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A.c. response of YBa2Cu3O7 with Y2BaCuO5 inclusions and of single crystal YBa2Cu3O7: similarities, differences and anomalies
A.c. response of YBazCuaO7 with Y2BaCuO5 inclusions and of single crystal YBa2Cu307: similarities, differences and anomalies* M.G. Karkut, L.K. Heill, V.M. E.D. Tuset and K. Fossheim
VinokurL M. SlaskiL L.T. Sagdahl,
Division of Physics, The Norwegian Institute of Technology and SINTEF Applied Physics, N 7034 Trondheim, Norway tMaterials Science Division, Argonne National Laboratory, Argonne, IL 60439 USA We have measured the a.c. magnetic permeability response function /z = #" + i#" in melt-processed melt-grown YBa2Cu307 with Y2BaCu05 inclusions (MPMG) and in single crystal YBa2Cu307 (SC) in magnetic fields of up to 8 T oriented either parallel or perpendicular to the crystalline c-axis. The Iossy part of the permeability #" (H, T) is used to probe the flux dynamics in the vicinity of the irreversibility line. For H Uc, the MPMG has a higher irreversibility temperature T~r,(H) than the SC sample, while for H .L c, T~,r(H) is similar for both samples. Because of the strong Hac dependence and the weak frequency dependence of #'(H,T) for H J_ c, we contend that the vortex system is in the glass phase. For H II c, the Hac dependence of #" is weak and its frequency dependence is strong, indicating that here the system is much closer to the glass/liquid transition. For the SC sample with H .L c, #"(T) exhibits an anomalous structure which appears only in finite applied d.c. fields and disappears at fields greater than 1.5 T.
Kaywords: flux dynamics; MPMG; a.c. response
The purpose of this work is twofold. There is great interest in understanding the enhanced levitation properties 1 of melt-processed melt-growth YBa2Cu307 with Y2BaCuO5 inclusions (MPMG) and so our strategy has been to compare results from a single crystal YBa2Cu307 (SC) with corresponding results from MPMG. At the same time, this strategy also allows us to explore the basic properties of the flux line system and its associated dynamics. The MPMG sample has been confirmed by X-ray diffraction to be single-crystal-like with a well defined c-axis and with the usual twinning of the a,b axes, as in single crystals. This investigation covers the following variables: material composition, temperature T, external magnetic field /~oHdc (0--8 T), a.c. field amplitude tzoHac ( 0 - 3 0 x 10 -4 T), excitation frequency f ( 1 2 H z - 1 2 1 k H z ) and field direction (nd¢llc and Hdc .L c, and Hac .1_ Hd¢ in all cases). The present work is a continuation of our a.c. permeability investigations z'3 on MPMG and SC samples and focuses on the responses of the samples to the a.c. excitation fields. *Paper presented at the conference 'Critical Currents in High Tc Superconductors', 2 2 - 24 April 1992, Vienna, Austria tPresent address: School of Physics, University of Birmingham, Birmingham BI5 2TT, UK OO11 - 2 2 7 5 / 9 3 / 0 1 0 0 6 0 - 05 © 1993 Butterworth - Heinemann Ltd
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Experimental The experimental technique has been described in other publications 4. Briefly, the MPMG sample was grown at the Superconductivity Research Laboratory, Tokyo. The sample was cut into the shape of a cube with dimensions of 1.38 x 1.25 x 1.25 mm 3. The Y211 inclusions were roughly spherical and had a diameter of - 0 . 5 #m. The single crystal (SC) sample was made at the University of Birmingham. The crystal dimensions for this sample were 1.100 × 1.065 x 1.015 mm 3. The demagnetization factors for H _Lc and HII c for both the samples were almost equal, thus simplifying comparison of the data. The complex a.c. permeability /z = #' + i#", or equivalently the magnetic susceptibility X = /~-1, was measured using a susceptometer constructed in-house. The excitation and pick-up coils were coaxial and parallel to the applied d.c. magnetic field. The pick-up coil was tightly wound around the sample. The induced voltage was proportional to the permeability and the real and imaginary parts of/~(H, 7) were recorded separately using a two-phase lock-in amplifier. The superconducting transition temperature Tc and the transition width ATofthe MPMG and SC samples were 90.3 K, 0.23 K, and 88.6 K, 0.40 K respectively.
A.c. response of YBCO: M.G. Karkut et al.
