PHYSICAL REVIEW B, VOLUME 65, 094507

Vortex-state metastability at low-field disorder-order transition

G. Ravikumar,1,2 H. Kupfer,1 A. Will, 1 R. Meier-Hirmer,1 and Th. Wolf31Institut fur Technische Physik, Forschungszentrum Karlsruhe GmbH and Universita¨t Karlsruhe, D-76021 Karlsruhe, Germany

2Technical Physics and Prototype Engineering Division, Bhabha Atomic Research Centre, Mumbai-400085, India3Institut fur Festkorperphysik, Forschungszentrum Karlsruhe GmbH, D-76021 Karlsruhe, Germany

~Received 2 August 2001; published 5 February 2002!

We report history-dependent critical currents across the disordered solid to Bragg glass transition occurringin the low-field region in V3Si and NdBa2Cu3O72x single crystals. This is in addition to the history depen-dence usually observed near the high-field Bragg-glass–disordered-solid transition. It is further shown that themetastablefrozen-indisordered vortex matter coexists with the ordered phase in the entire Bragg glass region.We conclude that the amount of the metastable disordered phase prior to the high-field Bragg-glass–disordered-solid transition is crucial in nucleating further growth of the disordered phase near the transition.This mechanism results in the onset of the high-field peak to occur at lower fields when thefrozen-indisor-dered phase prior to the transition is larger.

DOI: 10.1103/PhysRevB.65.094507 PACS number~s!: 74.60.Ge, 74.72.Jt

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In the mixed state of type-II superconductors, just abothe first critical field, the intervortex distance is comparato the London penetration depth. In this low-field regimpinning is always dominant and a highly disordered flux lilattice is therefore preferred. As the field is progressivincreased, a growing intervortex interaction stabilizesquasiordered Bragg glass phase~Fig. 1!. The field where thislow-field disorder-order~LF-O/D! transition1,2 occurs de-pends on the extent of quenched disorder in the superductor. At further higher fields, Bragg glass phase againdergoes a transition to a highly disordered state.3 This high-field order-disorder ~HF-O/D! transition ~Fig. 1! ischaracterized by a sharp increase in critical current denJc , known as peak effect or second magnetization peak4,5

The HF-O/D transition is usually accompanied by vortestate metastability and history dependence inJc .6–18 In ad-dition, we present experimental results to show the histdependence inJc also near the LF-O/D transition. It warecently argued that both the LF-O/D and HF-O/D transitioare first order in nature,2 consistent with observed historeffects. There is indeed a growing consensus that it iquenched-disorder-induced first-order transition of vormatter.2,15,19,20

The physical mechanism for the metastability in the vicity of the HF-O/D transition is a subject of current discusion. Paltielet al.2,23 proposed that the metastable-disordephase is injected at surface imperfections which dynamiccoexist with the stable-ordered phase prior to the transitBased on our experiments, we shall argue that the presof a small amount of metastable-disordered phase prior totransition nucleates the growth of the disordered phaseaccumulating more vortices as the field is increased. Four experiments, it appears that this mechanism is predonant over that proposed by Paltielet al.2,23

Magnetization experiments on a V3Si crystal (1.6 mm30.5 mm30.3 mm) with weak pinning (Tc517 K) and atwin-free NdBa2Cu3O72x (Nd123) crystal (1.4 mm30.5 mm30.2 mm) withTc595 K ~Ref. 18! are carriedout using an Oxford vibrating sample magnetometer. Nd1crystal was oriented with itsc axis parallel to the field. V3Sicrystal was oriented with the field parallel to its smalle

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dimension. Figure 2 shows the magnetic momentm versusfield H in increasing~forward curve! and decreasing~reversecurve! fields for the V3Si sample at 9.5 K~detailed measurements are carried out at this temperature although simresults can be obtained in a wide temperature range! mea-sured with a field sweep rate of 1.2 T/min. Forward curvemeasured from a sufficiently large negative field so thatduced currents are unidirectional. The initial sharp fall in tmagnetization hysteresis~or Jc) is associated with the disordered solid to Bragg glass transition as discussed aboveidentify the HF-O/D transition by the onset (Hon) of a sharpdecrease in magnetic moment occurring on the forward cuat around 6 T.5 Such a choice is justified later. The exalocation of the transition is, however, controversial due tooccurrence of metastability.

It is common to investigate the history dependentJc bymeans of minor magnetization curves.9–11,13,14,17,18For in-stance, near the HF-O/D transition, the minor curves staron the forward curve~point A in Fig. 2! saturate and do nomeet the reverse curve until much lower fields. On the othand, minor curves starting on the reverse curve~point B inFig. 2! overshoot the forward curve. As discussed in Ref.

FIG. 1. Schematic phase diagram in the mixed state of a typsuperconductor depicting the Bragg glass and disordered sphases. Thermal effects that are important in high-Tc materials are,however, ignored.Hc1 and Hc2 are the first and second criticafields respectively. HF-O/D and LF-O/D lines define the high- alow-field boundaries of the Bragg glass phase@see Paltielet al.~Ref. 2!#.

