- Email: [email protected]
Flux dynamics and vortex phase diagram of the new superconductor MgB2
Physica C 363 (2001) 170±178
www.elsevier.com/locate/physc
Flux dynamics and vortex phase diagram of the new superconductor MgB2 H.H. Wen *, S.L. Li, Z.W. Zhao, H. Jin, Y.M. Ni, Z.A. Ren, G.C. Che, Z.X. Zhao Institute of Physics and Center for Condensed Matter Physics, National Laboratory for Superconductivity, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, China Received 20 April 2001; received in revised form 4 June 2001; accepted 21 June 2001
Abstract Magnetic relaxation, critical current density and transport properties have been investigated on MgB2 bulks from 1.6 K to Tc at magnetic ®elds up to 8 T. A vortex phase diagram is depicted based on these measurements. Two phase g bulk bulk boundaries Hirr T and Hirr T characterizing dierent irreversible ¯ux motions are found. The Hirr T is characterized by the appearance of the linear resistivity. A large separation between the bulk irreversibility ®eld at 0 K and the upper critical ®eld Hc2 0 has been found, it is interpreted as either due to a quantum vortex liquid induced by strong quantum ¯uctuation of vortices at 0 K, or ¯ux ¯ow through weak-link channels. It is further found that the magnetic relaxation rate is weakly dependent on temperature but strongly dependent on ®eld indicating a trivial in¯uence of bulk thermal ¯uctuation on the vortex depinning process. Therefore the phase line Hirr T may be attributed to quantum g vortex melting in the rather clean system at a ®nite temperature. The second boundary Hirr T re¯ects the irreversible ¯ux motion in some local regions due to either very strong pinning or the surface barrier on the tiny grains. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: MgB2 ; Flux creep; Magnetization; Fluctuation eect; Phase diagram
1. Introduction The recently discovered new superconductor MgB2 generates enormous interests in the ®eld of superconductivity [1]. Many important thermodynamic parameters have already been derived, such as the upper critical ®eld Hc2 0 13±20.4 T [2±5], the Ginzburg±Landau parameter j 26 [5], and the bulk critical superconducting current density jc 8 104 A/cm2 at 4.2 K and 12 T [6] in
* Corresponding author. Tel.: +86-10-8264-9474; fax: +8610-6256-2605. E-mail address: [email protected] (H.H. Wen).
thin ®lms. One big issue concerns however how fast the critical current will decay under a magnetic ®eld and in which region on the ®eld-temperature (H ±T ) phase diagram the superconductor can carry a large critical current density (jc ). This jc is controlled by the mobility of the magnetic vortices, and vanishes at the melting point between the vortex solid and liquid. A ®nite linear resistivity qlin E=jj!0 will appear and the relaxation rate will reach 100% at this melting point showing the starting of the reversible ¯ux motion. In this paper we present an extensive investigation on the ¯ux dynamics by magnetic relaxation and transport measurement. A vortex phase diagram will be depicted based on these measurements.
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 9 3 6 - 4
H.H. Wen et al. / Physica C 363 (2001) 170±178
171
2. Experimental Samples investigated here were fabricated by both high pressure (HP) (P 6 GPa at 950°C for 0.5 h) and ambient pressure (AP) synthesis which was described very clearly in a recent publication [7]. HP synthesis is a good technique for producing the MgB2 superconductor since it can make the sample more dense and uniform (in sub-micron scale) and also prevent the oxidization of Mg element during the solid reaction. Our HP samples are very dense and look like metals with shiny surfaces after polishing. Scanning electron microscopy (SEM) shows that the HP sample is uniform in sub-micron scale but some disordered ®ne structures are found in 10 nm scale, being similar to the internal structure of large grains seen in the AP sample. X-ray diraction (XRD) analysis on both type of samples show that they are nearly in a single phase with the second phase (probably MgO or MgB4 ) <1 wt.%. For simplicity we present in this paper mainly the results from the HP samples. The resistance measurements were carried out using the standard four-probe technique with a Keithley 220 dc current source and a Keithley 182 nano-voltmeter, and the magnetic ®eld was applied with a vibrating sample magnetometor (VSM, Oxford 3001), with the ®eld range varying from 0 to 8 T. For transport measurement the sample was shaped into a rectangular shape with dimensions of 4 mm 3 mm 0:5 mm. Four silver pads were deposited onto the sample surface for electric contacts with low contacting resistance. The magnetic measurements were carried out by a superconducting quantum interference device (SQUID, Quantum Design MPMS 5.5 T) and a vibrating sample magnetometer (VSM 8T, Oxford 3001). To precisely calculate the critical current density jc the sample has been cut with a diamond saw into a rectangular shape with sizes of 3:2 mm length 2:7 mm width 0:4 mm thickness. 3. Results Fig. 1 shows the diamagnetic transition of one of the HP samples measured in the ®eld-cooled (FC) and zero-®eld-cooled (ZFC) process. All
Fig. 1. Temperature dependence of the superconducting diamagnetic moment measured in the ZFC and FC processes at a ®eld of 10 Oe. A perfect diamagnetic signal can be observed here. The inset shows the resistive transition with Tc0 and Tc (onset) of 38.9 and 39.9 K, respectively.
other samples show almost similar quality. In the FC process, the temperature was lowered from above Tc to a desired temperature below Tc under a magnetic ®eld, and the data are collected in warming up process with ®eld. Its signal generally describes the surface shielding current and the internal frozen magnetic ¯ux pro®le. In the ZFC process, the temperature was lowered from above Tc to a desired temperature below Tc at a zero ®eld and the data are collected in the warming up process with a ®eld. Its signal generally describes the internal magnetic ¯ux pro®le, which is ultimately related to the ¯ux motion. The inset shows the resistive measurement on the sample. In zero ®eld, the superconducting transition temperature Tc0 and Tc (onset) are 38.9 and 39.9 K. Both resistive and diamagnetic measurement show that the transitions are very sharp with a perfect diamagnetic signal seen from the M T curve. In Fig. 2 we show the magnetization hysteresis loops (MHLs) measured at temperatures ranging from 2 to 38 K. The symmetric MHLs observed at temperatures up to 38 K indicate the dominance of the bulk current instead of the surface shielding current. The MHLs measured at low temperatures, such as 2, 4 K show quite strong ¯ux jump which is discussed elsewhere [8]. It is easy to see that the
172
H.H. Wen et al. / Physica C 363 (2001) 170±178
Fig. 2. MHLs measured at 2, 4, 6, 8, 10, 14, 18, 22, 26, 30, 32, 35, 37 and 38 K (from outer to inner). All curves here show a symmetric behavior indicating the importance of bulk current instead of surface shielding current. The MHLs measured at low temperatures (e.g., 2±10 K) are too close to be distinguishable. Strong ¯ux jump has been observed at 2 and 4 K near the central peak.
MHLs measured at low temperatures (e.g., 2±10 K) are too close to be distinguishable. This indicates that both the critical current density jc and the irreversibility ®eld Hirr are weak temperature dependent functions in low temperature region. From these MHLs one can calculate jc via jc 20DM=Va 1 a=3b based on the Bean critical state model, where DM is the width of the MHL, V , a and b are the volume, width and length (a < b) of the sample, respectively. The result of jc is shown in Fig. 3. It is clear that the bulk critical current density jc of our sample is rather high. To investigate the ¯ux dynamics, the jc H curves have been measured with three dierent ®eld sweeping rate 200, 100 and 50 Oe/s. It is interesting to note that for all MHLs, there are small tails (shown in the inset to Fig. 3) in high ®eld region. Accordingly the jc H curves show also a small tail in high ®eld region. Since jc value in the small tail region is almost 4 104 times smaller than that in the low ®eld region, therefore it is safe to conclude that this small tail is due to some secondary eect, such as some local regions with very strong pinning or the surface pinning by the tiny grains. From the contour of jc vs. H shown in Fig. 3 one can see that there are two regions with two dif-
Fig. 3. Critical current density jc calculated based on the Bean critical state model. At each temperature the data has been measured with three ®eld sweeping rate: 200, 100, 50 Oe/s. The faster sweeping rate corresponds to a higher dissipation and thus higher current density. From these data one can calculate the dynamical magnetic relaxation rate Q. The jc H curves measured at low temperatures are very close to each other bulk showing a rather stable value of Hirr when T approaches 0 K. The dashed horizontal line marks the criterion of jc 30 A/cm2 bulk for determining the Hirr . While by following the small tail (which has been attributed to a secondary eect) to a criterion g of jc 3 A/cm2 , another phase line Hirr is determined.
