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ISSN 1063 7761, Journal of Experimental and Theoretical Physics, 2010, Vol. 110, No. 2, pp. 336­344. © Pleiades Publishing, Inc., 2010. Original Russian Text © A.V. Zaitsev, G.A. Ovsyannikov, K.Y. Constantinian, Yu.V. Kislinski, A.V. Shadrin, I.V. Borisenko, P.V. Komissinskiy, 2010, published in Zhurnal èksperimental'no i Teoretichesko Fiziki, 2010, Vol. 137, No. 2, pp. 380­389.

ELECTRONIC PROPERTIES OF SOLID

Superconducting Current in Hybrid Structures with an Antiferromagnetic Interlayer
A. V. Zaitseva, *, G. A. Ovsyannikova,b, K. Y. Constantiniana, **, Yu. V. Kislinskia, A. V. Shadrina, I. V. Borisenkoa, and P. V. Komissinskiya,c
a

Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow, 125009 Russia b Chalmers Institute of Technology, GÆteborg, SE 41296 Sweden c Technische UniversitÄt Darmstadt, D 64287, Darmstadt, Germany *e mail: zaitsev@hitech.cplire.ru **e mail: karen@hitech.cplire.ru
Received August 31, 2009

Abstract--It is shown experimentally that the superconducting current density in Nb/Au/Ca1 xSrxCuO2/YBa2Cu3O7­ hybrid superconducting heterostructures with a Ca1 xSrxCuO2 anti ferromagnetic (AF) cuprate interlayer is anomalously high for interlayer thicknesses dM = 10­50 nm and the characteristic damping length for superconducting correlations is on the order of 10 nm. The experimental results are explained on the basis of theoretical analysis of a junction of two superconductors (S' and S) con nected by a magnetic multilayer with the AF ordering of magnetization in the layers. It is shown that with such a magnetization ordering, anomalous proximity effect determined by the singlet component of the conden sate wavefunction may take place. As a result, the critical currents in S'/I/AF/S and S'/I/N/S structures (I denotes an insulator, and N, the normal metal) may coincide in order of magnitude even when the thick ness of the AF interlayer considerably exceeds the decay length of the condensate wavefunction in ferromag netic layers. DOI: 10.1134/S1063776110020172

1. INTRODUCTION The proximity effect in Josephson structures with magnetic interlayers has become the object of intense studies in recent years [1, 2]. The coherence length in oxides is much smaller than in metals, which consid erably complicates the preparation of oxide structures with magnetic interlayers. Nevertheless, the anoma lous proximity effect in cuprate superconductors was observed in lanthanum based structures [3] as well as in Nb/Au/CaxSr1­ xCuO2/YBa2Cu3O7­ hybrid het erojunctions [4, 5]. It was reported earlier [6, 7] that the Josephson effect was observed in superconducting cuprate ramp type junctions with an artificial inter layer with a thickness much larger than the coherence length estimated taking into account the interlayer magnetism. The results obtained in [6] were inter preted in study [7] based on the assumption of inter layer inhomogeneity and the existence of pinholes between superconductors. The percolation mecha nism of the superconducting current passing through anomalously thick interlayers was proposed in [8]. However, recent results obtained using a modified technique of cuprate film growth [3­5, 9] cannot be trivially explained by the presence of pinholes. For example, the results of measuring magnetic field dependences of the critical current in hybrid structures and Shapiro steps oscillating with the intensity of

action at ultrahigh frequencies [4, 5] confirm the existence of the Josephson effect described by the well known RSJ model [10], which is not observed in the presence of pinholes in the interlayer. The main attention so far has been paid to analysis of structures with ferromagnetic interlayers [1, 2], while S/AF hybrid structures have not been studied comprehensively. Various aspects of the theory of such structures were discussed in publications [11, 12], in which the antiferromagnet was treated as a structure with atomically thin magnetic layers. It was shown in [12] that the characteristic feature of the Josephson effect in S/AF/S structures is its dependence on whether the number of layers in the antiferromagnet is even or odd. However, some problems (including the possibility of achieving the anomalous proximity effect in the case of diffusive transport of electrons in struc tures with an AF interlayer) remain unsolved. Here, we report on the experimental results obtained for 18 chips each of which contains 5 hetero junctions with various areas: 10 â 10, 20 â 20, ..., 50 â 50 m2. The chips had different thicknesses dM of the magnetic interlayer and were formed on the basis of epitaxial cuprate superconducting films of YBa2Cu3O7­ (YBCO) and niobium (Nb) (Fig. 1). The magnetic interlayer (M) was prepared from a

