Flux pinning and vortex dynamics in high Tc superconducting films

Flux pinning and vortex dynamics in high Tc superconducting films* V.G. Prokhorov, G.G. Kaminsky, M . A . Kuznetsov and V . M . Pan

Ya.A.

Petrukhno,

A.L.

Kasatkin,

Institute of Metal Physics, 252142, Kiev, Ukraine The field dependences of the critical current, c u r r e n t - v o l t a g e characteristics and a.c. susceptibility have been investigated for superconducting YBa2Cu307 films prepared by laser ablation. It was shown that the flux line pinning in polycrystalline high Tc films occurs due to anisotropy of the superconducting parameters in the case of strong misorientation of adjacent grains and that it is connected with local suppression of the order parameter for smaller misorientation angles. Peculiarities of the resistive state in magnetic fields have led us to suppose that vortex motion occurs preferably along the grain boundaries, which form a network of so-called easy slip channels. Such microstructural features of the tested films lead to the double-peak behaviour of the dissipative part of the a.c. susceptibility.

Keywords: high Tc superconducting films; flux pinning; vortex dynamics

It is well known that the conducting ability of non-ideal type II superconductors in magnetic fields is determined by the peculiarities of their microstructure, i.e. those defects can be attributed to twin planes ~with orientations which can serve as pinning centres for vortex lines in bulk high Tc superconductor (HTSC) materials. These defects can be attributed to twin planes with orientations (110) and (1 10) for Y: 123, oxygen vacancies, dislocation loops, small scale inclusions of second phase YBaCuO5 and CuO, micropores and so on ~. Recently the idea of intrinsic pinning or vortex line pinning in the potential wells between the double CuO2 planes was discussed. A lot of researchers connect the possibility of this effect with the abnormally small value of coherent length ~, which allows the normal core of a vortex line to be localized between the superconducting double CuO2 planes. The main experimental data to prove the existence of this mechanism of pinning are considered to be the strong anisotropy of the critical current on sample rotation in an external magnetic field and the presence of two peaks in the temperature dependence of the dissipative part of the dynamic magnetic susceptibility X " 2,3.

On the other hand, one should not forget that the great majority of HTSC material specimens under investigation have a crystal structure which is far from perfect; and this is especially true for superconducting films, for which the mechanism of growth has proved to be unpredictable in many respects. The most typical defects of the samples are low angle grain boundaries, accumulation of dislocations, inclusion of second phases * Paper presented at the c o n f e r e n c e 'Critical Currents in High T c S u p e r c o n d u c t o r s ' , 2 2 - 24 April 1992, Vienna, Austria OO11 - 2 2 7 5 / 9 3 / 0 5 0 5 1 4 - 0 5 © 1 9 9 3 B u t t e r w o r t h - Heinemann Ltd

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and oxygen vacancies. Even if one succeeds in obtaining practically monocrystalline films with a high degree of texture along the c-axis, the misorientation angle in the a-b plane, as a rule, reaches several degrees. In this paper we try to explain a wide range of experimental results connected to the electrodynamic properties of the HTSC films. We take into account the presence of grain boundaries and similar microstructure defects.

Experimental procedure All measurements were made for YBa2Cu307 films prepared by laser ablation on to SrTiO3 and YSZ substrates. The grain size was (D) --- 5 0 - 1 0 0 nm along the c-axis and about 500 nm in the basal plane. The misorientation (of c-axes) of adjacent grains ranged from 1 - 2 ° up to 30 ° and was controlled by the film deposition conditions. Using a special deposition technique quasi-single crystalline films can also be made. Most of them have low angle grain boundaries (grains correspond to regions of coherent X-ray scattering). The misorientation angle relative to the c-axis does not exceed 0 . 4 - 0 . 5 ° and in the a-b plane its mean value (detected by X-ray analysis) was 4 - 5 ° . The film thickness was d = 200-300 nm. The superconducting transition temperature was Tc = 8 9 - 9 3 K, the transition width was ATc = 1.0-1.5 K and the residual resistivity was Po = p300/p0 -~ 2 . 6 - 3 . 0 . Samples 0 . 3 - 1 . 0 mm wide with 2 - 1 0 mm spacing between potential probes were prepared using the mask technique. The silver contacts were made via vacuum vapour deposition. The critical

