Surface barrier e�ect and the crossover in magnetizationrelaxation in 2H-NbSe2

P.K. Mishra a,*, G. Ravikumar a, T.V. Chandrasekhar Rao a, V.C. Sahni a,S.S. Banerjee b, S. Ramakrishnan b, A.K. Grover b, M.J. Higgins c

a Technical Physics and Prototype Engineering Division, Bhabha Atomic Research Centre, Mumbai 400 085, Indiab Department of Condensed Matter Physics and Material Sciences, Tata Institute of Fundamental Research, Mumbai 400 005, India

c NEC Research Institute, 4 Independence way, Princeton, NJ 08540, USA

Received 1 May 2000; received in revised form 16 May 2000; accepted 16 May 2000

Abstract

We have studied the low ®eld magnetization hysteresis and relaxation process in pure 2H-NbSe2 single crystal. Our

results show an order of magnitude di�erence in the relaxation rate for the ¯ux entry and the ¯ux exit. Also, we have

observed a characteristic change of slope in M(ln t) curve in the ¯ux-exit case. We analyse this asymmetry in the re-

laxation rate and the change of slope in M(ln t) curve in the framework of surface barrier controlled irreversible

magnetic behaviour. Ó 2000 Elsevier Science B.V. All rights reserved.

Keywords: Type II superconductors; Surface barrier; Magnetization relaxation

Time decay of magnetization due to ¯ux creepover surface barrier has been viewed as an enigmain recent years. The most intriguing aspect of thephenomenon lies in its experimental observation.However, in general, this is not so apparent inmost hard superconductors due to the strongerbulk pinning overshadowing the e�ect of weakersurface pinning component.

Present description of magnetization hysteresisand relaxation is based on Bean's critical state

model [1] and Anderson±Kim theory [2] of ther-mally activated ¯ux creep, respectively. Togetherthese provide a reasonably satisfactory picture ofthe role of the bulk pinning on the magnetizationhysteresis and the vortex dynamics. Within thisapproach, the magnetization relaxation rate re-mains symmetric for ®eld increasing and decreas-ing directions. In other words, the magnetizationdecay rate at a given magnetic ®eld is nearly thesame whether the critical state is reached by in-creasing or decreasing the magnetic ®eld. Experi-mental justi®cation for this prescription wasprovided by Beasley et al. [3] in the case of con-ventional superconductors. Unlike in bulk pinningdominated regime, the typical ®ngerprint of thesurface barrier pinning is found in magnetizationhysteresis loop measurements and is recognized by

Physica C 340 (2000) 65±70

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its asymmetric shape [6]. Intuitively, one can ex-pect that in situations where the ¯ux pinning iscontrolled by surface barrier e�ects, associatedmagnetization relaxation data may also show sim-ilar asymmetric behaviour.

In many weakly pinned superconductors, thesigni®cance of surface barrier, presumably ofBean±Livingston [4] type resulting in irreversiblemagnetic behaviour, has gained wide acclaimation.Amongst usually studied superconductors, theprominence of surface barrier is easily felt in high-Tc materials, especially at elevated temperatureswhere the strength of bulk pinning is substantiallyreduced by thermal ¯uctuations. In contrast, atlow temperatures, bulk pinning is expected to bethe main source of hysteretic magnetization. Inmost systems, whether high-Tc superconductor orconventional low-Tc superconductor, both types ofpinnings manifest their prominence in di�erenttemperature and magnetic ®eld regimes [5]. Cur-rent distribution measurements in di�erent super-conductors have revealed that current indeedremained mostly con®ned to the edges [10,11]where ¯ux lines enter or leave the sample.

It could also be possible to observe similar re-gimes in the time dependence of magnetization.However, complication arises when there is anoverlap of the e�ect of bulk pinning and surfacepinning. In order to have a comprehensive un-derstanding of the time decay of magnetization ina weakly pinned system, a careful simultaneousconsideration of both the bulk and the surfacepinning possibilities is necessary. Recent experi-mental studies on magnetization relaxation inhigh-Tc superconductors reveal the observation ofa crossover from one pinning regime to the otherwithin the experimental time window [7,8]. How-ever, these studies provide con¯icting conclusionsregarding the type of pinning that turn out ®rst inthe relaxation process.

Evidently, the best way to elucidate the e�ca-cies of surface barrier e�ect in the relaxation pro-cess is to look for a system with very weak bulkpinning. In this context, the weakly pinned singlecrystals of 2H-NbSe2 are attractive candidates. Inthis anisotropic superconductor, the ratio Jc=Jo,where Jc is the critical current density and Jo, thedepairing current density, is of the order of 10ÿ5,

which is three to four orders of magnitudes smallerthan that in high-Tc cuprates, making it amongstthe cleanest single crystal system available.