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this suggests thatJc is larger on the decreasing field brancthan on the increasing field branch. However, close to thepeak positionHp , the minor curves~starting atC and D!merge into the main magnetization loop, indicating thatJc isindependent of magnetic history.

In Figs. 3 and 4, we present minor curves in the low-fieregion ~around 1 T! for V3Si and Nd123 samples, respetively. Here, the minor curves starting from the forwacurve overshoot the reverse curve@Figs. 3~a! and 4~a!#. Onthe other hand, the minor curves starting from the revecurve saturate and do not meet the forward curve untmuch higher field@Figs. 3~b! and 4~b!#. This behavior, ex-actly opposite to that seen near the HF-O/D transition~Fig.2!, is observed over a wide temperature range, for fieabove 0.2 T. This behavior of minor curves clearly showshistory-dependentJc near the LF-O/D transition; i.e.,Jc islarger on the increasing field branch than on the decreasfield branch. This conclusion is just opposite to that near tHF-O/D transition. As expected, the effect in Nd123 is muweaker than in V3Si, because stronger thermal fluctuationshigh-Tc materials significantly weaken the observable mestability.

The history dependence inJc near the HF-O/D transitionwas recently explained by invoking supercooling9,11,15,21,22ofthe high-field disordered solid phase~high Jc) upon loweringthe field below the HF-O/D transition line~path 1 in Fig. 1!.Similarly, the quasiordered Bragg glass phasesuperheated15,22 by increasing the field above this line.14

Consequently, vortex matter is relatively more order~lower Jc) on the forward curve than on the reverse curThe termssupercoolingandsuperheatingare usually associated with first-order transitions where the free energytwo minima. In the case of the order-disorder transition mtiple free energy minima and metastable vortex configutions due to quenched disorder may effectively producesu-percoolingandsuperheatingeffects.

The history-dependentJc in the low-field region can beunderstood in a similar way. Here, the low-field disordersolid phase is superheated upon increasing the field~forwardcurve! above the LF-O/D line~path 2 in Fig. 1!. On the other

FIG. 2. Forward and reversem-H curves in a V3Si sampleindicating the HF-O/D and LF-O/D transitions and the peak fiHp . Typical behavior of minor curves starting from the forwa~solid line! and reverse curves~dotted line! near the HF-O/D tran-sition. Close toHp , the minor curves readily merge into the maloop.

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hand, upon decreasing the field below this line, the Braglass phase is supercooled, resulting in a relatively moredered~thus lowJc) vortex lattice on the reverse curve thaon the forward curve.

Jc ceases to be history dependent close to the peakHp , beyond which only the disordered phase can existthe ordered phase cannot be present even in the metasform. Similar arguments apply on the low-field side belowcertain fieldHL ~about 0.2 T! whereJc is no longer historydependent. The location of both HF-O/D and LF-O/D trasitions is limited by these two fieldsHp and HL , respec-tively. The low-field minor curves can be used to determthe field HL , below which the vortex matter is unambiguously in a disordered equilibrium state.

We now refocus on the minor curves drawn in Fig. 3~b!,which do not meet the forward curve up to a field of abouT, which is well aboveHon . Below Hon , they are almostparallel, each corresponding to a different metastable swith a specific amount offrozen-indisordered phase. Clearlythe position of the onset seems to be very sensitive tofrozen-in disorder. In the main panel, we show two dottlines, which are linear extrapolations of them-H data ~i!

FIG. 3. ~a! Minor curves starting from the forward curve in thlow-field region overshoot the reverse curve.~b! In the low-fieldregion, minor curves starting from the reverse curve saturate annot meet the forward curve until a field of about 7 T (.Hon). Notethe shift in the HF-O/D transition (Hon) to higher fields on theminor curves. The inset showsHon plotted as a function of theabsolute value ofm at a field of 5.5 T, on different minor curves.

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VORTEX-STATE METASTABILITY AT LOW-FIELD . . . PHYSICAL REVIEW B 65 094507

above 5 T on the low-field side and~ii ! below 7 T on thehigh-field side. The intersection point is used as the criterto determineHon , the position of HF-O/D transition, on different minor curves. In the inset,Hon measured on differenminor curves is plotted as a function of them value at 5.5 Ton that minor curve. As shown in the inset, this criterioused in obtainingHon , gives a total shift in the transition oabout 0.2 T. Alternative criteria—for instance, the fiewhere them value changes significantly from an almost costant value below the transition—would give a much highspread~about 0.6 T! in the transition field. Assuming that thdifferent magnetic moments at 5.5 T are a measure ofdifferent extents offrozen-inmetastable disorder prior to thHF-O/D transition, we conclude that the position of the trasition shifts to lower fields with increasing amountfrozen-in metastable disorder. Within the mechanism pposed by Paltielet al.,23 it is hard to imagine how the startinfield of the minor curves~for instance at 0.5 and 1.0 T! canaffect the disordered phase present at 5.5 T, because, othe minor curves, new vortices entering the system expence identical conditions at the edges. We propose thelowing mechanism to understand the shift in the transitfield on different minor curves.