Results and discussion Before presenting the results it will be useful briefly to give justification for using Iz"(H,T) as a tool to study the neighbourhood of the irreversibility line. It can be shown 5 that the peak in the a.c. absorption Iz"(H,7) occurs when the screening length 6, which characterizes the penetration of the a.c. field into the sample, becomes approximately equal to half of the relevant size of the sample, d. The precise condition will of course depend on the sample geometry. When the I - V characteristics of the sample are linear, the field penetration is given by the skin depth 6 = [2p(T)/#oC0] ~/2 where p(T) is the resistivity and 60 is the excitation frequency. Thus in the temperature range where Ohm's law is valid, in the normal state or in the vortex liquid state, /z"(H,T) will be frequency dependent but will not depend on the excitation field amplitude H,~. When the I - V characteristics are non-linear, which is the case when the system is in the vortex glass state or when H,¢ becomes sufficiently large, #"(H,T) becomes amplitude dependent. It has been s h o w n 6 that the distribution of a magnetic field in a glassy regime is analogous to that in the Bean critical state: B drops linearly from the surface and the corresponding current density J is constant over the depth of the field penetration except for an exponentially narrow region near the front of the flux centre of the sample. Thus a peak in the lossy part of the permeability lx"(H,7) will occur when the distance the a.c. field and the current penetrate into the sample, 6 = H, JJ, is equal to d/2. In this non-linear regime #"(H, 7) will depend only weakly on frequency. Therefore, depending on the frequency and amplitude of the a.c. excitation field and on the sample size, #"(H,7) will be related to the linear and/or the non-linear portions of the I - V curves. The irreversibility line describes the line in the H - T plane which indicates the onset of pinning that will manifest itself as non-linear behaviour: hence the justification for using /~"(H,T) as a probe of the neighbourhood of the irreversibility line. The loci of points determined by the peaks in i.t"(H, 7) have in the past been associated with the irreversibility line. For simplicity we continue this usage but we emphasize that these lines represent a dynamically determined boundary in the H, T plane which is not in general a phase boundary. These lines can be frequency and field dependent, and in principle these parameters can be used to determine the true irreversibility line following the procedure given, for example, in Reference 5. Since the range of our experimental parameters was too limited to determine precisely the true irreversibility line, for purposes of comparing the two samples we have chosen loss peak lines made at f = 121 Hz and /z0H,~ = 1 x 10-4 T. In Figure I we present the loss peak lines as a function of reduced temperature t = T/T~ for the MPMG and SC samples in applied fields both parallel and perpendicular to the c-axis. In all cases, f = 121 Hz and iz0H.~ = 1 x 10 -4 T. For both samples the dynamically determined irreversibility temperature Ti~(/-/) is considerably higher for H .1. c than for H IIc. This is in good agreement with the expected melting of the vortex lattice due to thermal fluctuations when the anisotropy is taken into account 7. For the Hllc
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orientation the irreversibility line of the MPMG sample is clearly at a higher temperature and field than the irreversibility line of the SC sample. The nonsuperconducting Y211 inclusions thus have the effect of raising the vortex melting temperature of the MPMG sample. A similar effect on the increase of T~rr(H) has been observed in single crystal YBCO into which long columnar defects have been introduced 8. The detailed nature of the pinning by Y211 inclusions is not yet known but the implication here is that the strong pinning nature of the Y211 inclusions provides additional stability to the vortex structure, resulting in a higher vortex melting temperature. These strong pins are of course superimposed upon the already existing random distribution of weak pins which act to provide the collective pinning of the flux lines. Interestingly, for the H .L c orientation, the reduced temperature irreversibility lines for both samples are essentially equal. Presumably this means that the vortex structure is maximally stable for this orientation and the addition of strong pinning sites cannot raise Ti,(H). It would also be interesting to compare this H_L c result with a defected single crystal YBCO in which the columns are introduced parallel to the CuO2 planes. Finally, as we will see below, even though the irreversibility temperature does not seem to be affected by the Y211 inclusions when H is perpendicular to the c-axis, the a.c. response, that is, the position of/z"(7) as a function of the a.c. amplitude, is indeed different for the two samples. We note that a.c. susceptibility measurements made by Wacenovsky et al. 9 on two MPMG samples which, unlike ours, also contain Ag precipitates, liave shown an increase in T~r,(H) as a function of 211 precipitate concentration. Before considering the a.c. field response in detail, we refer to Figures 2 and 3 to illustrate the difference in the frequency and a.c. field dependences for the two field orientations. Figure 2 is a plot of/~"(H,T) for different frequencies at a fixed a.c. excitation of 1 x 10 -4 T. The frequency dependence of the loss peak line for H _Lc is much weaker than when the configuration is
Cryogenics 1993 Vol 33, No 1
61
A.c. response of YBCO: M.G. Karkut et al. '
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weak frequency dependence. For HII c, the strong frequency and weak Hac dependence imply that the response is less non-linear and closer to the glass/liquid transition than the response for H.I.c. The results presented i n Figures 2 and 3 were obtained on the MPMG sample but similar overall behaviour has been observed from the SC sample. We look now in more detail at the a.c. response of the two samples at low (0.4 T) applied field perpendicular to the c-axis. In Figure 4 one immediately notices the anamolous structure of #"(H,T) for the SC sample for all a.c. fields. What we observe is a sharp dissipation onset (indicated by the dashed lines in Figure 4) at high temperatures followed by a very broad dissipative response with decreasing temperature. As is evident in Figure 4, this type of behaviour is not present in the MPMG sample, for which we observe only well rounded peaks. This anomalous feature of #"(T,H) is confined to the H.L c orientation. Figure 5 shows the a.c. response for HII c at 0.4 T for both the SC and the MPMG samples. Here the response is similar for both samples except for the displacement in temperature which is due to the higher irreversibility temperature of the MPMG sample, as discussed above. We also do not see any anomalous structure in zero applied field for H .L c. The absence of the anomaly for the H _L c configuration in 4 T and in 0 T should rule out the hypothesis that the sample is granular. In granular samples, two loss peaks are often observed: one at high Tdue to the grains and the second, broader and at lower T, due to the intergranular material. But this type of behaviour does occur in zero d.c. field and does not, of course, depend on orientation. Finally we point out another interesting feature of this anomaly: it goes away at higher applied d.c. fields. It also exists at /ZoHdc = 1.5 T but not at #oHd~ = 4 T. Figure 6 shows the a.c. response of iz"(H,1) for the single crystal sample when c is perpendicular to #oHd¢ = 4 T. Even though there is no dissipation peak at Ha~ = 26 x 10-4 T, only a broad maximum, one cannot say there is anything anomalous about these curves taken at 4 T.
