Resistive transition of crystalline Y1Ba2Cu3O7−x in magnetic fields

Resistive transition of crystalline Y,Ba2Cu307.xin magnetic fields T.K. Worthington, F.H. Holtzberg and C.A. Feild IBM, Thomas J. Watson Research Center, PO Box 218, Yorktown Heights, NY 10598, USA Transport and a.c. susceptibility data on a crystalline sample of Y1Ba2Cu307-x in fields up to 9 T along the c-axis are presented. Careful study of the I - V curves and the frequency dependent a.c. susceptibility indicate that the critical current develops suddenly at a line in the H - T phase diagram that coincides with the irreversibility line as measured by a.c. susceptibility. Above this line, which is interpreted as the melting of a pinned vortex regime, the I - V curves are linear and the resistance has a flux flow like character. However, the R versus T behaviour in the melted region supports the interpretation of two different regions of flux flow viscosity.

Keywords: critical currents; Y - B a - C u - O compounds; resistive transition

One of the few anomalous superconducting properties of Y1Ba2CuaO7_x is the observation that the resistive transition broadens significantly in a magnetic field. Grain boundary effects and the anisotropy in He2 clearly affected the earliest work I but the broadening is also observed in crystals2. There have been numerous attempts to explain the effect in terms of flux creep 3, flux flow4 and fluctuations5, but none of these approaches alone has been completely successful. Recent experiments indicate that the reversible (dia)magnetization develops at a line well above the zero resistance line6 [ for the remainder of this paper this line will be referred to as the mean field transition, /-/~2(T)] and well above theoretical predictions of the vortex lattice melting line 7. Mechanical measurements s also indicate that the melting line occurs significantly below H°(T). This paper presents transport and a.c. susceptibility measurements on a crystalline sample of YIBaECU307_x with fields of 0 - 9 T applied along the crystalline c-axis. These measurements support the viewpoint that the vortices move in an unpinned, viscous fashion in a temperature region below H°(T) and that there is a transition to a pinned regime at a well defined melting line in the H - T phase diagram. The transport data are compared with frequency dependent a.c. susceptibility data taken on the same crystal; the comparison suggests that thermally activated flux creep takes place below this line. The resistance data in the vortex liquid region indicate the existence of two separate vortex liquid regimes.

Experimental results The sample for these experiments is a 1.4 x 0.8 × 0.025 mm platelet of YiBa2Cu307_x 9. The current contacts were formed by mounting the crystal in a thermal evaporator with one of the 0.8 × 0.025 mm faces exposed

and cutting off the end of the crystal with a razor blade while evaporating gold. After repeating this process on the other end of the crystal, a 1.4 x 0.8 nun face was masked with aluminium foil and four gold pads were evaporated. The pads at the ends of the crystal made contact with the gold that had been evaporated onto the cut surfaces. The spacing between the voltage probes was 0.5 mm. After patterning, the crystal was glued onto a sapphire wafer. Gold wires were attached to the gold pads with silver epoxy. This produced current contacts with very low resistance ( < 0.1 fl) and voltage contacts with a few ohms resistance. This technique gives very low contact resistance without heating the crystal above 150°C. The sapphire wafer was mounted with grease on a copper plate containing a platinum thermometer and heater in a variable temperature flow cryostat inside a 9 T superconducting magnet. The gas flow temperature was maintained at 60 K and the temperature of the sample was controlled with a heater on the copper block and measured with the platinum thermometer. The temperatures in Figure 7 are corrected for the magnetoresistance of the thermometer 1°. The correction is ---.0.5 K at 9 T. The transport measurements were made using a Keithley 220 current source and a Keithley 181 voltmeter. For each measurement the voltage was measured for plus and minus current directions. Figure 1 shows the resistance versus temperature at several fields up to 9 T. The zero field point is actually 50 G and the nominal zero resistance temperature is 93.0 K. The zero field resistance shows the canonical straight line behaviour at high temperature. These curves show the often observed shoulder, which is increasingly evident at higher fields, at ~ 3 0 % of the normal state resistance. Previously it has been argued that this represents a cross-over from flux flow to flux creep behaviourtl; however the I - V curves indicate that this cross-over occurs at lower resistance levels.