336


SUPERCONDUCTING CURRENT IN HYBRID STRUCTURES M Nb Au YBCO 60
100

337

80

200 150

(002)CSCO

(002)CSCO (110)NGO/ (001)CSCO

40
50

20
Fig. 1. Schematic representation of variation in the con densate wavefunction for heterostructures under investiga tion. The current is set along the c (horizontal) axis of the structure. The bold line shows the interface between the Au film and the M interlayer that makes the main contribution to the resistance of the structure. In the theoretical analy sis, the M interlayer is represented as a multilayer structure with collinear directions of magnetization in the layers.

0 28.5

29.0

29.5 , deg

0 10

(007)YBCO

(002)CSCO

5

(110)NGO/ (001)YBCO/ (001)CSCO

0

(CSCO) film, which is an antiferro magnet with a NÈel temperature of several kelvin [13]. The model of the S'/I/AF/S structure is studied theoretically (I is a low transparency barrier); in this model, the AF structure is treated as one consisting of series connected ferromagnetic layers (whose planes are oriented perpendicular to the direction of the cur rent) with alternating antiparallel directions of mag netization. The experimental results and theoretical analysis of the proximity effect in these heterojunc tions are considered taking into account a barrier between the antiferromagnet and the superconductor.
Ca1
xSrxCuO2

54

56

58 2, deg

Fig. 2. X ray 2­ spectra and rocking curves ( scan) of CSCO films (x = 0.15) with a thickness of dM = 50 nm deposited on NGO substrates (top). The 2­ spectrum for the CSCO/YBCO/NGO heterostructure (dM = 100 nm) (bottom).

2. EXPERIMENTAL TECHNIQUE One of the electrodes of the Nb/Au/M/YBCO het erojunctions was made of the S' superconductor with a bilayer structure consisting of niobium (Nb) films with superconducting transition temperature T '' = 9 K c and gold (Au). The proximity effect between the superconductor and metal films (Nb/Au bilayer) ensured the superconducting transition temperature T 'c = 8­8.5 of the bilayer. The second electrode of the heterojunction was prepared from a YBCO supercon ducting cuprate epitaxial film with superconducting transition temperature Tc = 88­89 K. The M inter layer was a thin (dM = 10­80 nm) Ca1­ xSrxCuO2 film (with x = 0.5 or 0.15), viz., AF material [13, 14]. The CSCO/YBCO epitaxial heterostructure was prepared in situ by laser ablation at T = 800°C on a neodymium gallate (NdGaO3, NGO) substrate. In most structures used in the experiment, (110) NGO substrates were used on which growth c oriented [001] YBCO films and, accordingly, CSCO/YBCO heterostructures ensured the transport of electric current in the c direc tion. Tilting of the crystallographic plane (7 10 2) ori entation of the NGO substrate was also used for pre paring heterojunctions in which current transport took place predominantly in the [110] direction of YBCO. After preparation of the CSCO/YBCO heterostruc ture and its cooling without vacuum break, a protect