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Figure 3 Loss peak/~" plotted as a function of applied field and temperature for different amplitudes of the excitation field Hac for the MPMG sample. The excitation frequency is 121 Hz. There is only a weak Hac dependence on/~" for H II c whereas for H .L c the Hac dependence is so strong that for large enough Hac the loss peak curves fall below those for H II c
HII c. In both cases the line goes to higher temperatures as the frequency is increased. Figure 3 is a plot of #"(H,7) for different a.c. fields at a fixed frequency of 121 Hz. Here the H~¢ dependence is much stronger for H .L c than for H IIc. This is as expected since for H _Lc there will be two components to the screening current. The component perpendicular to the CuO2 planes, J_L will have the effect, via the Lorentz force, of sliding the vortices between, and parallel to, the CuO2 planes. This clearly is the most dissipative situation that can arise and hence explains the strong a.c. field dependence for this orientation. Taking the results of Figures 2 and 3 together and recalling our discussion about I~"(H,T), we can say that the peak in/z" occurs below the glass transition for H_L c because there is a strong Hac and
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Cryogenics 1993 Vol 33, No 1
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A.c. response of YBCO: M.G. Karkut et al. I
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Figure 6 #" as a function of temperature for different applied Hac for the SC sample for H _L c. Now the applied field Hdc = 4 T. Even though the dissipation extends to very low temperatures for the larger a.c. fields, there is no anomaly in /," (T) as there is in
Figure 4
Another way to see this is to plot d#"/dT versus T as we have done in Figure 7. These curves are the calculated derivatives of the SC curves in Figure 4. A smoothing procedure for #"(T,H) has been employed to obtain the reasonably smooth d#"(T,H)/dT curves in Figure 7. The procedure was to redefine /~" at a temperature T/ as a weighted average of the current value at T~ and at the two nearest neighbour temperatures T~_, and T~+I. This was repeated a total of ten times and produced sufficiently smooth, but still faithful to the original, #"(T) curves so that meaningful numerical derivatives could be taken. The four curves are displaced for clarity with the horizontal lines marking the zero for each curve. In all four cases the high temperature minimum does not go smoothly to zero as the temperature is decreased, but flattens out before crossing zero at lower temperatures. We have marked the onset of this feature by the arrows. It is this flatten-
ing out of d#"/dTbefore reaching zero which signals the anomaly in #" (H, 7). (The derivative for the 30 G curve only approaches zero because the maximum in the dissipation has not yet been reached at 80 K.) This flattening out occurs between 86.8 and 87 K for all four curves and is independent of the applied a.c. field. This a.c. field independence is in marked contrast to the strong a.c. field dependence of the #" peak positions corresponding to the zero crossings in Figure 7. Thus these curves indicate that the system goes from linear to strongly non-linear behaviour as the temperature is decreased below 87 K. We can highlight the anomaly of the 8 G curve in the SC sample for H_L c = 0.4 T when we compare, in Figure 8, the d#"/dT curves for the MPMG at 0.4 T (top), the SC at 0.4 T (centre) and the SC at 4 T (bottom). The excitation field was 8 G for these three derivative curves. The flattened out feature is present only in the middle curve, thus confirming that the anomalous behaviour only exists in this sample for intermediate applied fields. What is the cause of this anomalous structure? We cannot yet rule out a slight misorientation of the sample which could produce a small Hdc component parallel to the c-axis. Then, for this cubic shaped sample, the configuration would be Hac .L c and Hd¢llc and this could
Cryogenics 1993 Vol 33, No 1 63
A.c. response of YBCO: M.G. Karkut et al.