Close toHon , apparently a small amount of metastabdisordered phase can nucleate further growth of the didered phase by accumulating more vortices as the fielincreased. The growth is faster when the initial frozendisorder is larger~or more nucleating sites!. In the absence ofrozen-in disorder, vortex matter continues to be relativeordered up to much higher fields, leading to an apparent sin the onset field to higher values. On the minor curves,frozen-inmetastable disordered phase prior to the transiis smaller and therefore the onset of the peak occurs at hifields. In other words, thefrozen-indisordered phase~nucle-ating sites! prevents superheating of the ordered phasetriggering the transition, analogous to the case in stand

FIG. 4. Low-field~below 1 T! minor curves in Nd123 crystal a69 K. In ~a! minor curves starting from the forward curve~notshown! overshoot the reverse curve as in Fig. 3~a!. ~b! Minor curves~dotted lines! starting from the reverse curve~not shown! do notmeet the forward curve as in Fig. 3~b!.

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first-order transitions. We may therefore argue thatHon mea-sured on the forward curve, with a higher amountfrozen-indisorder prior to the transition, is likely to be closeto the real HF-O/D transition.

In the following experiment, we demonstrate the possibity of frozen-inmetastable disorder, in the entire Bragg glaregion ~between LF-O/D and HF-O/D lines!, both on in-creasing and decreasing field branches. It was shown eathat the metastable-disordered phase can be annealedor fully eliminated by repeatedly cycling the field by a smaamplitude.14,15The idea is, when the field is cycled, vorticemove from their metastable configuration and reorganizea stable configuration~so-called process ofannealing!.

Figure 5~a! shows a part of the main hysteresis looaround 5.15 T where magnetization hysteresis is significalower than in the peak region as well as in the low-fieregion ~see Fig. 2!. We also plot the minor hysteresis loopstarting from the forward curve, obtained by repeatedlycling the field with an amplitudeDH50.1 T, which is morethan adequate to reverse the induced currents throughousample. As shown in Fig. 5~a!, the width of the minor hys-teresis loop collapses with each successive field cyclesaturates on the loop shown by connected squares. Thewidth of the loop after several cycles~for clarity some of theloops are omitted! is almost an order of magnitude smallthan the width of the main hysteresis loop at that field. Tsaturated hysteresis loop obtained is essentially the seven when the minor loops are initiated from the reve

FIG. 5. ~a! Minor hysteresis loops initiated on the forwarcurve, obtained~around 5.15 T! by repeatedly cycling the fieldcollapse into the loop shown as solid squares after many cycles~b!A similar experiment near 4.05 T. Note that the saturated loopnow closer to the reverse curve, while it is closer to the forwacurve at 5.15 T. The main hysteresis loop~forward and reversecurves! in the respective field ranges is in the dark line.

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curve, indicating the existence of a unique stable vorstate.14,15

We show a similar result near 4.05 T in Fig. 5~b!, i.e.,minor loops starting from the forward curve with repeatfield cycling, collapsing to a stable state~again some of theintermediate loops are omitted for clarity!. We note that thefinal saturated loop~shown as solid squares! at 4.05 T is nowcloser to the reverse curve while at 5.15 T it is closer toforward curve. This is expected because at 4.05 T, the sucooled metastable phase from above the HF-O/D line~re-verse curve! is annealedbetter than at 5.15 T. On the othehand, the superheated disordered phase from the LF-O/D~forward curve! is more annealed at 5.15 T than at 4.05 T.conclusion, the stable vortex state in the Bragg glass regis much more ordered than it appears from the width ofmain hysteresis loop.

The extent of collapse in the magnetization hystereupon field cycling suggests a significant presence ofmetastable disordered phase coexisting with the thermonamically stable Bragg glass phase, both on forwardreverse curves. On the forward curve, the low-field disdered phase~stable below the LF-O/D line! extends deepinto the Bragg glass region as a superheated metasphase. Similarly, the disordered phase, stable above theO/D line, extends deep into the Bragg glass region as apercooled metastable phase. We further note that upon

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creasing the field after eliminating the metastable phaserepeated field cycling,Hon is much higher than that on thforward curve. This further supports our point that tamount of frozen-in disorder is crucial in determining thonset of the peak effect.

In conclusion, we reported the occurrence of histodependent critical currents near the low-field disordersolid–Bragg-glass transition in V3Si and NdBa2Cu3O72xsingle crystals. The nature of the history dependence in ccal currents near this transition region is just the oppositethat seen near the high-field Bragg-glass–disordered-stransition. It is also shown that the disordered vortex phpredominantly coexists as a metastable phase in the Bglass region with the stable-ordered phase. The onset opeak effect shifts to lower fields with increasing amountmetastable disordered phase. We conclude that the presof the disordered phase prior to the Bragg-glass–disordesolid transition is crucial in nucleating the growth of thdisordered phase at the onset of the peak effect. We furargue that the onset field may be closer to the true positiothe HF-O/D transition.

G.R. is grateful to the Alexander von Humboldt StiftunGermany for supporting his stay in ITP, FZK. The authoare grateful to Professor Shobo Bhattacharya, ProfessoMatsushita, and Dr. Gautam I. Menon for useful discussio

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