Si multilayers

NanoShuctured

Pergamon PII SO9659773(99)00146-4

Materials,

Vol.

12, pp. 409412, 1999 Elsevier Science Ltd 0 1999 Acta Metallurgica Inc. Printed in the USA. All rights reserved 096%9773/99/$-&front matter

SUPERCONDUCTIVITY REE NTRANCE IN STRONG MAGNETIC FIELDS IN MO/S1 MULTILAYERS. N.Ya.Fogel, M.Yu.Mikhailov, OLYuzephovich, Yu.V.Bomze. B.Verkin Institute for Low Temperature Physics and Engineering, 47 Lenin Avenue, 3 10164 Kharkov, Ukraine. E-mail: fogel@ilt. kharkov. ua Abstract - Novel reentrance phenomenon is discovered on MoBi multilayers which occurs in parallel to the layers and slightly inclined magnetic fields. This effect may be explained in terms of the intrinsic pinning and vortex lattice (XL) commensurability with underlying layered structure. The locations of the zero resistance regions correspond to the stable VL configurations or to the transitions between two commensurate lattices. It is suggested that resistive method may be used as a new tool of the VL structure study in layered superconductors. 01999 Acta Metallurgica Inc.

INTRODUCTION Vortex lattice (VL) structure in layered superconductors differs essentially from the simple triangular one observed in homogeneous type II superconductors, unless the magnetic field H is parallel to the c axis. Different type arrangements of VL are predicted theoretically for the cases when magnetic field is parallel or inclined to the layer planes. Different theoretical approaches including anisotropic 3D London and Ginzburg-Landau (GL) models, as well as the Lawrence-Don&h (LD) model were used (l-8). According to the results of Ref.1 obtained within the London approximation, the unit cell of the VL should be strongly distorted with respect to the equilateral triangle, and VL parameters should depend intrinsically on the anisotropy parameter ~-(1M/m)‘” and the angle between H and anisotropy axis. Here M is the effective mass along c, m is the in-plane mass. The commensurability effect has been outside the scope of this work. The latter was considered in the paper (2) of Ivlev, Kopnin and Pokrovsky (IKP). It was shown that in the case of HII, when the intrinsic pinning energy Er exceeds the elastic energy of a VL shear deformation Eel, the vortices cannot cross the layers, period 20 along c is fixed and it is determined by the initial conditions under which VL was formed. This means that VL should be always commensurable with the layered structure period s at any H values (the distance between vortices in the direction normal to the layers ZO=Ns, N is an integer). In the opposite limit case VL parameters are determined by the applied magnetic field. It was shown that the free energy of the rhombic lattice in the commensurate state as a function of H displays two minima corresponding to the different orientations of the unit cell vectors with respect to the layer planes. In the instability region there is a lot of metastable states corresponding to the different displacements of the vortex rows relative to each other in the neighboring interlayers (2,3). They can be 409

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dynamically accessible at the H variation (4). In the framework of LD approach for relatively high parallel magnetic fields a sequence of the first-order phase transitions between VLs with different N is predicted (4). For the tilted fields many versions of the vortex arrangement are suggested (5-7). The most exotic among possible VL configurations in the tilted magnetic fields is so-named combined lattice consisting of two vortex “species” oriented in different directions (5,6). Obviously, due to the nonstandard VL structure and intrinsic pinning many unusual effects can arise in layered superconductors. In the tilted fields the direction of magnetization vector M in many cases does not coincide with the external field direction (1,7). In parallel magnetic fields the critical current should be an oscillating function of magnetic field (8). EXPERIMENTAL

DATA AND DISCUSSION.

The experiments have been carried out on two Mo/Si multilayered samples: sample A with MO layer thickness dMO=22A and Si layer thickness dS,=34k sample B with the same dMO value and dsi value of 44A. The number of bilayers in the both samples is 50. The sample preparation and characterization are described in Ref.9. The sample wavelength and individual layer thicknesses are determined from small angle X-ray diffractometry. At all orientations of H with respect to the layers the transport current I directed along the layers was always perpendicular to H. The precision of H alignment with the layer planes was about 0.2”. In Fig. la the resistance as a function of N at different temperatures for the angle &O is shown for sample A (&O for H parallel to the layers). Beginning from some reduced 1.5 temperature (PO.96) on R vs H curve a step appears which develops at lower temperatures 1 .o into a minimum. At further T diminishing instead of R minimum the zero resistance 0.5 region appears which manifests reentrance of superconductivity. After ZRR at still larger E 0’ O fields resistance appears again. As we keep rr IO going down in temperature, the ZRR becomes wider. For understanding the reentrance phenomenon scale it should be mentioned that normaI resistance of sample A is 42.4 Ohm. 5 Resistance as a function of Hi, for another sample is shown in Fig. lb. Reentrance behavior is very sensitive to 0 0 1 2 3 the deviation of H orientation from parallel to I-A T the layer planes (Fig.2). The R minima are observed until some critical angle B,,. Fig. 1. Resistance as a function of parallel Reentrance phenomenon is also magnetic field at diferent reduced sensitive to the magnetic history. When one temperatures t=T/T, for sample A (a) and begins measurements with the first switching sample B (b). The arrows show values of H, on of H sweep at sufficiently low temperature, and H, (see the text).