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Figure 8 dg"/dTas a function of reduced temperature for H _L c for the MPMG sample at #elide = 0 . 4 T and Hac = 8 G (top), the SC sample at Hdc = 0 . 4 T and Hac = 8 G (middle) and the SC sample at Hd¢ = 4 T and Hac = 8 G. The curves are displaced for clarity and the horizontal lines mark the zero for each curve. There is no anomalous flattened out feature for the top and bottom curves
possibly produce a signal comparable to what we observe. A small a.c. component parallel to the c-axis would produce a much smaller signal since the response is proportional to the a.c. amplitude and this Hacllc would only be a small fraction of Ha¢ _Lc for small misorientation. Another possible explanation for the anomalous structure in #"(T,H) is that it is the a.c. response counterpart to the recent I - V measurements made on single crystal YBa2Cu307 samples with enhanced disorder by Worthington et al. ~o. They claim to observe separate glass and melting transitions at relatively low d.c. fields on these samples. They speculate that the higher T transition is a remnant of a first-order melting transition and exists, in a clean system, at the same temperature with the glass transition. With disorder the melting transition becomes rounded and as the disorder becomes sufficiently strong the melting transition becomes unobservable. Whatever the precise explanation, there are several similarities between our observed anomaly in lz"(T,l-1) and the glass and the I - V curves reported in Reference 10: the anomaly in/z"(H,T) is not present at zero applied d.c. field, it goes away at higher d.c. fields and it goes away with disorder i.e. it is not present in the more disordered MPMG sample. This is all suggestive. However, these results must be considered as preliminary and we are now making measurements over a wider range of a.c. and d.c. fields in order to map out the evolution of this anomalous structure. We are also looking at the frequency response as a function of field in order to determine the nature of the response.
Summary We have measured the a.c. permeability as a function of
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Cryogenics 1993 Vol 33, No 1
temperature, frequency and applied d.c. and a.c. fields parallel and perpendicular to the crystalline c-axis to investigate the region near the irreversibility line for a single-crystal-like sample of YBa2Cu307 with Y2BaCuO5 inclusions and for a single crystal YBa2Cu307 sample. For both samples Tier(H) for H ± c exists at higher fields and temperatures than for H IIc in accord with ideas of vortex melting in an anisotropic solid. For the H IIc orientation, the presumed strong pinning Y2BaCuO7 inclusions in the MPMG sample have the effect of raising Tir~(H) to higher fields and temperature than that of the single crystal sample. We believe these strong pinning sites add additional stability to the otherwise collectively pinned vortex structure, thereby raising its melting temperature. For our typical experimental conditions, the weak frequency and strong a.c. field dependence of the absorption peak for H .1. c lead us to conclude that the vortex system is in the glass state, while the strong frequency and weak a.c. field dependence of the absorption peak for HIIc make us believe that the vortex system is much closer to the glass/liquid boundary. Finally we observe an anomalous structure in # " ( T , H ) for the SC sample for H_L c. This anomaly exists only for finite applied d.c. fields and it disappears when ~Hdc > 1.5 T. By plotting dg " / d T versus T we see that the onset of non-linearity in the SC sample occurs just below 87 K when goH .l- c = 0 . 4 T.
Acknowledgements The authors are indebted to Norsk Hydro for partial support of this project. One of us (MS) acknowledges a fellowship from NTNF, and one of us (LKH) e x p r e s s e s his gratitude to NAVF for a stipend. VMV acknowledges support from the US Department of Energy, BES-Materials Sciences, under Contract No. W-31-109-ENG-38 and from the NSF funded Science and Technology Center for Superconductivity under Grant No. DMR 88-09854. We thank P. Tuset, O.M. Nes, Wu Ting and T. Suzuki for useful discussions.
References 1 Murakami, M., Mod Phys Lett (1990) IM 163 2 Fossheim, K., Karkut, M.G., Heill, L.K., Slaski, M., Sagdalfl, L.T., Vinokur, V.M., Murakami, M., Fujimoto, H., Koshizuka, N., Tanaka, S., Gencer, F., Abeil, J.S. and Cough, C.E. Phys Scripta (1992) I"42 20 3 Slaski, M., Sagdahl, L.T., Heill, L.K., Fossheim, K., Murakami, M., Fujimoto, H., Koshizuka, N. and Tanaka, S. Physica C (1991) 185-189 2495; Slaski, M., Sagdahl, L.T., Heill, L.K. and Fossheim, K. Supercond Sci Tech (1992) 5 $340 4 Sagdahl, L.T., Gj61mesli, S., I.~egreid, T., Fossheim, K. and Assmus, W., Phys Rev B (1990)42 6797; Sagdahl, L.T., Laegreid, T., Fossheim, K., Murakami, M., Fujimoto, H., Koshizuka, N. and Tanaka, S. Physica C (1991) 172 495 5 Geshkenbein, V.B., Vinokur, V.M. and Fehrenbacher, R. Phys Rev B (1991) 43 3748 6 Vinokur, V.M., Fiegerman, M.V. and Geshkenbein, V.B. Phys Rev Lett (1991) 67 915 7 Biatter, G., Geshkenbein, V.B. and Larkin, A.L Preprint ETH Zurich, 1991 8 Civale, L., Marwick, A.D., Worthington, T.K., Kirk, M.A., Thompson, J.R., ICrusin-Eibaum, L., Sun, Y., Clem, J.R. and Holtzberg, F. Phys Rev Lea (1991)67 648 9 Waeenovsky, M., Miletieh, R., Weber, H.W. and Murakami, M. Supercond Sci Technol (1992) 5 S184 10 Worthington, T.K., Fisher, M.P.A., Toner, J., Zabel, T.H., Fetid, C.A. and Heltzberg, F. Bull Am Phys Soc (1992)37 592
VinokurL M. SlaskiL L.T. Sagdahl,
Division of Physics, The Norwegian Institute of Technology and SINTEF Applied Physics, N 7034 Trondheim, Norway tMaterials Science Division, Argonne National Laboratory, Argonne, IL 60439 USA We have measured the a.c. magnetic permeability response function /z = #" + i#" in melt-processed melt-grown YBa2Cu307 with Y2BaCu05 inclusions (MPMG) and in single crystal YBa2Cu307 (SC) in magnetic fields of up to 8 T oriented either parallel or perpendicular to the crystalline c-axis. The Iossy part of the permeability #" (H, T) is used to probe the flux dynamics in the vicinity of the irreversibility line. For H Uc, the MPMG has a higher irreversibility temperature T~r,(H) than the SC sample, while for H .L c, T~,r(H) is similar for both samples. Because of the strong Hac dependence and the weak frequency dependence of #'(H,T) for H J_ c, we contend that the vortex system is in the glass phase. For H II c, the Hac dependence of #" is weak and its frequency dependence is strong, indicating that here the system is much closer to the glass/liquid transition. For the SC sample with H .L c, #"(T) exhibits an anomalous structure which appears only in finite applied d.c. fields and disappears at fields greater than 1.5 T.