ferent properties of ¯ux dynamics: one before the tail with a sharp drop of jc and another one in the tail region. Accordingly there are two ways to determine the so-called irreversibility line Hirr T . The ®rst way is to take a criterion for jc 30 A/ cm2 just before the appearance of the tail. This bulk is named as the bulk irreversibility line Hirr T which signals the sharp drop of jc before the appearance of the tail and re¯ects the irreversible ¯ux motion in clean samples. The second way is just to follow the small tail to a criterion of 3 A/cm2 . In this way one can determine a higher irreversibilg ity line Hirr T which marks a boundary above which a complete reversible ¯ux motion occurs. As mentioned above, the small tail in our present samples is due to a secondary eect, therefore the bulk major part of the vortex system melt at Hirr T . bulk Thus we may conclude that the Hirr T re¯ects the melting of the vortex matter in the clean limit, for example, in single crystals. If more pinning centers are introduced into the sample, one should be possible to push the Hirr T more close to the upper critical ®eld Hc2 T .
H.H. Wen et al. / Physica C 363 (2001) 170±178
The second method to determine the irreversibility line Hirr T and the upper critical ®eld Hc2 T is to measure the temperature dependence of magnetization in the FC and ZFC processes as shown in Fig. 4 for a second piece of HP synthesized MgB2 bulk measured on SQUID. A typical example for how to determine Hirr T and Hc2 T is shown in the inset of Fig. 4. The Hirr T and Hc2 T is determined from the point at which the magnetization start to deviate from the normal state linear background, while the Hirr T line is determined by taking the deviating point between ZFC± FC M T curves with a criterion of DMZFC±FC 10 4 emu. The third method to determine the Hirr T and Hc2 T is to measure the resistive transitions at dierent magnetic ®elds. As shown in Fig. 5, a parallel shift of RT curves at higher magnetic ®elds is observed although a gradual broadening behavior appears in the low dissipation part. This is in contrast to that in the high Tc cuprate superconductors (HTS) in which the ®eld induced
173
Fig. 5. Resistive transition of high pressure sintered MgB2 samples at various magnetic ®elds. The R T curves shift parallel to lower temperatures when higher magnetic ®elds are applied.
broadening eect is much stronger and almost no parallel shift of R T curves has been observed. At a ®eld of 8 T, a ®nite resistance appears down to the lowest temperature (4.2 K) here showing already a rather low irreversibility temperature Tirr . The Hirr T was determined by taking a criterion of 10 5 X, while for the upper critical ®eld Hc2 T , both we and Takano et al. [4] have determined the upper critical point Tc2 from the point at which the resistance starts to deviate from the normal state resistance. All the phase lines determined by using the three methods mentioned above will be presented and discussed below.
4. Discussion 4.1. Vortex phase diagram of MgB2 Fig. 4. Temperature dependence of the magnetization measured in the ZFC and FC processes on another HP bulk by SQUID at ®elds of 0.1, 0.5, 1, 2, 3, 4 and 5.5 T. All ®lled symbols are corresponding to the magnetization measured in the ZFC process. In the main frame all the FC M T curves are crowded in a small region. As shown in the inset, the Hc2 T is determined from the point at which the magnetization starts to deviate from the normal state linear background, while the Hirr T line is determined by taking the deviating point between ZFC±FC M T curves with a criterion of DMZFC±FC 10 4 emu. In the measurement by a SQUID the small tail of MHL is hard to be observed due to the slow data acquisition speed.
The phase lines of Hirr T and Hc2 T determined by following the dierent methods mentioned above are shown in Fig. 6. It is clear that the bulk bulk irreversibility line Hirr T determined from MHL measurement at the point just before the appearance of the small tail shown in Fig. 3 terminates at about 8 T at 2 K, which is very close to that determined by resistive measurement and from the M±T measurement (Fig. 4). This strongly indicates bulk that the Hirr T is a vortex melting line which signals the appearance of a ®nite linear resistivity.
174
H.H. Wen et al. / Physica C 363 (2001) 170±178
Fig. 6. H ±T phase diagram for the new superconductor MgB2 . bulk The ®lled circles represent the bulk irreversibility lines Hirr in this work measured by VSM from MHL with criterion of jc 30 A/m2 ; half-®lled circles, Hirr T for another HP sample measured by SQUID from ZFC±FC M T with criterion of DM 10 4 emu; open circles, Hirr of MgB2 ®lm with Tc 38 K and jc 0 T; 14 K 1:8 107 A/cm2 ; open diamond, Hirr of the HP sample measured by resistive transport. The triangles g represent the Hirr T : ®lled triangles, determined directly from the small tail; open triangles, following the tendency of tail (shown by the three dashed lines in Fig. 3) to a criterion of jc 3 A/cm2 . The ®lled squares represent the Hc2 T data of Takano et al. from resistive measurement; open squares, Hc2 T data in this work from the M T measurement by SQUID; ®lled diamond, Hc2 T data in this work by transport measurement. All the lines are guides to the eye.
By following the small tail to a lower criterion, g another irreversibility line Hirr T is determined. g The extrapolated value Hirr reaches about 12 T at 2 K. There is a large separation between these two phase lines characterizing dierent irreversible ¯ux motion. It is important to note that Larbalestier et al. [9] have found the similar feature where they bulk regard the lower phase line Hirr T as the Kramer line. Together plotted in Fig. 6 are the upper critical ®eld Hc2 T determined from Fig. 4 the temperature dependent magnetization by de®ning the Hc2 T as the point at which the magnetization starts to deviate from the normal state linear background [10] and Fig. 5 the resistive measurement by Takano et al. [4] and by us on HP samples. Although the samples are from dierent groups and dierent techniques have been used to obtain the data, the vortex phase diagram derived here has a good consistency. A striking result shown by this
bulk T extrapovortex phase diagram is that the Hirr lates to a rather low ®eld at 0 K, here for example, bulk Hirr 0 8 T, while the Hc2 T extrapolates to a much higher value (Hc2 0 15 T) [2,11] 1 at 0 K. There is a large separation between the two ®elds bulk Hirr 0 and Hc2 0. This eect can be attributed to either the possible existence of the quantum vortex liquid at 0 K, or the easy ¯ux ¯ow through the weak link regions between the grains. However, worthy of noting is that, the grain size of our sample is much larger than the penetration depth k and the average spacing a0 between the vortices, therefore if there is irreversible ¯ux motion on grains one should be possible to measure it. In this sense we assume that the large separation between Hirr 0 and Hc2 0 is not induced by the weak link property. If following the hypothesis of the vortex liquid above Hirr T , we would conclude that there is a large region of magnetic ®eld for the existence of a vortex liquid at 0 K. This can be attributed to a quantum ¯uctuation eect of vortices in bulk MgB2 . Although the lowest temperature in our present experiment is 1.6 K, however, from the experimental data one cannot ®nd any tendency for Hirr T to turn upward rapidly to meet the Hc2 0. One may argue that the Hirr T probably can be increased to higher values by introducing more pinning centers into this sample. This is basically correct since recently a higher irreversibility line Hirr T has been found in some MgB2 thin ®lms [6] and bulk samples irradiated by protons [12]. Actually in our recent experiment on MgB2 thin ®lms (shown in Fig. 6 by open circles), the irreversibility line Hirr T is also close to that of bulks. This indicates that the large separation between the bulk Hirr 0 and Hc2 0 may be an intrinsic property of MgB2 in the clean limit. It can be interpreted as the quantum vortex melting due to the strong quantum ¯uctuation which smears the perfect vortex lattice
1 Although the upper critical ®eld Hc2 T has been measured up to only 5.5 T here (and Takano et al. measured up to 9 T), from the data shown in Fig. 6 one can derive a slope of d l0 H =dT 0:62 0:2 T/K near Tc . At present, since the mechanism of the new superconductor MgB2 is unknown, we can only use the WHH relation l0 Hc2 0 0:69Tc d l0 H =dT [11] to derive l0 Hc2 0 which is found to be 17 T. It is much higher than the extrapolated value l0 Hirr 0 8 T.