ing Au film was deposited to suppress diffusion of oxy gen from CSCO/YBCO. The next Nb layer and the additional Au sublayer were deposited by magnetron sputtering with preliminary plasma cleaning of the surface of the initial Au layer. The structure topology was formed using photolithography as well as plasmo chemical and ion beam etching [4, 5, 15]. The struc ture had the shape of a square with a linear size of L = 10­50 m. As a result, we obtained structures with an AF interlayer, viz., S'/I/AF/S heterojunctions in which the Au/CSCO interface plays the role of the I barrier (see Fig. 1). Nb/Au/YBCO heterojunctions without an AF interlayer were prepared and tested analogously for comparison. Measurements in all types of heterojunctions were taken under identical conditions. Figure 2 (top) shows the X ray 2­ spectra and rocking curves for autonomous epitaxial CSCO films with x = 0.15 and dM = 50 nm, deposited on NGO sub strates. The results of X ray diffraction analysis of the CSCO/YBCO heterostructure (dM = 100 nm) are shown in the bottom part of Fig. 2. It can be seen that the width (2) of the (002) peak of the 2­ scan of the autonomous CSCO film deposited on the NGO substrate is smaller than (2) for the CSCO film in the CSCO/YBCO heterostructure and is close to (2) of the YBCO film. The results of comparison of the lattice constants of CSCO films in the CSCO/YBCO heterostructure and autonomous CSCO films are given in Table 1. It can be seen that the deposition of CSCO onto YBCO slightly deteriorates the quality of CSCO films (the width of the rocking curve increases) and slightly changes the lattice con stants. No other phases differing from autonomous
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ZAITSEV et al.

Table 1. Crystallographic parameters of autonomous CSCO films and CSCO/YBCO heterostructures deposited on NGO substrates CSCO Structure x = 0.15 Peak (002) CSCO a, nm 0.321 0.07° (002) CSCO 0.322 0.2°* x = 0.15 (007) YBCO 1.169 0.2°* x = 0.5 (002) CSCO 0.334 0.4° (002) CSCO 0.336 0.5°* x = 0.5 (007) YBCO 1.177 0.5°* CSCO/YBCO CSCO CSCO/YBCO

Note: Asterisks mark estimates of the rocking curve from the 2­ scan.

CSCO in chemical composition and orientation were observed. 3. RESISTIVITY MEASUREMENTS At T > Tc, the temperature dependence R(T) of the heterojunction resistance is determined by the resis tance of the YBCO film due to its high resistivity at T > Tc, which exceeds the total contribution of the remaining layers and their interfaces. In the tempera ture range T 'c < T < Tc, the resistance of the YBCO film is zero, and R(T) for heterojunctions with dM 50 nm exhibited a weak dependence on temperature and was determined by the sum of the resistances of CSCO/YBCO, Au/CSCO, and Nb/Au interfaces, as well as conducting Nb films and the AF interlayer of CSCO (Fig. 3). The resistivity of the Nb/Au interface proved to be low ( ~ 10­12 cm2), which makes a contribution to total resistance R of the heterojunction
R, 700 600 500 400 300 200 100 3 0 50 100 150 200 250 300 T, K 2 1

Fig. 3. Temperature dependence of resistance: 1--no. 612 sample, dM = 20 nm, L2 = 10 â 10 m2; 2--no. 610 sam ple, dM = 40 nm, L2 = 50 â 50 m2; 3--dM/L2 ( is the resistivity) for an autonomous Ca0.5Sr0.5CuO2 film depos ited on the NGO substrate, dM = 40 nm, L2 = 50 â 50 m2.