Kaywords: flux dynamics; MPMG; a.c. response
The purpose of this work is twofold. There is great interest in understanding the enhanced levitation properties 1 of melt-processed melt-growth YBa2Cu307 with Y2BaCuO5 inclusions (MPMG) and so our strategy has been to compare results from a single crystal YBa2Cu307 (SC) with corresponding results from MPMG. At the same time, this strategy also allows us to explore the basic properties of the flux line system and its associated dynamics. The MPMG sample has been confirmed by X-ray diffraction to be single-crystal-like with a well defined c-axis and with the usual twinning of the a,b axes, as in single crystals. This investigation covers the following variables: material composition, temperature T, external magnetic field /~oHdc (0--8 T), a.c. field amplitude tzoHac ( 0 - 3 0 x 10 -4 T), excitation frequency f ( 1 2 H z - 1 2 1 k H z ) and field direction (nd¢llc and Hdc .L c, and Hac .1_ Hd¢ in all cases). The present work is a continuation of our a.c. permeability investigations z'3 on MPMG and SC samples and focuses on the responses of the samples to the a.c. excitation fields. *Paper presented at the conference 'Critical Currents in High Tc Superconductors', 2 2 - 24 April 1992, Vienna, Austria tPresent address: School of Physics, University of Birmingham, Birmingham BI5 2TT, UK OO11 - 2 2 7 5 / 9 3 / 0 1 0 0 6 0 - 05 © 1993 Butterworth - Heinemann Ltd
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Cryogenics 1993 Vol 33, No 1
Experimental The experimental technique has been described in other publications 4. Briefly, the MPMG sample was grown at the Superconductivity Research Laboratory, Tokyo. The sample was cut into the shape of a cube with dimensions of 1.38 x 1.25 x 1.25 mm 3. The Y211 inclusions were roughly spherical and had a diameter of - 0 . 5 #m. The single crystal (SC) sample was made at the University of Birmingham. The crystal dimensions for this sample were 1.100 × 1.065 x 1.015 mm 3. The demagnetization factors for H _Lc and HII c for both the samples were almost equal, thus simplifying comparison of the data. The complex a.c. permeability /z = #' + i#", or equivalently the magnetic susceptibility X = /~-1, was measured using a susceptometer constructed in-house. The excitation and pick-up coils were coaxial and parallel to the applied d.c. magnetic field. The pick-up coil was tightly wound around the sample. The induced voltage was proportional to the permeability and the real and imaginary parts of/~(H, 7) were recorded separately using a two-phase lock-in amplifier. The superconducting transition temperature Tc and the transition width ATofthe MPMG and SC samples were 90.3 K, 0.23 K, and 88.6 K, 0.40 K respectively.
A.c. response of YBCO: M.G. Karkut et al.