H.H. Wen et al. / Physica C 363 (2001) 170±178
leading to the vanishing of the shear module C66 of the vortex matter (probably within grains). Dense disorders will strengthen the shear module and thus enhance the bulk irreversibility line. By irradiating the MgB2 samples with protons, Bugoslavsky et al. [12] found that jc is not suppressed but strongly increased. This suggests that the low value of bulk Hirr T measured in unirradiated bulks or rather pure ®lms (like our samples here) is not due to the weak links since otherwise the jc value would drop even faster with increasing the magnetic ®eld after the irradiation. This further indicates that the rabulk ther low Hirr T observed in our present work re¯ects the melting of the vortex matter in samples with relatively pure structural details rather than the breaking of the Josephson couplings between grains. In addition, as mentioned above, the bulk Hirr T found in present work is very close (or identical) to those by other authors [5,13] found in bulks, therefore it shows a more intrinsic feature corresponding to the melting of vortex matter in the rather pure system. 4.2. Large separation between Hirr 0 and Hc2 0 and possible evidence for strong quantum ¯uctuation of vortices In order to investigate the ¯ux dynamics in the bulk vortex solid state below Hirr T and to see more clearly what happens when Hirr T is approached, we have carried out the dynamical relaxation measurement. According to Schnack et al. [14] and Jirsa et al. [15], in a ®eld sweeping process, if the ®eld sweeping rate is high enough, the quantity Q d ln DM=d ln dH =dt is close to the relaxation rate S d ln M=d ln t measured in the conventional relaxation method, where Q is called as the dynamical relaxation rate, DM the width of the MHL, dH =dt the ®eld sweeping rate. The raw data with three dierent sweeping rate (200, 100, and 50 Oe/s) are shown in Fig. 3. The Q values vs. ®eld for dierent temperatures are determined and shown in Fig. 7. It is clear that the relaxation rate increases monotonically with the external magnetic ®eld and extrapolates to 100% at the bulk melting bulk point Hirr . Here we concentrate on the ¯ux dynamics before the setting in of the small tail. At 2 K it is found from the Q H data that the vortex
175
Fig. 7. Field dependence of the relaxation rate at temperatures of 2, 4, 6, 8, 10, 14, 18, 22, 26, 30, 32, 35, 37 K. The dashed line is a guide to the eye for 2 K. It is clear that Q will rise to 100% at bulk 8 T at 2 K. Since Hirr is rather stable at low temperatures, it is bulk 0 8 T being much smaller than anticipated that Hirr Hc2 0 15 T (here we choose the lower reported value of Hc2 0 obtained by Bud'ko et al. in Ref. [2]).
melting ®eld (where Q 100%) is about 8 T, being bulk (T 2 K) determined from the very close to Hirr bulk jc H curve. It is known that the Hirr T is rather stable in low temperature region, therefore we can bulk anticipate a rather low value of Hirr 0 which is below 9 T being much lower than Hc2 0. Again bulk one can see a large separation between Hirr 0 and Hc2 0. This eect has recently been found also in rather pure MgB2 ®lms [16] with Tc 0 38 K and jc 0 T; 14 K 1:8 107 A/cm2 , in bulks made under AP and even powders. All these may strongly suggest the existence of the quantum vortex liquid due to strong quantum ¯uctuation of vortices in the pure system of MgB2 . Theoretically, quantum melting of the vortex solid has been proposed by some authors [17±21] and preliminarily veri®ed by experiments [22,23]. Solid evidence is, however, still lacking mainly because either the values of Hirr 0 and Hc2 0 T are too high to be accessible, such as in the classical Chevrel phase PbMoS system [24,25], or the separation between them is too small [22,23] leading to a diculty in drawing any unambiguous conclusions. Here we try to have a rough consideration on the quantum melting ®eld Hm proposed by Blatter et al. [17±19] for 2D system
176
Hm 0=Hc2 0 1
H.H. Wen et al. / Physica C 363 (2001) 170±178
p3 CL2 RQ =4R2D
1:2 exp
1
where CL is the Lindermann number, RQ h=e2 4:1 kX, R2D is the sheet resistance. Since the new MgB2 sample has a much higher charge density and thus a much lower sheet resistivity, according to above relation, Hm should be more close to Hc2 0 comparing to HTS. This is in contrast to the experimental observations which may be explained as that the MgB2 is not a quasi-2D system. Another approach was proposed by Rozhkov and Stroud [26], Hm 0=Hc2 0 B0 = B0 Hc2 0
2
2
with B0 bmp C 2 sU0 =4pk 0 q2 , where s is the spacing between layers, mp is the pair mass, q the pair charge (2e), C the light velocity, k 0 the penetration depth at 0 K, b 0:1. If comparing again the present new superconductor MgB2 with HTS, k 0, q and b are more or less in the same scale, the dierence comes from mp and s. Therefore a preliminary conclusion would be that in MgB2 either the pair mass mp or the layer spacing s is much smaller than that of HTS. The precise reason for the strong quantum ¯uctuation of vortices in MgB2 is still unknown. 4.3. Residual relaxation rate at 0 K and weak temperature dependence of the relaxation rate Fig. 8 shows the temperature dependence of the dynamical relaxation rate Q. The arrows point at the irreversibility temperatures at the correbulk sponding ®elds Hirr T . It is clear that the relaxation rate extrapolates to a ®nite value at 0 K for all ®elds. This eect was also observed in high Tc cuprate superconductors and attributed to the quantum tunneling of vortices. The dierence between the MgB2 and the HTS is that the residual relaxation rate Q at 0 K in the former case has a strong ®eld dependence, but in the latter case is weakly dependent on the ®eld, especially for the 3D YBa2 Cu3 O7 system. Another striking point for MgB2 is that in wide temperature region the relaxation rate keeps rather stable against the thermal activation and ¯uctuation. However, when the bulk bulk melting point Hirr T is approached the
Fig. 8. Temperature dependence of the relaxation rate at ®elds of 1, 2, 3, 4, 5, 6 T. The dashed lines are guides to the eye. The bulk arrows point at the bulk irreversibility temperatures Tirr determined from the jc H curve.
relaxation rate will quickly jump to 100%. The magnetic relaxation rate has been determined also with the conventional relaxation method, that is to measure the time dependence of the relaxation rate via S d ln M=d ln t. The raw data are shown in the inset of Fig. 9 and the relaxation rate for 0.5 and 1 T are determined and shown in the main frame of Fig. 9. It is clear the quantum creep rate (if any) at a low ®eld (0.5 T) is only about 0.1% being an order of magnitude lower than that of HTS. Again the relaxation rate S shows a very weak temperature dependence at a ®nite temperature. For example, from 0 to 30 K at 1 T, S increases from 0.1% to about 5%. But when the melting temperature/®eld is reached (35 K at 1 T), the relaxation rate rises sharply from 5% at 30 K to 100% at 35 K. The small relaxation rate at a relatively low ®eld has also been measured by Thompson et al. [27] who regarded it as a highly stable superconducting current density in MgB2 . Actually the relaxation rate can be rather high when the magnetic ®eld is increased to a higher value. The extremely small relaxation rate and weak temperature dependence at a ®nite temperature at a low ®eld is probably induced by a strong pinning barrier relative to the thermal energy, i.e., kB T Uc , where Uc is the intrinsic pinning energy. Recently it was concluded [28,29] that the Uc is in
H.H. Wen et al. / Physica C 363 (2001) 170±178
177
motion. As mentioned in this paper and shown by the data in Figs. 8 and 9, the quantum tunneling may give a strong in¯uence on the ¯ux dynamics of MgB2 in very wide temperature region. The strong vortex pinning in MgB2 may be induced by the twin boundaries or weak link regions and the quantum vortex melting in polycrystalline bulks may ®rst occur on the grains. In this case the irradiation on MgB2 bulks by heavy ions and protons will increase the critical current density and enhance the irreversibility of ¯ux motion. Fig. 9. The magnetic relaxation rate determined by S d ln M=d ln t at ®elds of 0.5 and 1 T. The inset shows the original data of magnetization versus time, a good linear relation has been found between M and ln t manifesting a Kim± Anderson type of eective pinning barrier.
