived the boundary condition for

the interface of 0- and π- segments in DJJ. This condition was further

applied for the determination of the equation for the slow varying part of

Finally the conditions of experimental realization of "

-junctions" in the

discussed system have been formulated.

Model of S(FN)I(FN)S Multilayer

We consider S(FN)I(FN)S type structures as shown in Fig. 1, which

consists of a superconductor electrode with ferromagnetic and normal

layers on top of it. The F/N bilayer is additionally covered by an insulator,

I, to form the tunnel barrier and the second superconducting electrode

having the same structure.

Josephson Effect in Composite Junctions with Ferromagnetic Materials 175

Fig. 1. Schematic view of S(FN)I(FN)S Josephson junctions

We assume that the S layers are bulk and that the dirty limit conditions

are fulfilled in all metals. We further assume that the F metal is a

monodomain ferromagnet with a value of the exchange integral equal to H

and that the effective constant of electron-phonon interaction is equal to

zero in the F and N layers. For simplicity we also assume that interfaces are

not magnetically active and can be described by spin independent

suppression parameters

,,,

BNBN

BFBF

ξρ

===

,,,

BB FF

NN NN NN

γγγ

ξρξρξ

===

where R

, R

and A

, A

are the resistances and the areas of the

SF, SN and NF interfaces respectively;

S(F,N)

is the resistivity of the S(F,N)

layer and the coherence lengths are related to the diffusion constants D

S(F,N)

= (D

S(F,N)

/2πT

)

1/2

. This approach is valid for relatively weak

ferromagnetic materials when the exchange integral is smaller than 0.1 eV

and spin dependent corrections to resistivity can be neglected. Under the

above assumptions we can reduce the problem to the solution of the Usadel

equations. To simplify it further we assume that γ

<<γ

, γ

<<γ

so that

the rigid boundary conditions

1,2 1,2

22 22

sin exp{ }, cos

SS SS

FiG

θχθ

ωω

∆

== ==

+∆ +∆

(1)

are

valid for the superconductor. Here ∆ and

are the magnitude and

phase of the order parameter in the electrodes, F

S1,2

and G

are the Usadel

Green's functions We will assume additionally that the transparency of the

tunnel barrier is much smaller than the transparency of SN and SF

176 M.Yu. Kupriyanov, A.A. Golubov, M. Siegel

interfaces of the structure thus reducing the problem to examination of the

proximity effect in S(FN) electrodes.

Proximity Effect in S(F/N) System

To study the proximity effect we choose the x axis perpendicular to the

plane of the NF-interface and the y axis perpendicular to the plane of the

SF- and SN-interfaces with the origin at the NF-interface, as it is shown in

Fig.1. The Usadel functions G and F obey the normalization condition

1GFF

ωωω

−

+=, which allows for the so-called

parameterization. Making

use of the boundary conditions [17] at the SF (y=0, -∞<x≤0), SN (y=0,

0≤x<∞) and FN (x=0, 0≤y≤d

, d

) interfaces and demanding the absence of

a current across free interfaces, in the limit of small F and N layers

thickness (d

F,N

) we can reduce the problem to the solution of one

dimensional equations

,0))(sin(

cos

)(cos

=∞−−

∂

∞

NNNN

SCBNM

NBNMC

θθθξ

θπωγ

θγπ

(2)

,0))(sin(

cos

)(cos

=−∞−−

∂

−∞

FFFF

SCBFM

FBNMC

θθθξ

θπγω

θγπ

(3)

where

iHdd

FFBFBFMNNBNBNM

,/,/ and

θπγω

∆

=∞ arctan,

cos

sin

arctan)(

, S

SCBFM

Solution of equations (2), (3) has the form

,exp

)()0(

tanarctan4)(

























−













∞−

+∞=

θθ

(4)

,exp

)()0(

tanarctan4)(





































−∞−

+−∞=

θθ

(5)

Josephson Effect in Composite Junctions with Ferromagnetic Materials 177

where the effective decay lengths are

)(cos2

222

CSBNMCBNM

BNMC

πθωγπγω

γπ

(6)

222

)(cos2

CSBFMCBFM

BFMC

πθωγπγω

γπ

(7)

The integration constants

(0) and

(0) in (4),(5) have to be determined

from the boundary conditions at the FN interface (x = 0)

).sin(,

FNFFBFFFFNN

xxx

θθθξγθξγθξ

−=

∂

(8)

They can be found analytically in the limit of large transparency of the

interface between the F and N metal. Then the condition (8) in the first

approximation may be simplified to the continuity of Usadel functions at

FN interface

)0()0()0(

. In this case

θθ













−∞

∞

−∞

∞

+∞= ,

)(

cos

)(

cos

)(

sin

)(

sin

arctan2)()0(

(9)

The developed theory of proximity effect in complex S(F/N) proximity

multilayers opens the way for examination of spatially resolved density of

states (DoS) in the F/N film. To calculate the DoS we need

)(Re)(

iGN −→= .

In the SN bilayer

)(

∞

→x DoS does not depend on H and is given by

[18-20]

sign

γγ

γεε

εε

−∆

∆−

)(

Re)(

where

N is the total DoS for both spin directions at the Fermi level in the

normal state. The DoS has a minigap at

∆

, and the peaks at

and

∆=

. The minigap

characterizes the strength of superconducting

correlations induced into N metal due to the proximity effect.

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

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