Results and discussion Before presenting the results it will be useful briefly to give justification for using Iz"(H,T) as a tool to study the neighbourhood of the irreversibility line. It can be shown 5 that the peak in the a.c. absorption Iz"(H,7) occurs when the screening length 6, which characterizes the penetration of the a.c. field into the sample, becomes approximately equal to half of the relevant size of the sample, d. The precise condition will of course depend on the sample geometry. When the I - V characteristics of the sample are linear, the field penetration is given by the skin depth 6 = [2p(T)/#oC0] ~/2 where p(T) is the resistivity and 60 is the excitation frequency. Thus in the temperature range where Ohm's law is valid, in the normal state or in the vortex liquid state, /z"(H,T) will be frequency dependent but will not depend on the excitation field amplitude H,~. When the I - V characteristics are non-linear, which is the case when the system is in the vortex glass state or when H,¢ becomes sufficiently large, #"(H,T) becomes amplitude dependent. It has been s h o w n 6 that the distribution of a magnetic field in a glassy regime is analogous to that in the Bean critical state: B drops linearly from the surface and the corresponding current density J is constant over the depth of the field penetration except for an exponentially narrow region near the front of the flux centre of the sample. Thus a peak in the lossy part of the permeability lx"(H,7) will occur when the distance the a.c. field and the current penetrate into the sample, 6 = H, JJ, is equal to d/2. In this non-linear regime #"(H, 7) will depend only weakly on frequency. Therefore, depending on the frequency and amplitude of the a.c. excitation field and on the sample size, #"(H,7) will be related to the linear and/or the non-linear portions of the I - V curves. The irreversibility line describes the line in the H - T plane which indicates the onset of pinning that will manifest itself as non-linear behaviour: hence the justification for using /~"(H,T) as a probe of the neighbourhood of the irreversibility line. The loci of points determined by the peaks in i.t"(H, 7) have in the past been associated with the irreversibility line. For simplicity we continue this usage but we emphasize that these lines represent a dynamically determined boundary in the H, T plane which is not in general a phase boundary. These lines can be frequency and field dependent, and in principle these parameters can be used to determine the true irreversibility line following the procedure given, for example, in Reference 5. Since the range of our experimental parameters was too limited to determine precisely the true irreversibility line, for purposes of comparing the two samples we have chosen loss peak lines made at f = 121 Hz and /z0H,~ = 1 x 10-4 T. In Figure I we present the loss peak lines as a function of reduced temperature t = T/T~ for the MPMG and SC samples in applied fields both parallel and perpendicular to the c-axis. In all cases, f = 121 Hz and iz0H.~ = 1 x 10 -4 T. For both samples the dynamically determined irreversibility temperature Ti~(/-/) is considerably higher for H .1. c than for H IIc. This is in good agreement with the expected melting of the vortex lattice due to thermal fluctuations when the anisotropy is taken into account 7. For the Hllc
/
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orientation the irreversibility line of the MPMG sample is clearly at a higher temperature and field than the irreversibility line of the SC sample. The nonsuperconducting Y211 inclusions thus have the effect of raising the vortex melting temperature of the MPMG sample. A similar effect on the increase of T~rr(H) has been observed in single crystal YBCO into which long columnar defects have been introduced 8. The detailed nature of the pinning by Y211 inclusions is not yet known but the implication here is that the strong pinning nature of the Y211 inclusions provides additional stability to the vortex structure, resulting in a higher vortex melting temperature. These strong pins are of course superimposed upon the already existing random distribution of weak pins which act to provide the collective pinning of the flux lines. Interestingly, for the H .L c orientation, the reduced temperature irreversibility lines for both samples are essentially equal. Presumably this means that the vortex structure is maximally stable for this orientation and the addition of strong pinning sites cannot raise Ti,(H). It would also be interesting to compare this H_L c result with a defected single crystal YBCO in which the columns are introduced parallel to the CuO2 planes. Finally, as we will see below, even though the irreversibility temperature does not seem to be affected by the Y211 inclusions when H is perpendicular to the c-axis, the a.c. response, that is, the position of/z"(7) as a function of the a.c. amplitude, is indeed different for the two samples. We note that a.c. susceptibility measurements made by Wacenovsky et al. 9 on two MPMG samples which, unlike ours, also contain Ag precipitates, liave shown an increase in T~r,(H) as a function of 211 precipitate concentration. Before considering the a.c. field response in detail, we refer to Figures 2 and 3 to illustrate the difference in the frequency and a.c. field dependences for the two field orientations. Figure 2 is a plot of/~"(H,T) for different frequencies at a fixed a.c. excitation of 1 x 10 -4 T. The frequency dependence of the loss peak line for H _Lc is much weaker than when the configuration is
Cryogenics 1993 Vol 33, No 1
61
A.c. response of YBCO: M.G. Karkut et al. '
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weak frequency dependence. For HII c, the strong frequency and weak Hac dependence imply that the response is less non-linear and closer to the glass/liquid transition than the response for H.I.c. The results presented i n Figures 2 and 3 were obtained on the MPMG sample but similar overall behaviour has been observed from the SC sample. We look now in more detail at the a.c. response of the two samples at low (0.4 T) applied field perpendicular to the c-axis. In Figure 4 one immediately notices the anamolous structure of #"(H,T) for the SC sample for all a.c. fields. What we observe is a sharp dissipation onset (indicated by the dashed lines in Figure 4) at high temperatures followed by a very broad dissipative response with decreasing temperature. As is evident in Figure 4, this type of behaviour is not present in the MPMG sample, for which we observe only well rounded peaks. This anomalous feature of #"(T,H) is confined to the H.L c orientation. Figure 5 shows the a.c. response for HII c at 0.4 T for both the SC and the MPMG samples. Here the response is similar for both samples except for the displacement in temperature which is due to the higher irreversibility temperature of the MPMG sample, as discussed above. We also do not see any anomalous structure in zero applied field for H .L c. The absence of the anomaly for the H _L c configuration in 4 T and in 0 T should rule out the hypothesis that the sample is granular. In granular samples, two loss peaks are often observed: one at high Tdue to the grains and the second, broader and at lower T, due to the intergranular material. But this type of behaviour does occur in zero d.c. field and does not, of course, depend on orientation. Finally we point out another interesting feature of this anomaly: it goes away at higher applied d.c. fields. It also exists at /ZoHdc = 1.5 T but not at #oHd~ = 4 T. Figure 6 shows the a.c. response of iz"(H,1) for the single crystal sample when c is perpendicular to #oHd¢ = 4 T. Even though there is no dissipation peak at Ha~ = 26 x 10-4 T, only a broad maximum, one cannot say there is anything anomalous about these curves taken at 4 T.