less than 10­6 [16]. Taking into account the epitaxial growth of the CSCO/YBCO structure and close values of the Fermi velocity in the components, we can assume that resistance RCSCO/YBCO of the interface is low as compared to the resistance of the Au/CSCO interface, for which the difference in the Fermi veloc ities of Au and CSCO is significant. Resistivity mea surements in autonomous CSCO films with x = 0.5 deposited on NGO substrates resulted in high values of resistivity = 103­104 cm2 at low temperatures [14], which gives a contribution to the resistance of the het erojunction of more than 1 k. It should be noted that the (T) dependence for autonomous CSCO films are typical of systems with hopping conductivities, in which ln() = ln(0) + (T0/T)1/4 (0 and T0 are exper imental constants and the exponent is determined by the dimensionality of the system and corresponds to variable range 3D hopping conductivity in our case). However, the R(T) dependences for heterojunctions with small interlayer thicknesses dM < 50 nm do not exhibit an increase in resistance with decreasing T in the temperature range T < Tc, which was observed for autonomous CSCO films. It can be seen from Fig. 3 that the resistances of heterojunctions (curves 1 and 2) weakly depend on temperature and are much lower than the resistance of the CSCO interlayer (curve 3) obtained from the calculation based on the resistivity of the autonomous CSCO film. It was shown in [9] that in spite of weak (on the order of one to two atomic cells) cation diffusion at the interface between cuprates, superconductivity may appear at the metal­ insulator interface in cuprates due to electron rear rangement or nonstoichiometry in oxygen. Theoreti cal analysis of the boundary of a strongly correlated Mott insulator shows [17, 18] that charge percolation from one region to another causes a considerable rear rangement in the electron subsystem, which in partic ular leads to metal type conductivity (most likely, this effect is observed in our case). At the same time, we cannot rule out that transition of thin (dM < 50 nm) CSCO layers to the metal state may be due to oxygen nonstoichiometry of the boundary layer [19], which was observed in [18] upon an increase in the oxygen concentration in growing CSCO films. Due to the
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interaction of boundary oxygen atoms in the CSCO film with the YBCO surface in the heterojunctions studied here, the electron conductivity of thin layers in the CSCO interlayer may change substantially, leading to the observed dM dependence of the heterojunctions in the interval of T < Tc. As a result, for dM < 50 nm, the resistance of heterojunctions is mainly determined by the resistance of the Au/CSCO interface. The contri bution of the resistance of the CSCO interlayer is sub stantial for higher values of dM > 50 nm (see Fig. 3); however, the critical current is strongly suppressed in this case. The characteristic resistance RNS of heterojunc tions (S = L2 is the heterojunction area) measured at T = 4.2 K increases exponentially with dM (Fig. 4). If the main contribution to RNS comes from the inter layer, we would observe the linear growth with dM shown by the dotted curve in Fig. 4. The exponential dependence RNS(dM) may be due to modification of the electric parameters (conductivity) of the CSCO interlayer due to oxygen nonstoichiometry of thin (dM < 50 nm) films [18, 19] or rearrangement of the electron subsystem of the M interlayer [17, 18]. It fol lows from experimental data that the doping level in CSCO at the interface with Au is an exponential func tion of the distance to the source of doping of the YBCO film, which is typical of diffusion processes. Analysis of the electrical conductivity of heterojunc tions at high voltages (up to 100 mV) indicates that their (V) dependences differ from the dependence typical of superconducting contacts with direct con ductivity and are rather close to the dependence typi cal of tunnel type junctions (probably, due to a low transparency of the Au/Ca1­ xSrxCuO2 interface). 4. CRITICAL CURRENT Temperature dependences Ic(T) of the structure with dM < 50 nm follows the temperature dependence of superconducting parameter Nb in the Nb film for structures without AF interlayers [15]. It is noteworthy that no quadratic increase in the critical current with decreasing temperature, which is typical of SNS struc tures, is observed in this case [20]. We did not observe the dependence of the characteristic voltage Vc = IcRN

RNS, cm2 10-1 10 10 10 10
-2 CSCOdM

-3

-4 -5

10-

6

0

20

40

60

80

100 dM, nm

Fig. 4. Dependence of characteristic resistance RNS of heterojunctions on interlayer thickness dM ( ). Resistance of heterojunctions without M interlayer ( ). The bold line shows the exponential dependence RNS(dM) with a char acteristic growth length of 6 ± 1 nm, obtained from statis tical processing of experimental data. Fine lines show the error in determining the characteristic length. The dotted curve is the product of resistivity CSCO of the M interlayer, which was determined from measurements on an autono mous film, by thickness dM.

of the structure (Ic is the critical current and RN is the normal resistance of the heterojunctions) on the thickness of the CSCO interlayer either (see Table 2). It should be noted that in all heterojunctions studied here with a critical current Ic > 1 A, thickness dM amounts to tens of nanometers; i.e., the penetration depth of superconducting correlations in CSCO con siderably exceeds the coherence length of the FeMn polycrystalline AF interlayer, which constitutes a few nanometers [21]. The penetration depth for supercon ducting correlations in CSCO can be estimated from the measurements of the jc(dM) dependence of the superconducting current density on the thickness. Figure 5 shows such experimental data. Statistical processing of the jc(ds) dependence gives the decay depth of the superconducting wavefunction AF = 7 ± 1 nm.