the scale of 1000 K being much higher than the thermal energy kB T . Therefore for the new superconductor MgB2 the pinning well is too deep leading to a trivial in¯uence of the thermal activation and ¯uctuation. It thus naturally suggests that the quantum ¯uctuation and tunneling plays an more important role. Therefore, together with the fact discussed in last sub-section, it is tempting to suggest that the melting between a vortex solid and a liquid is due to quantum ¯uctuation instead of the thermal ¯uctuation. From the inset of Fig. 9 one can see that the magnetization follows roughly the relation M t; T M 0; T A ln t indicating the Kim± Anderson linear U j relation, where U is the eective pinning barrier and j is the externally applied current density. Therefore in the vortex tunneling or activation process in MgB2 , a ¯ux segment with a ®xed length is involved. This is rather dierent from HTS in which the collective pinning and creep are dominant and the optimal hopping/tunneling length (volume) of vortex line (bundle) varies with the external force (current) leading to a non-linear U j relation. Recently Qin et al. [30] derived a non-linear U j relation for MgB2 bulks based on the so-called Maley's method [31]. One should however take cautions to derive U j relation by using Maley's method here since it is only applicable to the thermally activated ¯ux
5. Conclusion In rather pure samples of MgB2 the irreversibility ®eld is rather low comparing to the upper critical ®eld in low temperature region. This eect has been attributed to either the possible existence of the quantum vortex liquid due to strong quantum ¯uctuation of vortices, or the easy ¯ux ¯ow through the weak link channels. The temperature and ®eld dependence of the relaxation rate may further suggest that the vortex melting at a ®nite temperature is also induced by strong quantum ¯uctuation in pure systems, such as single crystals and bulks. A small tail following the jc H curve in high ®eld region is attributed to a secondary eect induced by strong pinning or surface barrier on some tiny grains. This opens a way for the higher irreversibility line when more pinning centers are introduced into the pure sample. Magnetic relaxation measurement shows that the intrinsic pinning barrier is much higher than the thermal energy, this may also interpret the trivial importance of the thermal activation and thermal ¯uctuation. In comparison the quantum tunneling and the ¯uctuation shows a much stronger in¯uence. The reason for such a strong quantum eect is still unknown, but it may be related to the superconducting mechanism of MgB2 , such as the relatively low upper critical ®eld. Acknowledgements This work is supported by the National Science Foundation of China (NSFC 19825111) and the Ministry of Science and Technology of China
178
H.H. Wen et al. / Physica C 363 (2001) 170±178
(project: NKBRSF-G1999064602). HHW gratefully acknowledges Prof. B. Ivlev and Dr. A.F.Th. Hoekstra for fruitful discussions, and continuing ®nancial support from the Alexander von Humboldt foundation, Germany.
References [1] J. Nagamatsu, N. Nakagawa, T. Maranaka, Y. Zenitani, J. Akimitsu, Nature 410 (2001) 63. [2] S.L. Bud'ko, C. Petrovic, G. Lapertot, C.E. Cunningham, P.C. Can®eld, cond-mat/0102413 (2001). [3] P.C. Can®eld, D.K. Finnemore, S.L. Bud'ko, J.E. Ostenson, G. Lapertot, C.E. Cunningham, C. Petrovic, condmat/0102289 (2001). [4] Y. Takano, H. Takeya, H. Fujii, H. Kumakura, T. Hatano, K. Togano, H. Kito, H. Ihara, cond-mat/ 0102167 (2001). [5] D.K. Finnemore, J.E. Ostenson, S.L. Bud'ko, G. Lapertot, P.C. Can®eld, cond-mat/0102114 (2001). [6] C.B. Eom, M.K. Lee, J.H. Choi, L. Belenky, X. Song, L.D. Cooley, M.T. Naus, S. Patnaik, J. Jiang, M. Rikel, A. Polyanskii, A. Gurevich, X.Y. Cai, S.D. Bu, S.E. Babcock, E.E. Hellstrom, D.C. Larbalestier, N. Rogado, K.A. Regan, M.A. Hayward, T. He, J.S. Slusky, K. Inumaru, M.K. Haas, R.J. Cava, Nature 411 (2001) 558. [7] Z.A. Ren, G.C. Che, Z.X. Zhao, H. Chen, C. Dong, Y.M. Ni, S.L. Jia, H.H. Wen, Chin. Phys. Lett. 18 (2001) 589. [8] Z.W. Zhao, H.H. Wen, S.L. Li, Z.A. Ren, G.C. Che, Z.X. Zhao, in press. [9] D.C. Larbalestier et al., Nature 410 (2001) 186. [10] H.H. Wen, S.L. Li, Z.W. Zhao, Y.M. Ni, Z.A. Ren, G.C. Che, H.P. Yang, Z.Y. Liu, Z.X. Zhao, Chin. Phys. Lett. 18 (2001) 816.
[11] N.R. Werthamer, E. Helfand, P.C. Hohemberg, Phys. Rev. 147 (1966) 362. [12] Y. Bugoslavsky, L.F. Cohen, G.K. Perkins, M. Polichetti, T.J. Tate, R. Gwilliam, A.D. Caplin, Nature 411 (2001) 561. [13] Y. Bugoslavsky, G.K. Perkins, X. Qi, L.F. Cohen, A.D. Caplin, Nature 410 (2001) 563. [14] H.G. Schnack, R. Griessen, J.G. Lensink, C.J. Van der Beek, P.H. Kes, Physica C 197 (1992) 337. [15] M. Jirsa, L. Pust, Physica C 207 (1993) 85. [16] H.H. Wen, S.L. Li, Z.W. Li, W.N. Kang, H.J. Kim, E.M. Choi, S.I. Lee, in press. [17] G. Blatter, B. Ivlev, Phys. Rev. Lett. 70 (1993) 2621. [18] G. Blatter, B.I. Ivlev, Phys. Rev. B 50 (1994) 10272. [19] G. Blatter et al., Phys. Rev. B 50 (1994) 13013. [20] A. Kramer, S. Doniach, Phys. Rev. Lett. 81 (1998) 3523. [21] R. Ikeda, Int. J. Mod. Phys. B 10 (1996) 601. [22] T. Sasaki, W. Biberacher, K. Neumaier, W. Hehn, A. Andres, Phys. Rev. B 57 (1998) 10889. [23] S. Okuma, Y. Imamoto, M. Morita, Phys. Rev. Lett. 86 (2001) 3136. [24] C. Rossel, E. Sandvold, M. Sergent, R. Chevrel, M. Potel, Physica C 165 (1990) 233. [25] C. Rossel, O. Pena, H. Schmitt, M. Sergent, Physica C 181 (1991) 363. [26] A. Rozhkov, D. Stroud, Phys. Rev. B 54 (1996) R12697. [27] J.R. Thompson, M. Paranthaman, D.K. Christen, K.D. Sorge, H.J. Kim, J.G. Ossandon, cond-mat/0103514. [28] H. Jin, H.H. Wen, Chin. Phys. Lett. 18 (2001) 823. [29] Z.W. Zhao, H.H. Wen, S.L. Li, Y.M. Ni, Z.A. Ren, G.C. Che, H.P. Yang, Z.Y. Liu, Z.X. Zhao, Chin. Phys. 10 (2001) 340. [30] M.J. Qin, X.L. Wang, H.K. Liu, S.X. Dou, cond-mat/ 0104112. [31] M.P. Maley, J.O. Willis, H. Lessure, M.E. McHenry, Phys. Rev. B 42 (1990) 2639.