T (K) .
Figure 3 Loss peak/~" plotted as a function of applied field and temperature for different amplitudes of the excitation field Hac for the MPMG sample. The excitation frequency is 121 Hz. There is only a weak Hac dependence on/~" for H II c whereas for H .L c the Hac dependence is so strong that for large enough Hac the loss peak curves fall below those for H II c
HII c. In both cases the line goes to higher temperatures as the frequency is increased. Figure 3 is a plot of #"(H,7) for different a.c. fields at a fixed frequency of 121 Hz. Here the H~¢ dependence is much stronger for H .L c than for H IIc. This is as expected since for H _Lc there will be two components to the screening current. The component perpendicular to the CuO2 planes, J_L will have the effect, via the Lorentz force, of sliding the vortices between, and parallel to, the CuO2 planes. This clearly is the most dissipative situation that can arise and hence explains the strong a.c. field dependence for this orientation. Taking the results of Figures 2 and 3 together and recalling our discussion about I~"(H,T), we can say that the peak in/z" occurs below the glass transition for H_L c because there is a strong Hac and
62
Cryogenics 1993 Vol 33, No 1
.
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A.c. response of YBCO: M.G. Karkut et al. I
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Figure 6 #" as a function of temperature for different applied Hac for the SC sample for H _L c. Now the applied field Hdc = 4 T. Even though the dissipation extends to very low temperatures for the larger a.c. fields, there is no anomaly in /," (T) as there is in
Figure 4
Another way to see this is to plot d#"/dT versus T as we have done in Figure 7. These curves are the calculated derivatives of the SC curves in Figure 4. A smoothing procedure for #"(T,H) has been employed to obtain the reasonably smooth d#"(T,H)/dT curves in Figure 7. The procedure was to redefine /~" at a temperature T/ as a weighted average of the current value at T~ and at the two nearest neighbour temperatures T~_, and T~+I. This was repeated a total of ten times and produced sufficiently smooth, but still faithful to the original, #"(T) curves so that meaningful numerical derivatives could be taken. The four curves are displaced for clarity with the horizontal lines marking the zero for each curve. In all four cases the high temperature minimum does not go smoothly to zero as the temperature is decreased, but flattens out before crossing zero at lower temperatures. We have marked the onset of this feature by the arrows. It is this flatten-
ing out of d#"/dTbefore reaching zero which signals the anomaly in #" (H, 7). (The derivative for the 30 G curve only approaches zero because the maximum in the dissipation has not yet been reached at 80 K.) This flattening out occurs between 86.8 and 87 K for all four curves and is independent of the applied a.c. field. This a.c. field independence is in marked contrast to the strong a.c. field dependence of the #" peak positions corresponding to the zero crossings in Figure 7. Thus these curves indicate that the system goes from linear to strongly non-linear behaviour as the temperature is decreased below 87 K. We can highlight the anomaly of the 8 G curve in the SC sample for H_L c = 0.4 T when we compare, in Figure 8, the d#"/dT curves for the MPMG at 0.4 T (top), the SC at 0.4 T (centre) and the SC at 4 T (bottom). The excitation field was 8 G for these three derivative curves. The flattened out feature is present only in the middle curve, thus confirming that the anomalous behaviour only exists in this sample for intermediate applied fields. What is the cause of this anomalous structure? We cannot yet rule out a slight misorientation of the sample which could produce a small Hdc component parallel to the c-axis. Then, for this cubic shaped sample, the configuration would be Hac .L c and Hd¢llc and this could
Cryogenics 1993 Vol 33, No 1 63
A.c. response of YBCO: M.G. Karkut et al.