Table 2. Electrophysical parameters of heterostructures at T = 4.2 K Sample no. 269 271 273 274 610 612 Tilt angle of substrate 0 0 11° 11° 0 0 x 0.15 0.15 0.5 0.5 0.5 0.5 dM, nm 50 20 20 50 40 12 L, m 10 10 10 10 50 10 Ic, A 44 50 335 2.5 0.6 202
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RN, 3.4 1.9 0.8 60 93 1.73
No. 2 2010

C, pF 0.65 1.9 2 0.06 ­ 0.55

q 0.2 0.08 0.3 0.13 ­ ­

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2

ZAITSEV et al.

10

2

Hex/kT = 2 10
1

5 10
0

10

ture Tc). The transparency of the barrier associated with the I barrier is regarded as smaller than the trans parency of the M/S interface; consequently, the effect of superconductor S' on the condensate function in the M interlayer can be disregarded. In the case under investigation, the condensate Green function has two components, f ( = ±1), corresponding to opposite spin orientations. Let us analyze the "dirty limit" in which mean free path l is much smaller than the layer thickness and, in addition, Hex 1, where is the time of scattering from impurities. In this case, the iso tropic part of Green function f = s f ­ s satis fies a wave type equation (s 1) xx s ­ k s = 0 ,
2 2

10

-1

(1)
1/2

0

10

20

30

40

50

60 d, nm

in which k = [ 2 ( + i H ex ( x ) ) / D ] , where D is the diffusion coefficient in the F layers = T(2m + 1) is the Matsubara frequency assume that > 0). In the case of AF ordering in layers, the solution for s for 0 < x < dM = Nd (N is number of ferromagnetic layers) can be written in form s ( x ) = A n cosh k ( x ­ x x
n­1 n+1 n­1

Fig. 5. Experimental results on the dependence of the superconducting current density on dM for heterostruc tures with a CSCO interlayer with doping level of x = 0.5 ( ) and for heterostructures without the M interlayer ( ). Dashed lines show the theoretical dependences of the crit ical current on the thickness of the AF interlayer for three values of normalized exchange field Hex/kT = 2, 5, and 10. Theoretical dependences are the normalized critical current density choosing interlayer thickness in accor dance with the condition of best matching of the theory to experiment (AF = 10 nm).

(2) and (we th e the the )

) + B n sinh k ( x ­ x



n­1

< x < xn , cosh k ­ ( x ­ x n )

(3) x < xn + 1 , continuity of we can obtain coefficients: (4)

5. THEORETICAL MODEL To confirm some of the experimental results and analyze the qualitative features of the proximity effect in the heterostructures studied here, let us consider a model of the S'/I/M/S structure with a magnetic mul tilayer M located between two superconductors S and S' (see Fig. 1). In this model, we assume that the M interlayer consists of metallic ferromagnetic (F) layers with a thickness d much larger than the atomic spacing and that the exchange field Hex with antiparallel (or parallel) orientations in adjacent layers lies in the plane of these layers. We also assume that exchange field Hex is much smaller than the Fermi energy. In our calculations, we suppose that S and S' superconduc tors exhibit the s type of superconducting pairing.
1

A

+ B n + 1 sinh k ­ ( x ­ x n ) , x n < where xn = nd. Taking into account the function s and its derivatives for x = xn, the following recurrence relation for the A B
n+1 n+1

=M A n B

n n

, ,

in which matrix M is defined as M = 1 0 0 q cosh sinh sinh cosh (5)