Flux pinning and vortex dynamics in HTSC films: V.G. Prokhorov et al. current was assumed to be the value of current which results in a 1 /~V cm-1 sample voltage. The resistive transition curves were measured with a computerized lock-in device using a sequence of rectangular bipolar current pulses (quasi-direct current). The duration of the pulses was ---2.3 ns and the repetition frequency was 20 Hz. The I - V curves were measured in the same way. To reduce sample heating the current pulse duration was ---36 #s and the repetition frequency was = 870 Hz 4. The a.c. susceptibility experiments were performed with a compensated mutual inductance bridge. A primary coil produced an alternating sinusoidal field with an amplitude from hAc = 1 to 100 Oe. The measured frequency ranged between f = 120 and 5000 Hz. Two astatically wound coils were used to register the response of the sample to the time varying magnetic field. The sample was placed within one of these pick-up coils. The in-phase and out-of-phase components of the fundamental of the pick-up coils' voltage, which are proportional to the out-of-phase and in-phase components of the susceptibility (X" and X', respectively), were measured using a lock-in amplifier. With a superconducting magnet it was possible to superimpose a d.c. magnetic field (H < 4 T) on the a.c. field. During all the experiments both the a.c. and d.c. components of the applied magnetic field were perpendicular to the film surface. Measurements were carried out at different magnetic fields (a.c. and d.c.) while the temperature was changed from Tc down to the end of the transition.

Flux pinning anisotropy Figure ] shows the dependences of critical current density on applied magnetic field for two polycrystalline films. For adjacent grains the misorientation angle with respect to the c-axes was O >_ 10 ° in the first film (z~, • ) a n d 0 _ > 1 ° i n t h e s e c o n d o n e ( o , • ) . A s o n e can see, decreasing the misorientation angle results in the strongest Jc(B) dependence at both orientations of the external magnetic field (B _L FS and B II FS). This phenomenon cannot be attributed to the creation of weak links at low values of 0, because the magnitude of critical current density remains sufficiently high at zero magnetic field. Probably, in this case, changes occur in the concentration and efficiency of pinning centres. The anisotropy of Jc(B) behaviour results in the anisotropy of the volume pinning force (see Figure 2) because of three principal features. Firstly, possible anisotropy of the shape of pinning centres; secondly, the influence of the free surface of a film as an extra pinning centre; and thirdly, the intrinsic pinning which is vortex line pinning on CuO2 planes due to local suppression of the superconducting order parameter. It appears that the most probable reason for pinning anisotropy of polycrystalline films is the specific shape of the grains. In reality, the field dependence of the volume pinning force obeys the Fp(B) o¢ b l/2 rule, where b = B/Bc2. As has been noted in references 5 and 6 such Fp(B) behaviour could occur because of flux line pinning at grain boundaries, where the superconducting order parameter is locally suppressed. Moreover, it is worth

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noting that the Fp(b) behaviour is identical for both orientations of applied magnetic field. For intrinsic pinning a direct summation of elementary pinning forces is necessary, since the number of vortices is always less than the number of pinning centres. Moreover, the summation needs to be done over the flux lines and the volume pinning force needs to obey

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Flux pinning and vortex dynamics in HTSC films: V.G. Prokhorov et al.

the standard Fp(b)o¢ b rule (for small values of B). Therefore, by changing the external magnetic field orientation from B .L FS to B UFS the Fp(b) behaviour has to change from b ~/2 to b. However, there is no such cross-over in the experimental Fp(b) dependences. On the other hand, due to the approximate equality of film dimensions (width and thickness) the surface contribution to the net volume pinning force has to be nearly the same for different samples. But, on the contrary, the samples with the highest F~noax values for B II FS have the smallest F~pax values for B _L FS. Thus intrinsic and surface pinning cannot explain the anisotropic behaviour of the volume pinning force. An electron microscopy investigation shows that the samples have a grain structure with grains which are disc-like in shape. The thicknesses of grains were 5-10 times less than the diameters (d II FS). Therefore, the number of plane defects (pinning centres) per unit volume is several times higher for the B II FS orientation than for the B _L FS one. We should take into account that 7