www.elsevier.com/locate/physc
Flux dynamics and vortex phase diagram of the new superconductor MgB2 H.H. Wen *, S.L. Li, Z.W. Zhao, H. Jin, Y.M. Ni, Z.A. Ren, G.C. Che, Z.X. Zhao Institute of Physics and Center for Condensed Matter Physics, National Laboratory for Superconductivity, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, China Received 20 April 2001; received in revised form 4 June 2001; accepted 21 June 2001
Abstract Magnetic relaxation, critical current density and transport properties have been investigated on MgB2 bulks from 1.6 K to Tc at magnetic ®elds up to 8 T. A vortex phase diagram is depicted based on these measurements. Two phase g bulk bulk boundaries Hirr T and Hirr T characterizing dierent irreversible ¯ux motions are found. The Hirr T is characterized by the appearance of the linear resistivity. A large separation between the bulk irreversibility ®eld at 0 K and the upper critical ®eld Hc2 0 has been found, it is interpreted as either due to a quantum vortex liquid induced by strong quantum ¯uctuation of vortices at 0 K, or ¯ux ¯ow through weak-link channels. It is further found that the magnetic relaxation rate is weakly dependent on temperature but strongly dependent on ®eld indicating a trivial in¯uence of bulk thermal ¯uctuation on the vortex depinning process. Therefore the phase line Hirr T may be attributed to quantum g vortex melting in the rather clean system at a ®nite temperature. The second boundary Hirr T re¯ects the irreversible ¯ux motion in some local regions due to either very strong pinning or the surface barrier on the tiny grains. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: MgB2 ; Flux creep; Magnetization; Fluctuation eect; Phase diagram
1. Introduction The recently discovered new superconductor MgB2 generates enormous interests in the ®eld of superconductivity [1]. Many important thermodynamic parameters have already been derived, such as the upper critical ®eld Hc2 0 13±20.4 T [2±5], the Ginzburg±Landau parameter j 26 [5], and the bulk critical superconducting current density jc 8 104 A/cm2 at 4.2 K and 12 T [6] in
* Corresponding author. Tel.: +86-10-8264-9474; fax: +8610-6256-2605. E-mail address: [email protected] (H.H. Wen).
thin ®lms. One big issue concerns however how fast the critical current will decay under a magnetic ®eld and in which region on the ®eld-temperature (H ±T ) phase diagram the superconductor can carry a large critical current density (jc ). This jc is controlled by the mobility of the magnetic vortices, and vanishes at the melting point between the vortex solid and liquid. A ®nite linear resistivity qlin E=jj!0 will appear and the relaxation rate will reach 100% at this melting point showing the starting of the reversible ¯ux motion. In this paper we present an extensive investigation on the ¯ux dynamics by magnetic relaxation and transport measurement. A vortex phase diagram will be depicted based on these measurements.
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 9 3 6 - 4
H.H. Wen et al. / Physica C 363 (2001) 170±178
171
2. Experimental Samples investigated here were fabricated by both high pressure (HP) (P 6 GPa at 950°C for 0.5 h) and ambient pressure (AP) synthesis which was described very clearly in a recent publication [7]. HP synthesis is a good technique for producing the MgB2 superconductor since it can make the sample more dense and uniform (in sub-micron scale) and also prevent the oxidization of Mg element during the solid reaction. Our HP samples are very dense and look like metals with shiny surfaces after polishing. Scanning electron microscopy (SEM) shows that the HP sample is uniform in sub-micron scale but some disordered ®ne structures are found in 10 nm scale, being similar to the internal structure of large grains seen in the AP sample. X-ray diraction (XRD) analysis on both type of samples show that they are nearly in a single phase with the second phase (probably MgO or MgB4 ) <1 wt.%. For simplicity we present in this paper mainly the results from the HP samples. The resistance measurements were carried out using the standard four-probe technique with a Keithley 220 dc current source and a Keithley 182 nano-voltmeter, and the magnetic ®eld was applied with a vibrating sample magnetometor (VSM, Oxford 3001), with the ®eld range varying from 0 to 8 T. For transport measurement the sample was shaped into a rectangular shape with dimensions of 4 mm 3 mm 0:5 mm. Four silver pads were deposited onto the sample surface for electric contacts with low contacting resistance. The magnetic measurements were carried out by a superconducting quantum interference device (SQUID, Quantum Design MPMS 5.5 T) and a vibrating sample magnetometer (VSM 8T, Oxford 3001). To precisely calculate the critical current density jc the sample has been cut with a diamond saw into a rectangular shape with sizes of 3:2 mm length 2:7 mm width 0:4 mm thickness. 3. Results Fig. 1 shows the diamagnetic transition of one of the HP samples measured in the ®eld-cooled (FC) and zero-®eld-cooled (ZFC) process. All
Fig. 1. Temperature dependence of the superconducting diamagnetic moment measured in the ZFC and FC processes at a ®eld of 10 Oe. A perfect diamagnetic signal can be observed here. The inset shows the resistive transition with Tc0 and Tc (onset) of 38.9 and 39.9 K, respectively.
other samples show almost similar quality. In the FC process, the temperature was lowered from above Tc to a desired temperature below Tc under a magnetic ®eld, and the data are collected in warming up process with ®eld. Its signal generally describes the surface shielding current and the internal frozen magnetic ¯ux pro®le. In the ZFC process, the temperature was lowered from above Tc to a desired temperature below Tc at a zero ®eld and the data are collected in the warming up process with a ®eld. Its signal generally describes the internal magnetic ¯ux pro®le, which is ultimately related to the ¯ux motion. The inset shows the resistive measurement on the sample. In zero ®eld, the superconducting transition temperature Tc0 and Tc (onset) are 38.9 and 39.9 K. Both resistive and diamagnetic measurement show that the transitions are very sharp with a perfect diamagnetic signal seen from the M T curve. In Fig. 2 we show the magnetization hysteresis loops (MHLs) measured at temperatures ranging from 2 to 38 K. The symmetric MHLs observed at temperatures up to 38 K indicate the dominance of the bulk current instead of the surface shielding current. The MHLs measured at low temperatures, such as 2, 4 K show quite strong ¯ux jump which is discussed elsewhere [8]. It is easy to see that the
172
H.H. Wen et al. / Physica C 363 (2001) 170±178
Fig. 2. MHLs measured at 2, 4, 6, 8, 10, 14, 18, 22, 26, 30, 32, 35, 37 and 38 K (from outer to inner). All curves here show a symmetric behavior indicating the importance of bulk current instead of surface shielding current. The MHLs measured at low temperatures (e.g., 2±10 K) are too close to be distinguishable. Strong ¯ux jump has been observed at 2 and 4 K near the central peak.
MHLs measured at low temperatures (e.g., 2±10 K) are too close to be distinguishable. This indicates that both the critical current density jc and the irreversibility ®eld Hirr are weak temperature dependent functions in low temperature region. From these MHLs one can calculate jc via jc 20DM=Va 1 a=3b based on the Bean critical state model, where DM is the width of the MHL, V , a and b are the volume, width and length (a < b) of the sample, respectively. The result of jc is shown in Fig. 3. It is clear that the bulk critical current density jc of our sample is rather high. To investigate the ¯ux dynamics, the jc H curves have been measured with three dierent ®eld sweeping rate 200, 100 and 50 Oe/s. It is interesting to note that for all MHLs, there are small tails (shown in the inset to Fig. 3) in high ®eld region. Accordingly the jc H curves show also a small tail in high ®eld region. Since jc value in the small tail region is almost 4 104 times smaller than that in the low ®eld region, therefore it is safe to conclude that this small tail is due to some secondary eect, such as some local regions with very strong pinning or the surface pinning by the tiny grains. From the contour of jc vs. H shown in Fig. 3 one can see that there are two regions with two dif-
Fig. 3. Critical current density jc calculated based on the Bean critical state model. At each temperature the data has been measured with three ®eld sweeping rate: 200, 100, 50 Oe/s. The faster sweeping rate corresponds to a higher dissipation and thus higher current density. From these data one can calculate the dynamical magnetic relaxation rate Q. The jc H curves measured at low temperatures are very close to each other bulk showing a rather stable value of Hirr when T approaches 0 K. The dashed horizontal line marks the criterion of jc 30 A/cm2 bulk for determining the Hirr . While by following the small tail (which has been attributed to a secondary eect) to a criterion g of jc 3 A/cm2 , another phase line Hirr is determined.