0011-2275/90/050417-05 © 1990 Butterworth & Co (Publishers) Ltd

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resistance of one of the coils was monitored. At low frequency ( < 2000 Hz) one of the coils was used to generate a small a.c. field and the second coil was used with a lockin amplifier as a detector. The applied field in both experiments was ~ 10.50e. Figure 6 shows field dependence of the peak in X" at 0.5 MHz, along with the field dependence of the onset of the critical current. On this plot an estimate has been sketched in for H°(T) and the temperature dependence of the shoulder in the R - T behaviour. Figure 7 shows the frequency dependence of the X" peak at 7 T. There are two novel features of these data. First, the sudden onset of non-linearity in I - V along the same irreversibility line measured by a.c. susceptibility. Above this line in the H - T diagram shown in Figure 6, the I - V curves are strictly linear within the experimental accuracy. The second is the shoulder in tht=~R - T data which occurs entirely within the linear I - V regime. The high current differential resistance indicates that this behaviour continues into the pinned regime. Discussion

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point 6. Here, the Bardeen-Stephen model 2 which features a simple temperature indpendent viscosity has been used to evaluate the resistance in this regime H R= R,(T) - H~2(T) A value of 2.4 T K-' for dHc2/dT has been used which seems to describe the behaviour of the crystals 1~. In Figure 5 the extrapolation of the normal state resistance has been plotted from a fit to the data above 150 K and an estimate of the Bardeen-Stephen flux flow resistance, assuming a transition temperature of 90.33 K in 7 T. The point where the normal state resistance and the flux flow resistance meet is Tc(H). The qualitative agreement between the simple flux flow model and the data is very good. Above the mean field transition, the difference between the measured resistance and the extrapolated normal state resistance has been interpreted in terms of a fluctuation enhanced conductivity 13. The results of this analysis yield values of the coherence length which are in good agreement with magnetization 6. Although it has not been calculated, it is plausible to assume that the fluctuations continue to

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Resistive transition of Y1Ba2Cu307_x: T.K. Worthington et al. enhance the conductivity below the transition. As the temperature is decreased, the fluctuations become less important and the resistance merges into the flux flow region. There have been more detailed calculations of the flux flow resistance, which may be necessary to describe the behaviour near Tc14; however, because of their complexity and the complication of fluctuation effects near H ° ( T ) no attempt will be made to perform a quantitative comparison in this paper. The data, however, diverge from the Bardeen-Stephen value below ~ 83 K in 7 T, yet the I - V curves remain strictly linear until the sudden onset of a critical current at 80.4 K. The linear I - V curves and the upward curvature of R versus T in this region suggest viscous flux motion but with an increased viscosity. A possible cause for this increased viscosity will be discussed later. At a well defined temperature there is a dramatic change in the I - V curves from linear to non-linear behaviour. This change seems most naturally described as the onset of a critical current intercept in the I - V curves, as defined by the straight line extrapolation of the data at high currents. The authors contend that this line represents an indication of the melting of a pinned flux phase. In the absence of any pinning, it is expected that there would be a melting transition from a flux liquid phase to a flux lattice 7. Furthermore, this transition should take place significantly below H ° ( T ) because of the large K and effective mass anisotropy in this material. However, pinning is important, even in high quality crystals, as is evident from the large critical current at low temperatures 15. The pinning potential develops at the mean field transition; however, in the vortex liquid regime the pins will not support a critical current because the unpinned lines can flow around the pinned lines. Although true long range crystalline order is not expected if pinning is present 16 , at the unpinned system s lattice melting temperature, local crystalline order and a shear modulus develop, allowing pinned vortices to hold unpinned vortices in place. This leads to the strong nonlinearity in the I - V curves and the offset critical current. The a.c. susceptibility results also support this contention. In previous papers 17'18 it has been argued that the a.c. susceptibility transition is an indication of the onset of a critical current which screens the vortices from the a.c. field. The coincidence of the a.c. susceptibility transition and the onset of the transport critical current shown in Figure 6, indicates that this is a very homogeneous sample. Since a vortex liquid does not support a critical current, the a.c. susceptibility transition also indicates the melting line. The field dependence of the a.c. susceptibility line in this crystal is H oc (1 - T c / T ) 1"33, as has been observed in other crystals by the present authors ~9 and by others 2°, whereas Houghton et al. 7 predict a (1 - To~ T) 2 behaviour near To. Gammel et al. 8 report a linear field dependence above 1.5 T. The fact that they cannot observe the mechanically induced melting at low field makes it difficult to confirm that these methods measure the same transition. The nature of the pinned regime in this sample is not clear. Two possibilities will be examined: A n d e r s o n Kim 2j flux creep, where the thermal activation of single flux lines over a pinning barrier implies a linear I - V region at low current for all non-zero temperatures; and Fisher's 22 vortex glass model, which predicts that due to frustration between the pinning sites and the flux lattice