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where N is the number of planes (grain boundaries), fp is the elementary pinning force and ao is the flux line lattice period. This equation agrees with the data obtained for samples with the smallest c misorientation angles, when the fp value does not depend upon the field orientation and the ao value is constant (and is that corresponding to B = Bm when Fp = Fp ax at B .L FS). For example, for sample 2 in Figure 2 the misorientation angle was --- 1 - 2 °. An increase of this angle for adjacent grains results in their spheroidization (ball-like structure) and in a lowering of the anisotropy of the volume pinning force (sample 1 in Figure 2). For the quasi-single crystal films the field dependence of the volume pinning force in the low field region is: Fp o¢ b3/4(1- b) 2. Such a dependence for Fp(b) has been determined in the so-called insulate vortex limit 8"9. It has been obtained for the interaction of vortex lines with planar crystal defects in traditional superconductors. Thus, there are grain boundaries in quasi-single crystal films, too. Due to misorientation of neighbouring grains in the a-b plane these boundaries can serve as pinning centres for vortex lines. Probably in this case the Welch concept ~°, based on space changes in the GL parameter Ar(r)/r, is valid. In polycrystalline samples with strong c-axis misorientation the mechanism of vortex line pinning is quite different.

creep). Then the power dependence follows

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We have shown earlier ~2 that in the low field region pf(B) o~B 1/2 and the Bardeen-Stephen model is unusable. The field dependence of Of can be explained by assuming that the vortices move along onedimensional ESC rather than within the whole volume. Since these channels are not identical there is some distribution of pinning forces and critical currents. An increase of transport current causes an increase of the amount of effective channels. For the I - V curve we can write

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In previous publications ll'12 it was shown that the main peculiarities in HTSC film electrodynamics are due to the creation of easy slip channels (ESC). On the grain boundaries the superconducting order parameter is locally suppressed and the activation energy of vortex lines is less than in the rest of the sample volume. Thus, the channels are formed along planar defects. The non-linear (almost exponential) part is the main feature of I - V curves at low electric fields (usual for

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Flux pinning and vortex dynamics in HTSC films: V.G. Prokhorov et al.

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2 [J~2(B) - J~, (B)] J~t and J~2 are the minimum and maximum values of critical current in a channel. Equation (5) corresponds to the experimental data when J~t -- J~ and n(T, B) = 2. It is worth noting that similar results have been obtained for conventional type II superconductors ~5. In the suggested model of ESC the Re(B) and J~(B) dependences determine the field dependence of the parameter o~ [see Equation (2)]. In the low field region Rf oc B ~n and in the higher field region R e oc B, but the vortex motion in the one-dimensional ESC can change the field dependence of the critical current. In reality, at low magnetic field the number of pinning centres always exceeds the number of vortex lines. Thus, we can consider the single vortex line to be an isolated one. Summation over all the elementary pinning forces fp can be made along the single vortex lines and Fp =fpnf = fp/a2o, where nf is the concentration of vortex lines and a o is the lattice constant. When all vortices move under the Lorentz force, Jc (B) = Fp/B = fp/4~o. Therefore the behaviour of the Jc(B) dependence is determined by the fp(B) behaviour. If the neighbouring vortices do not overlap, the elementary pinning force has almost no field dependence. Taking into account that the vortices move through ESC, one can write that Fp =fp/aoW and Jc oc B -~/2, where w is the width of a channel. Thus, for both types of vortex motion, through ESC and the bulk material, the dependence of parameter o~on the field is the same, ot o¢ B, but there is a dimensional cross-over of J~(B). The experimental data in Figure 3 support these conclusions. With the framework of the ESC model one can explain the drastic fall of the Jc(B) dependence in the initial section that has often been observed in experiments 6.