In this paper, we present the e�ect of surfacebarrier on time decay of magnetization in a cleancrystal of 2H-NbSe2. Our observation shows thatthe relaxation rate in the ¯ux-exit case i.e., relax-ation-out case is much larger than that in the ¯ux-entry or relaxation-in case. The most interestingfeature that is seen in the experiment is the cross-over in the relaxation process in the ¯ux-exit case,i.e., when the magnetic ®eld is being reversed. Weinterpret this as a crossover from surface relaxationto bulk relaxation during the time decay of mag-netization. We try to explain this on the basis of atheoretical model developed by Burlachkov [9].

The 2H-NbSe2 single crystal used in the presentstudy has a Tc of 7.1 K. The typical dimensions ofthe sample are 4� 2� 0:30 mm3. Magnetizationdata were recorded using a commercial quantumdesign SQUID magnetometer (MPMS system)with the magnetic ®eld applied parallel to the caxis. We used a scan length of 2 cm in order tominimize the e�ect of magnetic ®eld inhomogene-ity of the superconducting magnet. Fig. 1 shows a

Fig. 1. Magnetization hysteresis loop ( ) at 5 K along with the

remanent magnetization (j). The magnetic ®eld is applied

parallel to the c axis. Arrows indicate the ®eld increasing (¯ux

entry) and decreasing (¯ux exit) directions of the hysteresis

loop.

66 P.K. Mishra et al. / Physica C 340 (2000) 65±70

portion of the magnetization hysteresis loop at low®elds at 5 K, along with the remanent magneti-zation Mrem plotted as a function of maximumapplied ®eld. Mrem is the magnetization value atzero ®eld on the reverse leg of a given M±H loop.For each Mrem(H ) in Fig. 1, the M±H loop isgenerated up to the corresponding ®eld H. In Fig.1, the surface barrier e�ect is ubiquitous throughdi�erent features. One can see a near-¯at region inthe reverse leg and the characteristic asymmetry ofthe hysteresis loop, which is an established signa-ture of the surface pinning.

The ¯ux invasion into the sample is very sharpat a ®eld Hp, and also the remanent magnetization,Mrem, is observed to decrease very sharply to zeronear the ®eld Hp. This shows the inability of ¯uxtrapping below Hp (i.e., Mrem � 0) and signi®esthat during the ascending branch up to the ®eld Hp

is nearly in the Meissner region. The above fea-tures are also observed at 6 and 6.5 K. Anotherimportant signature of the surface pinning, as in-ferred from the Clem model [6], is the 1/H de-pendence of the critical current for ®elds greaterthan the penetration ®eld Hp. In Fig. 2 we haveshown, for ®elds greater than Hp, the variation of

the width of the hysteresis DM �Mrev ÿMfor� whichis a measure of critical current density Jc with theinverse of the magnetic ®eld at three di�erenttemperatures. The linearity of these plots conformto the above prescription for surface barrierdominated irreversible behaviour.

Time dependent magnetization measurementwas carried out at 120 s interval for 2 h durationfor each ®eld setting. In Fig. 3, the logarithmicrelaxation rate dM=d�ln t) is plotted for both ®eldincrease (¯ux entry) and ®eld decrease (¯ux exit)cases as a function of applied ®eld. Note that the¯ux-exit relaxation rate is greater than that for ¯ux

Fig. 2. Width of the hysteresis loop (/ Jc) plotted as a function

of the inverse of the applied magnetic ®eld H, (for H > Hp), at

three di�erent temperatures. The linearity shows the dominance

of the surface barrier in the irreversibility.

Fig. 3. Logarithmic relaxation rate both for ¯ux entry and ¯ux

exit at (a) 5 K and (b) 6.5 K plotted at di�erent magnetic ®elds.

Circles and triangles represent the ¯ux-entry and ¯ux-exit re-

laxations respectively. At low magnetic ®eld, the di�erence be-

tween the two can be seen to be signi®cant.

P.K. Mishra et al. / Physica C 340 (2000) 65±70 67

entry. At lower ®elds, it is nearly 10 times fasterduring ¯ux exit as compared to that during ¯uxentry at corresponding magnetic ®elds.

Figs. 4(a) and (b) show the actual M vs. timedata during the ®eld reverse (¯ux exit) case fordi�erent ®elds: at 5 and 6.5 K, respectively. Here,the prominent feature to note is a crossover in thelogarithmic relaxation rate. The crossover can beviewed as a dynamic change in the regime ofrelaxation, i.e., from relaxation over one type ofbarrier to the other. The dynamic crossover has itsown magnetic ®eld dependence. At lower ®elds,this crossover feature is absent and it starts ap-pearing at moderately high ®elds. Again, as themagnetic ®eld increases, the crossover feature

shifts to shorter time scale. We need to point outhere that the slope values in M�ln t� plotted in Fig.3 corresponds to the major portion of the timewindow of the relaxation process. We also recallthat this crossover is absent in the ®eld increasing(¯ux entry) case within the same time window. InFig. 3, it can be seen that though the ¯ux-exit re-laxation rate at the low ®elds does not vary much,at higher ®elds, it approaches fast towards the¯ux-entry relaxation rate. At 6.5 K, this featurecan be seen to occur at H � 500 Oe (cf. Fig. 3(b)).