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1,o

E o,a 6 ‘2 0,M

E 6 ti 0,5

0,Ol n

0 0

1

2

3

4

5

6

H, T

Fig.2. Resistance as a function of magnetic field for diflerent its orientations with respect to the layer planes for sample A.

-0

1

2

3

4

5

NT

Fig.3. Resistance as a function of Hi, at the diferent temperatures for sample A for a case when at t=0.882 the sample was in a virgin state. Thick arrows show values of H, thin vertical ones mark additional features of R vs H curves described in the text.

another realization of R vs H curves may be obtained on the same sample (Fig.3). In this case two ranges of ZRR are observed, i.e. reentrance of superconductivity arises twice 23 during one magnetic field sweep. I ‘.I I;R The natural assumption explaining appearance 0.03 2.0 J + : of reentrance is connected with nonmonotonic -; , . I dependence of the critical current I, on magnetic . : (1) f 1,5 HS,N=l :’ field. The measurements of 1, vs H dependences Eo,oz t 1.0: confrm this supposition as Fig.4 shows. 6 s Positions of the minima on R vs H curve d 0.5 coincide with locations of the maxima on 1, vs H curve, and vice versa For the interpretation of / 080 . M.93 . the data obtained let us, first of all, determine 0 A I I I , I I I I I I -0,s physical meaning of the temperature T0 where 0 0,5 1,o I,5 2,0 2,5 3,0 the signs of developing ZRR states appear. It H, T follows from the experimental data that Fig.4. I, and R as a function of beginning from this temperature transverse magnetic field for sample A (0 = 0 “), coherence length &(7’,) becomes equal to or less than s/Z, i.e. below T0 the confinement of the vortex cores between superconducting layers starts to develop. In this situation intrinsic pinning should become more pronounced, and transition to the limit &>&I may be expected. Thus, T0 manifests by itself the transition to the regime of strong layering (2). Among a large variety of possible VL configurations proposed theoretically there are arrangements corresponding to the commensurate lattices. When E,>>E,I the lattice should be commensurate with SL wavelength at all magnetic field values (2). According to IKP the stable states of the commensurate lattices correspond to the conditions: p=?&,p=n& HI

rI ’

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Here p is a reduced magnetic field:

Using formulae [ 11, [2] one can define H, values corresponding to the stable states (i.e. to the free energy minima) for different commensurability orders. The anisotropy parameter y is equal to 11.8 and 23.5 for samples A and B respectively. It appears that two calculated values of H, for N=l get in the both ZRR ranges for sample A (these values are shown by thick arrows in Fig.3). The same situation is observed for sample B (Fig. lb). Beside the stable VL configurations rather different VL states may exist which are dynamically accessible at the magnetic field variation (2,3). Under the conditions of strong pinning shear instability of the commensurate lattice leads to the breaking of symmetry: neighboring vortex chains locked between superconducting layers may be shifted one relative to another (3). A lot of these “shifted” lattices correspond to the metastable states, i.e. to the local minima of free energy. One may believe that metastable states of VL may be probed in dynamic experiments, i.e. by resistive or critical current measurements. We suggest that a number of additional features observed on R vs H curves along with the main minima (in particular, like steps; see thin arrows in Fig.3), may be an evidence of these metastable states. The predictions about VL structure in layered superconductors obtained in the paper of Bulaevskii and Clem (4) (BC) in the framework of LD model are rather different from those obtained on the base of 3D anisotropic London or GL approach. The series of the phase transitions between different commensurate phases should occur at definite magnetic field values H,. For this effect the value of the characteristic field H,=OO/$ where Josephson cores of the vortices begin to overlap is essential. For sample A the transition between commensurate phases corresponding to .&,=s and &=2s should occur in the field HI-H0/3=1.84T, while the next transition in the field HrH0/8=0.69T. The position of the minima in Fig.la is just consistent with the field HI estimated above. However, at the field close to Hz=O.69T there is only a peculiarity on the derivative dR/dH. It is rather puzzling that in spite of the differences in the approach and predictions of GL and LD models, one can find on the same sample the patterns corresponding to the both scenarios in the same range of magnetic fields. Further experiments are needed for understand the correlation between VL initial state and the preferable scenario. 1. 2. 3. 4. 5. 6.

Campbell, J., Doria, M.M. andKogan, V.G., Phys.Rev.B, 38,2439, 1988. Ivlev, B.I., Kopnin, N.B. and Pokrovsky, V.L., J.Low Temp.Phys, SO, 187, 1990. Levitov, L.S..Phys.Rev.Lett.,66,224, 1991. Bulaevskii, L. and Clem, J.R., Phys.Rev.B., 44, 10234, 1991. Bulaevskii, L.N., Ledvij, M. and Kogan, V.G., Phys.Rev.B, 46,366, 1992. Daemen, L.L., Campbell, L. J., Simonov, A.Yu. and Kogan, V.G., Phys.Rev.Left., 70, 2948,1993.

Grishin, A.M., Martinovich, A.Yu., Yampol’skii, S.V., Zh.Eksp.Teor.Fiz. ,30,1930, 1990. Ami, S. and Maki, K., Progr. Theor.Phys., 53, 1, 1975. 9. Fogel, N.Ya., Buchstab, E.I., Pokhila, A.S., Erenburg, A.I. and Langer, V., Phys.Rev.B, 53,71, 1996.

7. 8.