ferent properties of ¯ux dynamics: one before the tail with a sharp drop of jc and another one in the tail region. Accordingly there are two ways to determine the so-called irreversibility line Hirr T . The ®rst way is to take a criterion for jc 30 A/ cm2 just before the appearance of the tail. This bulk is named as the bulk irreversibility line Hirr T which signals the sharp drop of jc before the appearance of the tail and re¯ects the irreversible ¯ux motion in clean samples. The second way is just to follow the small tail to a criterion of 3 A/cm2 . In this way one can determine a higher irreversibilg ity line Hirr T which marks a boundary above which a complete reversible ¯ux motion occurs. As mentioned above, the small tail in our present samples is due to a secondary eect, therefore the bulk major part of the vortex system melt at Hirr T . bulk Thus we may conclude that the Hirr T re¯ects the melting of the vortex matter in the clean limit, for example, in single crystals. If more pinning centers are introduced into the sample, one should be possible to push the Hirr T more close to the upper critical ®eld Hc2 T .
H.H. Wen et al. / Physica C 363 (2001) 170±178
The second method to determine the irreversibility line Hirr T and the upper critical ®eld Hc2 T is to measure the temperature dependence of magnetization in the FC and ZFC processes as shown in Fig. 4 for a second piece of HP synthesized MgB2 bulk measured on SQUID. A typical example for how to determine Hirr T and Hc2 T is shown in the inset of Fig. 4. The Hirr T and Hc2 T is determined from the point at which the magnetization start to deviate from the normal state linear background, while the Hirr T line is determined by taking the deviating point between ZFC± FC M T curves with a criterion of DMZFC±FC 10 4 emu. The third method to determine the Hirr T and Hc2 T is to measure the resistive transitions at dierent magnetic ®elds. As shown in Fig. 5, a parallel shift of RT curves at higher magnetic ®elds is observed although a gradual broadening behavior appears in the low dissipation part. This is in contrast to that in the high Tc cuprate superconductors (HTS) in which the ®eld induced
173
Fig. 5. Resistive transition of high pressure sintered MgB2 samples at various magnetic ®elds. The R T curves shift parallel to lower temperatures when higher magnetic ®elds are applied.
broadening eect is much stronger and almost no parallel shift of R T curves has been observed. At a ®eld of 8 T, a ®nite resistance appears down to the lowest temperature (4.2 K) here showing already a rather low irreversibility temperature Tirr . The Hirr T was determined by taking a criterion of 10 5 X, while for the upper critical ®eld Hc2 T , both we and Takano et al. [4] have determined the upper critical point Tc2 from the point at which the resistance starts to deviate from the normal state resistance. All the phase lines determined by using the three methods mentioned above will be presented and discussed below.
4. Discussion 4.1. Vortex phase diagram of MgB2 Fig. 4. Temperature dependence of the magnetization measured in the ZFC and FC processes on another HP bulk by SQUID at ®elds of 0.1, 0.5, 1, 2, 3, 4 and 5.5 T. All ®lled symbols are corresponding to the magnetization measured in the ZFC process. In the main frame all the FC M T curves are crowded in a small region. As shown in the inset, the Hc2 T is determined from the point at which the magnetization starts to deviate from the normal state linear background, while the Hirr T line is determined by taking the deviating point between ZFC±FC M T curves with a criterion of DMZFC±FC 10 4 emu. In the measurement by a SQUID the small tail of MHL is hard to be observed due to the slow data acquisition speed.
The phase lines of Hirr T and Hc2 T determined by following the dierent methods mentioned above are shown in Fig. 6. It is clear that the bulk bulk irreversibility line Hirr T determined from MHL measurement at the point just before the appearance of the small tail shown in Fig. 3 terminates at about 8 T at 2 K, which is very close to that determined by resistive measurement and from the M±T measurement (Fig. 4). This strongly indicates bulk that the Hirr T is a vortex melting line which signals the appearance of a ®nite linear resistivity.
174
H.H. Wen et al. / Physica C 363 (2001) 170±178
Fig. 6. H ±T phase diagram for the new superconductor MgB2 . bulk The ®lled circles represent the bulk irreversibility lines Hirr in this work measured by VSM from MHL with criterion of jc 30 A/m2 ; half-®lled circles, Hirr T for another HP sample measured by SQUID from ZFC±FC M T with criterion of DM 10 4 emu; open circles, Hirr of MgB2 ®lm with Tc 38 K and jc 0 T; 14 K 1:8 107 A/cm2 ; open diamond, Hirr of the HP sample measured by resistive transport. The triangles g represent the Hirr T : ®lled triangles, determined directly from the small tail; open triangles, following the tendency of tail (shown by the three dashed lines in Fig. 3) to a criterion of jc 3 A/cm2 . The ®lled squares represent the Hc2 T data of Takano et al. from resistive measurement; open squares, Hc2 T data in this work from the M T measurement by SQUID; ®lled diamond, Hc2 T data in this work by transport measurement. All the lines are guides to the eye.
By following the small tail to a lower criterion, g another irreversibility line Hirr T is determined. g The extrapolated value Hirr reaches about 12 T at 2 K. There is a large separation between these two phase lines characterizing dierent irreversible ¯ux motion. It is important to note that Larbalestier et al. [9] have found the similar feature where they bulk regard the lower phase line Hirr T as the Kramer line. Together plotted in Fig. 6 are the upper critical ®eld Hc2 T determined from Fig. 4 the temperature dependent magnetization by de®ning the Hc2 T as the point at which the magnetization starts to deviate from the normal state linear background [10] and Fig. 5 the resistive measurement by Takano et al. [4] and by us on HP samples. Although the samples are from dierent groups and dierent techniques have been used to obtain the data, the vortex phase diagram derived here has a good consistency. A striking result shown by this
bulk T extrapovortex phase diagram is that the Hirr lates to a rather low ®eld at 0 K, here for example, bulk Hirr 0 8 T, while the Hc2 T extrapolates to a much higher value (Hc2 0 15 T) [2,11] 1 at 0 K. There is a large separation between the two ®elds bulk Hirr 0 and Hc2 0. This eect can be attributed to either the possible existence of the quantum vortex liquid at 0 K, or the easy ¯ux ¯ow through the weak link regions between the grains. However, worthy of noting is that, the grain size of our sample is much larger than the penetration depth k and the average spacing a0 between the vortices, therefore if there is irreversible ¯ux motion on grains one should be possible to measure it. In this sense we assume that the large separation between Hirr 0 and Hc2 0 is not induced by the weak link property. If following the hypothesis of the vortex liquid above Hirr T , we would conclude that there is a large region of magnetic ®eld for the existence of a vortex liquid at 0 K. This can be attributed to a quantum ¯uctuation eect of vortices in bulk MgB2 . Although the lowest temperature in our present experiment is 1.6 K, however, from the experimental data one cannot ®nd any tendency for Hirr T to turn upward rapidly to meet the Hc2 0. One may argue that the Hirr T probably can be increased to higher values by introducing more pinning centers into this sample. This is basically correct since recently a higher irreversibility line Hirr T has been found in some MgB2 thin ®lms [6] and bulk samples irradiated by protons [12]. Actually in our recent experiment on MgB2 thin ®lms (shown in Fig. 6 by open circles), the irreversibility line Hirr T is also close to that of bulks. This indicates that the large separation between the bulk Hirr 0 and Hc2 0 may be an intrinsic property of MgB2 in the clean limit. It can be interpreted as the quantum vortex melting due to the strong quantum ¯uctuation which smears the perfect vortex lattice
1 Although the upper critical ®eld Hc2 T has been measured up to only 5.5 T here (and Takano et al. measured up to 9 T), from the data shown in Fig. 6 one can derive a slope of d l0 H =dT 0:62 0:2 T/K near Tc . At present, since the mechanism of the new superconductor MgB2 is unknown, we can only use the WHH relation l0 Hc2 0 0:69Tc d l0 H =dT [11] to derive l0 Hc2 0 which is found to be 17 T. It is much higher than the extrapolated value l0 Hirr 0 8 T.