The large di�erence in the relaxation rate in theabove two histories and the crossover phenome-non supports the assertion that surface pinningdoes indeed play a signi®cant role in magnetic

Fig. 4. Time dependence of the ¯ux exit magnetization at di�erent magnetic ®elds: (a) at 5 K and (b) at 6.5 K. The change in the slope

can be seen as a deviation from the solid line. The initial relaxation is over the surface barrier after which the crossover is to the slower

bulk relaxation.

68 P.K. Mishra et al. / Physica C 340 (2000) 65±70

behaviour of NbSe2 [10]. The di�erence in thesurface barrier e�ects in the two cases can providea plausible explanation for the above observations.In the ¯ux entry case, there is strong surface bar-rier e�ect. Flux lines have to surmount this ®rstbefore they penetrate the sample, whereas in thereverse case, the surface barrier e�ect is compara-tively weak and ¯ux lines escape the sample rathereasily as they are only subjected to residual bulkpinning.

Burlachkov's argument [9] could help us tocorrelate the observed crossover in the logarithmicdecay rate with an interplay of two di�erent pin-ning regimes each with its own characteristic re-laxation. His model provides a way out of thecomplicated situation when bulk pinning cannotbe ignored completely and has to be consideredsimultaneously along with the surface pinning forrelaxation purposes. Which of the two relaxationprocesses should be observed ®rst, depends on thecorresponding activation energies. Burlachkovasserts that the initial stage of the relaxation isdetermined by the lowest of the activation ener-gies, Ubulk and Usurf . If the bulk pinning is weaki.e., Ubulk < Usurf , then the bulk relaxation shouldbe observed ®rst. This implies that the bulk con-tribution to the total magnetization manifestsprominently in the time decay ®rst and the corre-sponding relaxation rate is thus the bulk relaxationrate. After the bulk relaxation has substantiallymanifested itself, the decay in magnetization dueto surface relaxation takes over at a rate Rsurf <Rbulk. On the other hand, if Usurf < Ubulk, the orderof the two relaxation processes gets reversed.

Keeping in view that high quality crystal of 2H-NbSe2 is well recognized very weak bulk pinningsample, the dominance of surface barrier e�ectsduring ¯ux entry has been elucidated [10]. Tosupport the notion of the weakness of the bulkpinning, we show the plot of pinning force densityFp vs. H in Fig. 5. The peak in Fp is extremelybroad and shallow at 5 K and tends to progres-sively become more ¯at as the sample gets warmedup to 6.5 K. The observed behaviour elucidates theweakness of the bulk pinning even at 5 K. Thuswhile for ¯ux entry, the bulk pinning is the weakeramongst the two, and the observed relaxation rateis the dominated bulk relaxation in our experi-

mental window. Alternatively, it can be stated thatthe ¯ux lines have to surmount the formidablesurface barrier in order to enter into the sampleand once inside, they relax over the residual bulkpinning sites. The bulk time decay of magnetiza-tion as observed is therefore a slow one and thetime window of 2 h is not su�cient to observea crossover to the time window where surfacerelaxation could dominate. On the other hand,during the ¯ux exit case, the surface barrier e�ect isvery weak. Thus, in that case, the initial relaxationis over the residual surface barriers. This processbeing very fast, allows us to see a crossover to theslower bulk relaxation within the time window of2 h. This can be conveniently seen in panels ofFig. 4(a) and (b). At shorter times (t � 102 s), themagnetization decay rate at di�erent ®elds isnearly the same. However, after some time, changein relaxation rate can branchout di�erent curves.At higher ®elds, the crossover in relaxation ratecan be clearly seen within the time window of thepresent study. After crossover, the relaxation rateapproaches to the value observed during the ¯uxentry. This clearly con®rms that during the ¯uxexit, the latter portion of the relaxation after thecrossover corresponds to the bulk relaxation andthe initial faster relaxation corresponds to thesurface relaxation.

Fig. 5. Pinning force density Fp�H� at three di�erent tempera-

tures.

P.K. Mishra et al. / Physica C 340 (2000) 65±70 69

In conclusion, we have presented a manifesta-tion of the magnetization relaxation over the sur-face barrier in a very weakly pinned system like2H-NbSe2. The e�cacy of the surface barrier inthis system has been highlighted through the ob-served asymmetry in the relaxation rates for the¯ux entry and the ¯ux exit. Relaxation rate duringthe ¯ux exit are typically much greater than duringthe ¯ux entry. During the ¯ux exit, we could see acrossover in the relaxation rate in the form of adistinct change in the slope of M�ln t�. This is ac-counted for in terms of di�erent strength of thetwo pinning processes.

Acknowledgements

It is a pleasure to acknowledge Prof. ShoboBhattacharya for many interesting discussions andthe insights provided by him.

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