The model considered here can be analyzed using the semiclassical equations for the Green functions (see, for example, [1, 2]). We will also assume that conditions are realized in which the superconducting condensate wavefunction in the region of ferromag netic layers can be treated as small (this is observed for transparency of the M/S boundary that is much smaller than unity at all temperatures or for an arbi trary transparency of the M/S boundary at a tempera ture close to the superconducting transition tempera
1

where q = [( + iHex)/( ­ iHex)]1/2, = kd, and n = (­1)n +1. Taking into account the boundary condition for x = 0, xs(0) = 0, we obtain B 1 = 0. Consequently, introducing the notation
N­1

n=1



M



n

= m ,

ij

(6)

In this section, to simplify calculations, we assume that Boltz mann constant k and Planck constant are equal to unity.

we obtain an expression that follows from formulas (4) and (5) and defines the relation between the values of (symmetric) condensate function for x = 0 and x = dM: s ( 0 ) = c s ( dM ) , (7)
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where c = 1 . 21 m cosh N + m N sinh N
11 N

Eilenberger equation (see, for example, [2]), which can be used to obtain the relation i c ( H ex ) = where W ( H ex ) =
1 S'

Function c connecting the values of the condensate function at the opposite edges of the M interlayer describes the evolution of the condensate Green func tion in the M structure. Analysis of this function shows that in the case of AF ordering of the magnetization in the M interlayer, the condensate Green function can penetrate into the M layer to a depth on the order of N = (D/T)1/2 even if H = (D/Hex)1/2 N, where H is the penetration depth for the condensate func tion in the case of ferromagnetic ordering of magneti zation in the layers. Such a situation is realized when the condition d = dM H holds. For a fixed thickness of the AF interlayer, the proximity effect becomes stronger upon an increase in the number of layers [22]. Thus, in contrast to ferromagnetic ordering, anoma lous long range proximity effect (LRPE) may take place in the case of AF ordering of magnetization in the layers. In contrast to the LRPE predicted in [23] and associated with the emergence of the triplet com ponent of the condensate Green function, which is observed in the case of noncollinear spatially nonuni form magnetization in ferromagnets, the LRPE con sidered here is associated with the singlet component of the condensate Green function. The triplet compo nent decaying in the M interlayer over the same length as the singlet component makes zero contribution to the Josephson current in the structure considered here. Manifestations of the LRPE and other features of the proximity effect in various weak links including structures with an M multilayer with the AF ordering of magnetization were analyzed by one of the authors in [22, 24] and by the authors of [25, 26]. Let us consider LRPE manifestations in structures of the S'/I/M/S type. The expression for the Joseph son current in such a structure with a low transpar ency barrier, which determines the resistance of the structure in the normal state, has the conventional form I = Icsin, where Ic(Hex) is defined by the for mula F ( H ex ) Ic (8) = i c ( H ex ) , Ic 0 F(0) where F ( H ex ) = Re

W ( H ex ) , W(0)

m=0

f

D Re f ( + iH ex, , x = 0 ) d ,

­1

= cos , being the angle between the direction of the momentum and the x axis; f (, , x) is the con densate Green function in the case of a normal inter layer; D is the transparency of the I barrier, and H ex = Hex/N for an odd number N of the layers and H ex = 0 for an even number N. Thus, in the clean limit, ic(Hex)= W(Hex/N)/W(0) for odd N and ic(Hex) = 1 for even N. The characteristic depth at which the ampli tude of function W( H ex ) (as well as of function W(0)) decreases exponentially with increasing dM is deter mined by the value of coherence length for clean limit N = F/T (for T 1). 6. DISCUSSION Figure 5 shows the theoretical dependences (dashed curves) for jc corresponding to three values of normalized exchange field Hex/kT in the F layers of the S'/I/M/S structure with an AF interlayer (N = 20), which were obtained for AF = 10 nm. The theoretical dependences are given for a low transparency of the M/S interface (exceeding the transparency of the I barrier) and identical S and S' superconductors. It should be noted that the form of the theoretical jc(dM) dependences does not change qualitatively in the case of different superconductors. In our experiment, the superconductors are not identical; moreover, the con densate function with the s symmetry in YBCO is not a dominant function. However, for the normalized values of jc(dM) shown in Fig. 5, the condensate Green function for the electrodes does not play an important role and the normalization of theoretical dependences (for AF = 10 nm) was chosen from the condition of best matching between experiment and theory. It can be seen that the theoretical dependence jc(dM) for Hex/kT = 2 describes the experimental data more correctly than the dependences obtained for higher values of Hex/kT. With increasing exchange field Hex, the value of jc decreases and the difference between the values of jc corresponding to even and odd number of F layers becomes more significant. It should be recalled that the radical difference between the Josephson current in S/AF/S junctions with even and odd numbers of layers was predicted earlier in [12], in which the model of an antiferromagnet with atomi cally thin layers was analyzed. The structures contain
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n=0