H.H. Wen et al. / Physica C 363 (2001) 170±178
leading to the vanishing of the shear module C66 of the vortex matter (probably within grains). Dense disorders will strengthen the shear module and thus enhance the bulk irreversibility line. By irradiating the MgB2 samples with protons, Bugoslavsky et al. [12] found that jc is not suppressed but strongly increased. This suggests that the low value of bulk Hirr T measured in unirradiated bulks or rather pure ®lms (like our samples here) is not due to the weak links since otherwise the jc value would drop even faster with increasing the magnetic ®eld after the irradiation. This further indicates that the rabulk ther low Hirr T observed in our present work re¯ects the melting of the vortex matter in samples with relatively pure structural details rather than the breaking of the Josephson couplings between grains. In addition, as mentioned above, the bulk Hirr T found in present work is very close (or identical) to those by other authors [5,13] found in bulks, therefore it shows a more intrinsic feature corresponding to the melting of vortex matter in the rather pure system. 4.2. Large separation between Hirr 0 and Hc2 0 and possible evidence for strong quantum ¯uctuation of vortices In order to investigate the ¯ux dynamics in the bulk vortex solid state below Hirr T and to see more clearly what happens when Hirr T is approached, we have carried out the dynamical relaxation measurement. According to Schnack et al. [14] and Jirsa et al. [15], in a ®eld sweeping process, if the ®eld sweeping rate is high enough, the quantity Q d ln DM=d ln dH =dt is close to the relaxation rate S d ln M=d ln t measured in the conventional relaxation method, where Q is called as the dynamical relaxation rate, DM the width of the MHL, dH =dt the ®eld sweeping rate. The raw data with three dierent sweeping rate (200, 100, and 50 Oe/s) are shown in Fig. 3. The Q values vs. ®eld for dierent temperatures are determined and shown in Fig. 7. It is clear that the relaxation rate increases monotonically with the external magnetic ®eld and extrapolates to 100% at the bulk melting bulk point Hirr . Here we concentrate on the ¯ux dynamics before the setting in of the small tail. At 2 K it is found from the Q H data that the vortex
175
Fig. 7. Field dependence of the relaxation rate at temperatures of 2, 4, 6, 8, 10, 14, 18, 22, 26, 30, 32, 35, 37 K. The dashed line is a guide to the eye for 2 K. It is clear that Q will rise to 100% at bulk 8 T at 2 K. Since Hirr is rather stable at low temperatures, it is bulk 0 8 T being much smaller than anticipated that Hirr Hc2 0 15 T (here we choose the lower reported value of Hc2 0 obtained by Bud'ko et al. in Ref. [2]).
melting ®eld (where Q 100%) is about 8 T, being bulk (T 2 K) determined from the very close to Hirr bulk jc H curve. It is known that the Hirr T is rather stable in low temperature region, therefore we can bulk anticipate a rather low value of Hirr 0 which is below 9 T being much lower than Hc2 0. Again bulk one can see a large separation between Hirr 0 and Hc2 0. This eect has recently been found also in rather pure MgB2 ®lms [16] with Tc 0 38 K and jc 0 T; 14 K 1:8 107 A/cm2 , in bulks made under AP and even powders. All these may strongly suggest the existence of the quantum vortex liquid due to strong quantum ¯uctuation of vortices in the pure system of MgB2 . Theoretically, quantum melting of the vortex solid has been proposed by some authors [17±21] and preliminarily veri®ed by experiments [22,23]. Solid evidence is, however, still lacking mainly because either the values of Hirr 0 and Hc2 0 T are too high to be accessible, such as in the classical Chevrel phase PbMoS system [24,25], or the separation between them is too small [22,23] leading to a diculty in drawing any unambiguous conclusions. Here we try to have a rough consideration on the quantum melting ®eld Hm proposed by Blatter et al. [17±19] for 2D system
176
Hm 0=Hc2 0 1
H.H. Wen et al. / Physica C 363 (2001) 170±178
p3 CL2 RQ =4R2D
1:2 exp
1
where CL is the Lindermann number, RQ h=e2 4:1 kX, R2D is the sheet resistance. Since the new MgB2 sample has a much higher charge density and thus a much lower sheet resistivity, according to above relation, Hm should be more close to Hc2 0 comparing to HTS. This is in contrast to the experimental observations which may be explained as that the MgB2 is not a quasi-2D system. Another approach was proposed by Rozhkov and Stroud [26], Hm 0=Hc2 0 B0 = B0 Hc2 0
2
2
with B0 bmp C 2 sU0 =4pk 0 q2 , where s is the spacing between layers, mp is the pair mass, q the pair charge (2e), C the light velocity, k 0 the penetration depth at 0 K, b 0:1. If comparing again the present new superconductor MgB2 with HTS, k 0, q and b are more or less in the same scale, the dierence comes from mp and s. Therefore a preliminary conclusion would be that in MgB2 either the pair mass mp or the layer spacing s is much smaller than that of HTS. The precise reason for the strong quantum ¯uctuation of vortices in MgB2 is still unknown. 4.3. Residual relaxation rate at 0 K and weak temperature dependence of the relaxation rate Fig. 8 shows the temperature dependence of the dynamical relaxation rate Q. The arrows point at the irreversibility temperatures at the correbulk sponding ®elds Hirr T . It is clear that the relaxation rate extrapolates to a ®nite value at 0 K for all ®elds. This eect was also observed in high Tc cuprate superconductors and attributed to the quantum tunneling of vortices. The dierence between the MgB2 and the HTS is that the residual relaxation rate Q at 0 K in the former case has a strong ®eld dependence, but in the latter case is weakly dependent on the ®eld, especially for the 3D YBa2 Cu3 O7 system. Another striking point for MgB2 is that in wide temperature region the relaxation rate keeps rather stable against the thermal activation and ¯uctuation. However, when the bulk bulk melting point Hirr T is approached the
Fig. 8. Temperature dependence of the relaxation rate at ®elds of 1, 2, 3, 4, 5, 6 T. The dashed lines are guides to the eye. The bulk arrows point at the bulk irreversibility temperatures Tirr determined from the jc H curve.
relaxation rate will quickly jump to 100%. The magnetic relaxation rate has been determined also with the conventional relaxation method, that is to measure the time dependence of the relaxation rate via S d ln M=d ln t. The raw data are shown in the inset of Fig. 9 and the relaxation rate for 0.5 and 1 T are determined and shown in the main frame of Fig. 9. It is clear the quantum creep rate (if any) at a low ®eld (0.5 T) is only about 0.1% being an order of magnitude lower than that of HTS. Again the relaxation rate S shows a very weak temperature dependence at a ®nite temperature. For example, from 0 to 30 K at 1 T, S increases from 0.1% to about 5%. But when the melting temperature/®eld is reached (35 K at 1 T), the relaxation rate rises sharply from 5% at 30 K to 100% at 35 K. The small relaxation rate at a relatively low ®eld has also been measured by Thompson et al. [27] who regarded it as a highly stable superconducting current density in MgB2 . Actually the relaxation rate can be rather high when the magnetic ®eld is increased to a higher value. The extremely small relaxation rate and weak temperature dependence at a ®nite temperature at a low ®eld is probably induced by a strong pinning barrier relative to the thermal energy, i.e., kB T Uc , where Uc is the intrinsic pinning energy. Recently it was concluded [28,29] that the Uc is in
H.H. Wen et al. / Physica C 363 (2001) 170±178
177
motion. As mentioned in this paper and shown by the data in Figs. 8 and 9, the quantum tunneling may give a strong in¯uence on the ¯ux dynamics of MgB2 in very wide temperature region. The strong vortex pinning in MgB2 may be induced by the twin boundaries or weak link regions and the quantum vortex melting in polycrystalline bulks may ®rst occur on the grains. In this case the irradiation on MgB2 bulks by heavy ions and protons will increase the critical current density and enhance the irreversibility of ¯ux motion. Fig. 9. The magnetic relaxation rate determined by S d ln M=d ln t at ®elds of 0.5 and 1 T. The inset shows the original data of magnetization versus time, a good linear relation has been found between M and ln t manifesting a Kim± Anderson type of eective pinning barrier.