I
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Figure 8 dg"/dTas a function of reduced temperature for H _L c for the MPMG sample at #elide = 0 . 4 T and Hac = 8 G (top), the SC sample at Hdc = 0 . 4 T and Hac = 8 G (middle) and the SC sample at Hd¢ = 4 T and Hac = 8 G. The curves are displaced for clarity and the horizontal lines mark the zero for each curve. There is no anomalous flattened out feature for the top and bottom curves
possibly produce a signal comparable to what we observe. A small a.c. component parallel to the c-axis would produce a much smaller signal since the response is proportional to the a.c. amplitude and this Hacllc would only be a small fraction of Ha¢ _Lc for small misorientation. Another possible explanation for the anomalous structure in #"(T,H) is that it is the a.c. response counterpart to the recent I - V measurements made on single crystal YBa2Cu307 samples with enhanced disorder by Worthington et al. ~o. They claim to observe separate glass and melting transitions at relatively low d.c. fields on these samples. They speculate that the higher T transition is a remnant of a first-order melting transition and exists, in a clean system, at the same temperature with the glass transition. With disorder the melting transition becomes rounded and as the disorder becomes sufficiently strong the melting transition becomes unobservable. Whatever the precise explanation, there are several similarities between our observed anomaly in lz"(T,l-1) and the glass and the I - V curves reported in Reference 10: the anomaly in/z"(H,T) is not present at zero applied d.c. field, it goes away at higher d.c. fields and it goes away with disorder i.e. it is not present in the more disordered MPMG sample. This is all suggestive. However, these results must be considered as preliminary and we are now making measurements over a wider range of a.c. and d.c. fields in order to map out the evolution of this anomalous structure. We are also looking at the frequency response as a function of field in order to determine the nature of the response.
Summary We have measured the a.c. permeability as a function of
64
Cryogenics 1993 Vol 33, No 1
temperature, frequency and applied d.c. and a.c. fields parallel and perpendicular to the crystalline c-axis to investigate the region near the irreversibility line for a single-crystal-like sample of YBa2Cu307 with Y2BaCuO5 inclusions and for a single crystal YBa2Cu307 sample. For both samples Tier(H) for H ± c exists at higher fields and temperatures than for H IIc in accord with ideas of vortex melting in an anisotropic solid. For the H IIc orientation, the presumed strong pinning Y2BaCuO7 inclusions in the MPMG sample have the effect of raising Tir~(H) to higher fields and temperature than that of the single crystal sample. We believe these strong pinning sites add additional stability to the otherwise collectively pinned vortex structure, thereby raising its melting temperature. For our typical experimental conditions, the weak frequency and strong a.c. field dependence of the absorption peak for H .1. c lead us to conclude that the vortex system is in the glass state, while the strong frequency and weak a.c. field dependence of the absorption peak for HIIc make us believe that the vortex system is much closer to the glass/liquid boundary. Finally we observe an anomalous structure in # " ( T , H ) for the SC sample for H_L c. This anomaly exists only for finite applied d.c. fields and it disappears when ~Hdc > 1.5 T. By plotting dg " / d T versus T we see that the onset of non-linearity in the SC sample occurs just below 87 K when goH .l- c = 0 . 4 T.
Acknowledgements The authors are indebted to Norsk Hydro for partial support of this project. One of us (MS) acknowledges a fellowship from NTNF, and one of us (LKH) e x p r e s s e s his gratitude to NAVF for a stipend. VMV acknowledges support from the US Department of Energy, BES-Materials Sciences, under Contract No. W-31-109-ENG-38 and from the NSF funded Science and Technology Center for Superconductivity under Grant No. DMR 88-09854. We thank P. Tuset, O.M. Nes, Wu Ting and T. Suzuki for useful discussions.
References 1 Murakami, M., Mod Phys Lett (1990) IM 163 2 Fossheim, K., Karkut, M.G., Heill, L.K., Slaski, M., Sagdalfl, L.T., Vinokur, V.M., Murakami, M., Fujimoto, H., Koshizuka, N., Tanaka, S., Gencer, F., Abeil, J.S. and Cough, C.E. Phys Scripta (1992) I"42 20 3 Slaski, M., Sagdahl, L.T., Heill, L.K., Fossheim, K., Murakami, M., Fujimoto, H., Koshizuka, N. and Tanaka, S. Physica C (1991) 185-189 2495; Slaski, M., Sagdahl, L.T., Heill, L.K. and Fossheim, K. Supercond Sci Tech (1992) 5 $340 4 Sagdahl, L.T., Gj61mesli, S., I.~egreid, T., Fossheim, K. and Assmus, W., Phys Rev B (1990)42 6797; Sagdahl, L.T., Laegreid, T., Fossheim, K., Murakami, M., Fujimoto, H., Koshizuka, N. and Tanaka, S. Physica C (1991) 172 495 5 Geshkenbein, V.B., Vinokur, V.M. and Fehrenbacher, R. Phys Rev B (1991) 43 3748 6 Vinokur, V.M., Fiegerman, M.V. and Geshkenbein, V.B. Phys Rev Lett (1991) 67 915 7 Biatter, G., Geshkenbein, V.B. and Larkin, A.L Preprint ETH Zurich, 1991 8 Civale, L., Marwick, A.D., Worthington, T.K., Kirk, M.A., Thompson, J.R., ICrusin-Eibaum, L., Sun, Y., Clem, J.R. and Holtzberg, F. Phys Rev Lea (1991)67 648 9 Waeenovsky, M., Miletieh, R., Weber, H.W. and Murakami, M. Supercond Sci Technol (1992) 5 S184 10 Worthington, T.K., Fisher, M.P.A., Toner, J., Zabel, T.H., Fetid, C.A. and Heltzberg, F. Bull Am Phys Soc (1992)37 592