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a glass state will exist below the melting line with zero linear resistance at low current. The flux creep model predicts that the I - V curves will remain linear at low current at all temperatures with, however, an exponentially vanishing slope. No such region was observed in this sample. Figure 3b demonstrates that after the I - V curve develops downward curvature, there is no indication of a return to linearity at low current; however, it is possible that the I - V curves become linear again below the experimental resolution. It can also be asked whether the current data are consistent with a cross-over between flux flow and flux creep. One theoretical model which may be applicable is the Ambegaokar- Halperin ( A - H ) treatment of thermal noise in Josephson junctions z3. This model involves solving the Brownian motion of a particle for a tilted sinusoidal potential. The A - H model predicts that the I - V curves should become linear at high current, ie. they should extrapolate through the origin. Additionally, the derivative of the I - V curves should show a maximum and then approach a constant value from above. These features have been observed in experiments on traditional superconductors 23. The present data do not show this behaviour, as is evident from the plot of dV/dI shown in Figure 3b. However, more data over a wider current and temperature range are needed to conclusively state that this model is not applicable. Fisher has calculated that in the presence of strong random pinning the melting transition will be a second order transition into a vortex glass phase 22. There is strong evidence of this transition in a thin film of Y]Ba2Cu307_x 25. The signature of such a transition is that as the temperature is decreased, the I - V curves change from linear to a single power law (n = 2.9 in films) at the glass transition, followed by downward curvature in the I - V curves as the resistance at low current drops exponentially to zero. The range of temperature over which this transition occurs will depend on the density of pinning defects in the sample. There is no indication of such scaling behaviour in this sample. However, the lower value of the critical current at low temperature in these crystals as compared to films z6 suggests that the pinning is weaker or less dense in the crystals. In the limit of no pinning whatsoever, the lattice melting transition is presumably first order, so that in the cleaner crystals the second order nature of the transition might be more difficult to observe. Aic. susceptibility provides another probe that can be used to study flux motion. The flux creep model predicts that the frequency dependence should follow

f oc e-U/kT where U is the pinning potential. In the vortex glass model it is expected that the frequency dependence should follow f oc (T - Tg)"(z+2-d) above the glass transition, with v(z + 2 - d) ~ 6.5 observed in films. Both the above behaviour patterns have been observed in other samples. The flux creep model seems to hold over a wide range of frequency and temperature in (Bi,Sr)4CUOx with a Tc of 11 K 27, and the vortex glass behaviour has been observed in films of Y]Ba2Cu307_x 28. The fact that the a.c. susceptibility