Temperature dependence of a.c. susceptibility Despite there being many studies of the a.c. susceptibility 16'17, the nature of the peak which appears on the X"(T) curves at the superconducting transition is not clear. The most popular point of view is that the location of the peak precisely corresponds to T~rr (the irreversibility temperature) ~'16. That is, the maximum of the curve is a transition point from the pinned state to the flux flow state of the superconductor. Some workers 18.19attribute this phenomenon to melting of the vortex lattice. The discovery of the two peak behaviour of X"(T) of HTSC films and single crystals has made interpretation of the experimental data somewhat more difficult. Unlike for ceramic specimens, the low temperature peak weakly depends on magnetic field. This is why we cannot use Clem s model 2° based on weakly coupled grains, since this model describes only granular systems. The inset in Figure 4 shows typical X"(T) curves with two peaks for the dissipative part of the susceptibility. The magnitude of the high temperature peak (Tm0 can be either lower or higher than the magnitude of the low temperature one (Tin2). At high d.c. values of external magnetic field both peaks become a single wide peak on the X"(T) curve. From Figure 4 it is also clear that the Tin, and Tin2

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peaks have a similar field dependence. At B <_ B* one can observe a rapid fall of the T,,/Tc ratio and at B >_ B* the Tm(B) dependence becomes weaker. Similar dependences have been observed in previous work 16. The (1 - tm) versus B dependences are shown in Figure 5, where t m = T m / T c. The formula 1 t oc n q, where q = 0.2, holds true for both peaks. It is worth noting that the power q appears to be significantly lower than in previous work 16. We can explain this fact by taking into account that we used a higher amplitude of a.c. magnetic field (hAc = 10 Oe). In addition, note that the value of q is very sensitive to the microstructure peculiarities of the films. For some specimens the value of q was = 1. As a rule, an increase of frequency of hnc shifts the peaks in the higher temperature region of the X"(7)

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Flux pinning and vortex dynamics in HTSC films: V.G. Prokhorov et al.

curve. Moreover, the effect is strongest in the highest field region when the frequency changes from 124 Hz to 1 kHz. At higher frequencies the Tm has no frequency dependence. The small magnitude of this effect and the large experimental error mean that we still cannot determine the exact shape of Tm([). Recently several groups 3,2~ reported the double peak behaviour of x"(T) of single crystals of Y:123 at intermediate orientations of the a.c. magnetic field with respect to the c and a-b crystallographic directions. Thus, inhomogeneity of specimens is the simplest explanation for the two peaks on the dissipative part of the a.c. susceptibility, i.e. the presence of a-orientated regions in c-orientated films and vice versa. In a magnetic field the peaks of x"(T) must shift with respect to one another at different orientations of the single crystals 3. Yet, in this case, it is unclear why the Tm~(B) and Tm2(B) dependences are identical, while the (dHc2/dl)/Tc value is strongly anisotropic. As specimens we also used polycrystalline films of Nb with widths = 500 nm and a mean grain size cx 100 nm. In Figure 6 we show the x"(T) characteristics, with the double peak. In order to obtain such characteristics it was necessary to keep the films in the atmosphere for a long time. The Tm(B) dependences of both peaks were the same in a wide range of magnetic fields and were similar to those of the YBa2Cu307 films. The B * = 0 . 1 - 0 . 2 T value corresponds to the one for HTSC samples. The grain boundaries are the main peculiarities of the Nb films. In the pure Nb films, where the grain boundaries are not oxidized, there is only a single narrow peak. Thus, one can suppose that the nature of the double peak behaviour is the same for low and high temperature films. This is determined by the microstructure of the samples. In both cases the grain boundaries can form the ESC due to local suppression of the superconducting order parameter. We will give a more detailed theoretical background in future publications.

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a.c. response: test for intrinsic pinning, in: Proc Int Workshop on Critical Current Limitations in HTSC (Eds Baran, M., Gorzkowski, W. and Szymczak, H.) World Scientific, Singapore (1992) 62-79 Prokhorov, V.G. and Kuznetsov, M.A. InvestigatiOn of I - V characterstics of the YBa2Cu307 films by pulse method Supercond Phys Chem Techn (Russia) (1991) 4 1929-1934 Matsushita, T., Iwakuma, M., Sudo, Y. et aft. Estimate of attainable critical current density in superconducting YBa2Cu3OT-x J Appl Phys (1987) 26 1424-1426 Pan, V.M., Gaponov, S.V., Kaminski, G.G. et al. Current carrying ability of YBa2CuaO7-x: high magnetic field influence Cryogenics (1989) 29 392-396 Pruymboom, A. and Kes, P.H. Elementary pinning force of grain boundaries Jpn J Appl Phys (1987) 26 1493-1494