the scale of 1000 K being much higher than the thermal energy kB T . Therefore for the new superconductor MgB2 the pinning well is too deep leading to a trivial in¯uence of the thermal activation and ¯uctuation. It thus naturally suggests that the quantum ¯uctuation and tunneling plays an more important role. Therefore, together with the fact discussed in last sub-section, it is tempting to suggest that the melting between a vortex solid and a liquid is due to quantum ¯uctuation instead of the thermal ¯uctuation. From the inset of Fig. 9 one can see that the magnetization follows roughly the relation M t; T M 0; T A ln t indicating the Kim± Anderson linear U j relation, where U is the eective pinning barrier and j is the externally applied current density. Therefore in the vortex tunneling or activation process in MgB2 , a ¯ux segment with a ®xed length is involved. This is rather dierent from HTS in which the collective pinning and creep are dominant and the optimal hopping/tunneling length (volume) of vortex line (bundle) varies with the external force (current) leading to a non-linear U j relation. Recently Qin et al. [30] derived a non-linear U j relation for MgB2 bulks based on the so-called Maley's method [31]. One should however take cautions to derive U j relation by using Maley's method here since it is only applicable to the thermally activated ¯ux
5. Conclusion In rather pure samples of MgB2 the irreversibility ®eld is rather low comparing to the upper critical ®eld in low temperature region. This eect has been attributed to either the possible existence of the quantum vortex liquid due to strong quantum ¯uctuation of vortices, or the easy ¯ux ¯ow through the weak link channels. The temperature and ®eld dependence of the relaxation rate may further suggest that the vortex melting at a ®nite temperature is also induced by strong quantum ¯uctuation in pure systems, such as single crystals and bulks. A small tail following the jc H curve in high ®eld region is attributed to a secondary eect induced by strong pinning or surface barrier on some tiny grains. This opens a way for the higher irreversibility line when more pinning centers are introduced into the pure sample. Magnetic relaxation measurement shows that the intrinsic pinning barrier is much higher than the thermal energy, this may also interpret the trivial importance of the thermal activation and thermal ¯uctuation. In comparison the quantum tunneling and the ¯uctuation shows a much stronger in¯uence. The reason for such a strong quantum eect is still unknown, but it may be related to the superconducting mechanism of MgB2 , such as the relatively low upper critical ®eld. Acknowledgements This work is supported by the National Science Foundation of China (NSFC 19825111) and the Ministry of Science and Technology of China
178
H.H. Wen et al. / Physica C 363 (2001) 170±178
(project: NKBRSF-G1999064602). HHW gratefully acknowledges Prof. B. Ivlev and Dr. A.F.Th. Hoekstra for fruitful discussions, and continuing ®nancial support from the Alexander von Humboldt foundation, Germany.
References [1] J. Nagamatsu, N. Nakagawa, T. Maranaka, Y. Zenitani, J. Akimitsu, Nature 410 (2001) 63. [2] S.L. Bud'ko, C. Petrovic, G. Lapertot, C.E. Cunningham, P.C. Can®eld, cond-mat/0102413 (2001). [3] P.C. Can®eld, D.K. Finnemore, S.L. Bud'ko, J.E. Ostenson, G. Lapertot, C.E. Cunningham, C. Petrovic, condmat/0102289 (2001). [4] Y. Takano, H. Takeya, H. Fujii, H. Kumakura, T. Hatano, K. Togano, H. Kito, H. Ihara, cond-mat/ 0102167 (2001). [5] D.K. Finnemore, J.E. Ostenson, S.L. Bud'ko, G. Lapertot, P.C. Can®eld, cond-mat/0102114 (2001). [6] C.B. Eom, M.K. Lee, J.H. Choi, L. Belenky, X. Song, L.D. Cooley, M.T. Naus, S. Patnaik, J. Jiang, M. Rikel, A. Polyanskii, A. Gurevich, X.Y. Cai, S.D. Bu, S.E. Babcock, E.E. Hellstrom, D.C. Larbalestier, N. Rogado, K.A. Regan, M.A. Hayward, T. He, J.S. Slusky, K. Inumaru, M.K. Haas, R.J. Cava, Nature 411 (2001) 558. [7] Z.A. Ren, G.C. Che, Z.X. Zhao, H. Chen, C. Dong, Y.M. Ni, S.L. Jia, H.H. Wen, Chin. Phys. Lett. 18 (2001) 589. [8] Z.W. Zhao, H.H. Wen, S.L. Li, Z.A. Ren, G.C. Che, Z.X. Zhao, in press. [9] D.C. Larbalestier et al., Nature 410 (2001) 186. [10] H.H. Wen, S.L. Li, Z.W. Zhao, Y.M. Ni, Z.A. Ren, G.C. Che, H.P. Yang, Z.Y. Liu, Z.X. Zhao, Chin. Phys. Lett. 18 (2001) 816.
[11] N.R. Werthamer, E. Helfand, P.C. Hohemberg, Phys. Rev. 147 (1966) 362. [12] Y. Bugoslavsky, L.F. Cohen, G.K. Perkins, M. Polichetti, T.J. Tate, R. Gwilliam, A.D. Caplin, Nature 411 (2001) 561. [13] Y. Bugoslavsky, G.K. Perkins, X. Qi, L.F. Cohen, A.D. Caplin, Nature 410 (2001) 563. [14] H.G. Schnack, R. Griessen, J.G. Lensink, C.J. Van der Beek, P.H. Kes, Physica C 197 (1992) 337. [15] M. Jirsa, L. Pust, Physica C 207 (1993) 85. [16] H.H. Wen, S.L. Li, Z.W. Li, W.N. Kang, H.J. Kim, E.M. Choi, S.I. Lee, in press. [17] G. Blatter, B. Ivlev, Phys. Rev. Lett. 70 (1993) 2621. [18] G. Blatter, B.I. Ivlev, Phys. Rev. B 50 (1994) 10272. [19] G. Blatter et al., Phys. Rev. B 50 (1994) 13013. [20] A. Kramer, S. Doniach, Phys. Rev. Lett. 81 (1998) 3523. [21] R. Ikeda, Int. J. Mod. Phys. B 10 (1996) 601. [22] T. Sasaki, W. Biberacher, K. Neumaier, W. Hehn, A. Andres, Phys. Rev. B 57 (1998) 10889. [23] S. Okuma, Y. Imamoto, M. Morita, Phys. Rev. Lett. 86 (2001) 3136. [24] C. Rossel, E. Sandvold, M. Sergent, R. Chevrel, M. Potel, Physica C 165 (1990) 233. [25] C. Rossel, O. Pena, H. Schmitt, M. Sergent, Physica C 181 (1991) 363. [26] A. Rozhkov, D. Stroud, Phys. Rev. B 54 (1996) R12697. [27] J.R. Thompson, M. Paranthaman, D.K. Christen, K.D. Sorge, H.J. Kim, J.G. Ossandon, cond-mat/0103514. [28] H. Jin, H.H. Wen, Chin. Phys. Lett. 18 (2001) 823. [29] Z.W. Zhao, H.H. Wen, S.L. Li, Y.M. Ni, Z.A. Ren, G.C. Che, H.P. Yang, Z.Y. Liu, Z.X. Zhao, Chin. Phys. 10 (2001) 340. [30] M.J. Qin, X.L. Wang, H.K. Liu, S.X. Dou, cond-mat/ 0104112. [31] M.P. Maley, J.O. Willis, H. Lessure, M.E. McHenry, Phys. Rev. B 42 (1990) 2639.