Resistive transition of Y1ea2Cu307_x" T.K. Worthington et ai. transition at low frequency take plate significantly below the onset of the critical current suggests flux creep as the correct description; however, to probe this region it is important that the experiment be carried out in the low current limit. A simple Bean 29 critical state model implies that for this sample, at 0 . 5 0 e applied field, 10 A c m -2 (2 mA) is required to shield the interior

from the a.c. field. Figure 4 indicates that this is not in the low current limit near the transition. Lower applied fields will be necessary to allow frequency dependent a.c. susceptibility to distinguish these models. In summary, the data on this crystal do not allow one to distinguish between these two models of the pinned phase; however, in either case there is a sharp transition at the melting line from a vortex liquid to a pinned regime, marked by the simultaneous appearance o f non-linearity in the I - V curves and the a.c. susceptibility transition. The shoulder in the R versus T curves remains an unexplained feature. This behaviour occurs significantly above the onset of the critical current and the I - V curves in this region are strictly linear within the experimental accuracy. This feature also occurs well above the a.c. susceptibility transition. The extracted values for differential resistance at high currents continue this behaviour into the region where the critical current becomes established, suggesting that this behaviour is associated with viscous flow rather than the beginning of pinned behaviour. Marcbetti and Nelson3°~ave recently proposed that there are two distinct regions in the vortex liquid regime; an entangled isotropic region at high temperature followed by a hexatic region, just above the melting line, where orientational order is established. In the hexatic region, the torsional rigidity of the flux lines would increase the effective viscosity 3f, leading to the observed decrease in resistance. What understanding can be drawn from this data? Clearly, no single physical picture is adequate to explain the broadening of the resistive transition in a magnetic field. There are four regions which have been labelled in the phase diagram in F i g u r e 6 f a region on both sides of the thermodynamic transition where the behaviour is dominated by fluctuations (F), two vortex liquid regions, which have tentatively been labelled isotropic (I) and hexatic (H), and a pinned frozen phase (P).

Acknowledgements It is a pleasure to acknowledge many helpful discussions with A.P. Malozemoff, M.P.A. Fisher, R.H. Koch and M.C. Marchetti. The authors would also like to thank M. McElfresh for his help in the struggle to develop the technique for producing low resistance contacts.

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2 3 4 5

6 7

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(1989) 12 2093 19 Worthington, T.K., Gallagher, W.J., Diuger, T.R., ltoitzberg, F., Kaiser, D.L. and Sandstrom, R.L. Physica C (1987) 153-155 32 20 Oh, B., Char, K., Kent, A.D., Naito, M., Beasley,M.R., Geballe, T.H., Hammond, R.H., Kapitulnik, A. and Graybeal, J.M. Phys Rev B (1988) 37 7861 21 Anderson, P.W. and Kim, Y.B. Rev Mod Phys (1964) 36 4756 22 Fisher, M.P.A. Phys Rev Lett (1989) 62 1415 23 Ambegaokar, V. and Halperin, B.I. Phys Rev Lett (1969) 61 1364 24 Takayama, T. J Low Temp Phys (1977) 27 359 25 Koch, R.H., Foglietti, V., Gallagher, W.J., Koren, G., Gupta, A. and Fisher, M.P.A. Phys Rev Len (1989) 63 1511 26 McGuire, T.R., Gupta, A., Koren, G., Laibowitz, R.B. and Dimos, D. Physica C (1989) 162-164 131 27 Worthington, T.K., Malozemoff, A.P., Holtzberg, F.H., Chandrashekhar, G.V. and Strobel, P. Proc 1STEC Workshop on Superconductivity (1989) 51 28 Worthington, T.K. unpublished 29 Bean, C.P. Phys Rev Lett (1962) 8 250 30 Marehetti, M.C. and Nelson, D.R. Phys Rev B (1990) 40 _1910 31 Marehetti, M.C. personal communication

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