8 Pruymboom, A., Hoodert, W.H., Zandbergen, H.W. and Kes, P.H. Grain boundary pinning in polycrystalline NbN films Jpn JAppl Phys (1987) 26 1531 - 1532 9 Prokhorov, V.G., Basul, B.A. and Kaminsky, G.G. Investigation ,of the d-pair mechanisms of pinning stabe in niobium films Fiz Niz Temp (Soy) (1991) 17 711-717 10 Welch, D.O. An approximate closed-form for the electronscattering-induced interaction between magnetic flux lines and grain boundaries 1EEE Trans Magn (1985) MAG-21 827-830

l 1 Pan, V.M., Prokhorov, V.G., Kasatkin, A.L. and Tretiatchenko,

Conclusions 12

The experimental results reveal that in the dynamic mixed state of HTSC the spatial anisotropy of the superconducting order parameter plays an important role (at least in the high temperature region). Analysis of these results allows us to propose the origin of the ESC. These channels are formed along the grain boundaries, where the superconducting order parameter is locally suppressed. The grain boundaries can be pinning centres for vortices located within the grains and, simultaneously, ESC for those located in the boundaries of the grains.

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References 1 Kes, P.H. Vortex pinning and creep experiments, in: Proc Syrup Phenomenology and Applications of High Temperature Superconductors Los Alamos, New Mexico, USA (1991) 2 Walkenhorst, A., Tome-Rose, G., Schmitt, M. et al. Thermally activated flux flow and anisotropy of the pinning force density in epitaxially grown YBa(CUl_xZnx)307 thin films, in: Proc lnt Workshop on Critical Current Limitations in HTSC (Eds Baran, M., Gorzkowski, W. and Szymczak, H.) World Scientific, Singapore (1992) 360-365

3 Krusin-EIbaum, L., Civale, L., Worthington, T.K. and Hoitzberg, F. Critical currents and angular dependence in magnetic

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C.G. Influence of planar defects on mixed state dynamics of high-To epitaxial films Physica C (1991) 180 199-202 Pan, V.M., Kaminsky, G.G., Kasatkin, A.L. et al. Structure and flux flow in thin YBa2Cu307 films Supercond Sci Technol (1992) 5 s48 - s54 W6nderweber, R. and Abd-EI-Hamed, M.O. Interpretation of I - V characteristics measured on epitaxially grown thin films of YBa2Cu307 Supercond Sci Technol (1992) 5 s113-sl 16 Sehindler, W., van Hasselt, P. et aL Critical current density and pinning potential in YBazCu307 single crystals and epitaxial thin films after fast neutron irradiation Supercond Sci Technol (1992) 5 s129-s132 Pan, V.M., Prokhorov, V.G., Kaminsky, G.G. et al. Influence of pins on the dynamical mixed state in superconducting films IEEE Trans Magn (1987) MAG-23 1440-1443 Emmen, J., Stollman, G.M. and De Junge, W. Frequency and field dependence of the irreversibility line in a YBa2Cu307-~ film Physica C (1990) 169 418-424 Loegel, B., Bolmaik, D. and Mehdaouj, A. The influence of thermal treatments, fabrication methods and shapes on the magnetic transition of high temperature superconducting compounds Physica C (1991) 179 15-21 Fisher, M.D.A. Vortex-glass superconductivity: a possible new phase in bulk high-T~ oxides Phys Rev Lett (1989) 62 1415-1418 Davis, L., Beasly, M. and Scalapino, D. Kosterlitz-Thouless transition in high-To superconductor films Phys Rev (1990) 42 99-104 Clem, J.R. Granular and superconducting-glass properties of the high-To superconductors Physica C (1988) 153/155 50-55 De la Cruz, F. and Durdn, C. Magnetic flux in high-To superconductors: thermal effects Supercond Sci Technol (1992) 5 s9-s14