s+ ( 0 ) fS' ,

fS ' is the condensate function of superconductor S', and Ic0 is the value of the critical current in the struc ture with a normal interlayer (S'/I/N/S) and with the same parameters (thickness, mean free path, and so on) as in the M interlayer. Let us now consider a pure interlayer in which the mean free path exceeds the thickness. In this case, the condensate function in the M interlayer obeys the

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342 ic 1.0 0.8 0.6 0.4 0.2 0 -0.2 0 1 2 10 5 2 3 4 5 10 Hex/kT = 2

ZAITSEV et al.

5 dM/N

Fig. 6. Theoretical dependences of normalized critical current ic on normalized thickness dM/N of the M inter layer for three values of normalized exchange field Hex/kT. Solid curves correspond to the AF interlayer, while dashed curves correspond to the F interlayer.

ing an arbitrary number of ferromagnetic layers (with a thickness much larger than atomic spacing) with AF ordering of magnetization (in particular, the depen dence of transport properties on the number of layers) were analyzed in [22]. Figure 6 shows the theoretical dependences of nor malized critical current ic(dM) (8) of heterojunctions with AF and F ordering of magnetization in the M interlayer. The critical current is normalized to the value of Ic0 observed in S'/I/N/S structures. It can be seen from Fig. 6 that in the case of the F interlayer, a stronger decrease in the value of ic is observed upon an increase in the thickness of the M interlayer, and the shape of the ic(dM) curves changes qualitatively. In par ticular, an increase in dM may induce a transition between the 0 and states of the heterojunctions under investigation. Such a transition was observed in experiments with S/F/S junctions with a single layer F barrier [27]. Note that for our heterojunctions, the condition of the smallness of the thickness d = dM/N H of a layer in the M interlayer is a necessary condi tion for the LRPE [22]. In experiments, the oscillating (containing zero minima) dependence of the critical current in hetero junctions on the external magnetic field [28] and the preserved symmetry of the current­voltage character istics (I­V curves) indicate the homogeneity of the M interlayer. To verify the correspondence of manifesta tion of the nonstationary Josephson effect to the RSJ model criteria [10], we analyzed the I­V characteris tics of heterojunctions under microwave radiation and the behavior of the selective detector response (V). We detected multiple oscillations of the critical cur rent and Shapiro steps; the maximal values of the first

Shapiro step approached the theoretical maximum upon an increase in the normalized frequency fe/fc of microwave radiation, where fc = (2e/h)IcRN. At the same time, a discrepancy with the RSJ model (in par ticular, the formation of fractional Shapiro steps) was observed. It is well known [29, 30] that the mixed (d and s) symmetry of the order parameter of one of the electrodes in the heterojunction facilitates the gen eration of the second harmonic in the dependence of the superconducting current on the phase difference of the waves functions of the electrodes (current­ phase relation, CPR). To find the deviation of this dependence from a sinusoid, we used the method developed earlier and based on the measurement of the amplitudes of the Shapiro steps emerging as a result of synchronization of intrinsic Josephson gener ation by an external monochromatic microwave signal at frequency fe [15]. In the presence of the second har monic on the CPR, fractional Shapiro steps appear in additional to integer Shapiro steps on the I­V curve for Vn = n(h/2e) fe; in particular, for n = 1/2, such steps are formed for voltage V1/2 = (1/2)V1. The experimen tal dependences of the critical current and of the inte ger and fractional steps on the microwave current were compared with the results of calcul