Vortex phase diagram via magnetization measurements for Htc in Bi2Sr2CaCu2O8

PHYSICA@ ELSEVIER

Physica C 246 (1995) 216-222

Vortex phase diagram via magnetization measurements for H [c in BizSrzCaCu208 Yuji Yamaguchi *, Nobuyuki Aoki 1, Fumitoshi Iga, Yoshikazu Nishihara ElectrotechnicalLaboratory, 1-1-4 Umezono, Tsukuba, Ibaraki 305, Japan Received 27 December 1994

Abstract DC and AC magnetization for H II c-axis of an air-annealed Bi2Sr2CaCu208 single crystal have been investigated in detail. In a DC magnetization ( M - H ) curve above 30 K a distinct kink has been observed at H k close to the irreversibility field (Hire), where a distinct change also in AC loss (X") has been observed. Below 40 K a prominent second peak has been exhibited in the M - H curve. It has been shown that the field ( H m) at the maximum r d M / d H [, where the second peak grows rapidly, is almost temperature independent. The X" v e r s u s HDC curve has exhibited a sharp dip near the H m. Also has been observed another characteristic field Ht, where a crossover in the magnetic relaxation occurs. These characteristic fields ( H k, H m and H t) give a well defined vortex phase diagram, which is discussed in relation to a flux-melting and a possible vortex/Bose glass transition.

1. Introduction The vortex phase diagram with a phase transition near the irreversibility field (nir r) [1] is one of the issues of the high-Tc superconductors. The transition has been proposed to be a flux-lattice melting [2], a vortex-glass [3] or a Bose-glass transition [4], depending on the sample peculiarities. The first observation of such a transition was reported by Gammel et al. [5] as a flux-melting transition in Y B a 2 C u 3 0 7 (Y-123) and Bi2Sr2CaCu20 8 (Bi-2212), following more precise experiments on Y-123 [6,7] and Bi-2212 [8-10]. On the other hand, clear evidence for a

* Corresponding author. 1 Present address: Japan Advanced Institute of Science and Technology-Hokuriku, 15-Asahidai, Tatsuguchi-chou, Noumigun, Ishikawa-ken 923-12, Japan.

vortex-glass transition was first observed in Y-123 films [11], and followed by many reports on Y-123 [6,12] and Bi-2212 [13,14]. A Bose-glass transition has been reported on irradiated Y-123 films [15,16]. The above classifications have been made based on the temperature dependence of the transition field, the critical exponents of static and dynamical properties and so on. However, the characteristics of the transition of Bi-2212 are not so clear compared with those of Y-123. Superconductivity of Bi-2212 has been considered to be a little different from that of Y-123 in the sense that the former is very close to a two-dimensional system [17,18] resulting in a remarkable effect from thermal fluctuation. The shape of the vortex is understood as a " p a n c a k e " [19] coupled through a Josephson-contact [20] or electromagnetic interaction between adjacent layers. The DC and A C magnetization in the superconducting state has been

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Y. Yaraaguchi et al. / Physica C 246 (1995) 216-222

revealed to be extremely anisotropic and complicated [21-23]. The AC loss near the irreversibility field has been extensively investigated, and the important role of thermal activation of the vortex has been clarified [24,25]. However, clearer information about these magnetic anomalies and the phase transition is required to understand the vortex dynamics in this compound. Recently, we have observed a very clear vortex transition in DC and AC magnetization for H [I c of an air-annealed Bi-2212 single crystal. In this paper we report these magnetization measurements and the observed phase diagram with some discussion relating to possible vortex-transition models.

2. Sample and measurement A boule of Bi2Sr2CaCu20 a single crystal was grown by a traveling-solvent floating-zone method. It was cleaved into a plate with 0.05 mm thickness along the c-axis and cut into a disc with 1.8 mm diameter. The specimen was air-annealed at 832°C for half an hour and cooled at a rate of 0.2°C/min in air down to 400°C. The superconducting transition temperature T~ extrapolated from the linear part of the temperature dependence of the in-phase AC susceptibility (X' versus T curve) was 82.2 + 0.1 K with a transition width (between the 10% and 90% value) of 0.35 K. The zero-field cooled magnetization (MzF c) at 1 . 3 0 e and 4.2 K parallel to the c-axis was 0.31 e m u / g and the field-cooled magnetization (MFc) was 0.05 emu/g. DC magnetization ( M ) was measured using a SQUID magnetometer (Quantum Design) at fixed temperatures. The in-phase (X') and out-of-phase (X") components of the AC susceptibility were measured with a mutual inductance bridge (Barrase-Provance) operated at 119 Hz and a two-phase lock-in amplifier (EG&G-PAR 5208) with variable frequency f. The AC amplitude (hAc) was changed between 6 mOe and 6 0 e . At fixed temperatures a superposed DC field (HDc) was swept at a rate ( H J t ) of 0.1 ~ 100 O e / s or step-by-step with a waiting time of 2 ~ 20 s. Both hAc and HDC were parallel to the c-axis. More details of the experimental set-up have been reported in a previous paper [251.

217

3. Experimental results

3.1. DC magnetization The field ( H ) dependence of the magnetization

(M) (M-H curve) of Mu, in the virgin state (zerofield cooled magnetization~ and that of Mdown (magnetization with decreasing field) at 30 ~ 45 K are shown in Fig. 1. The curves exhibited a distinct double peak as had been reported by other researchers [26-28]. Near the end of the second peak (peak at the higher field) in the Mup c u r v e a distinct kink was observed at H k as shown in Fig. l(b). The irreversibility field (Hirr), where AM = Mdown -- Mup became less than ~ 0.001 emu/g, was a little higher than H k. Magnetization curves of Mup at 20 ~ 25 K are shown in Fig. 2(a). At these temperatures the kink around the end of the second peak was not clear. With decreasing temperature the second peak shifted to the higher-field side, but the peak field depended on the sweep rate (i.e. step interval) as

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Y. Yamaguchiet al./ PhysicaC 246 (1995)216-222

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(dM/dH) of Bi2SrzCaCu208 for n llc at 20~ 25 K. The Hm(DC) indicates the field where - d M / d H takes its maximum. The kinks around 200 Oe and 1 kOe are artifacts due to an abrupt change in sweep rate (step interval at the measurement) of H.

shown in the Fig. 2(a) for 25 K. Instead of the peak field, the field H m where the derivative - d M / d H became maximum was almost independent of the sweep rate as shown in Fig. 2(b). The H m increased slightly with increasing temperature as 600 ~ 640 Oe at 20 ~ 40 K. The second peak vanished above 45 K, while the kink remained distinctly. In Fig. 3 magnetization curves at 70 K are shown focusing near the kink. The kink was sharp and very close to H i , , where A M became less than ~ 0.0005 e m u / g . The A M showed a slight hump just before H i , (the inset of Fig. 3). The kink was followed a magnetization j u m p ( S M ) , The temperature dependence of the 8 M is shown in Fig. 4. The ~ M decreased with increasing temperature up to 50 K and it got the opposite sense above 55 K.

3.2. AC susceptibility Typical X" versus HDC curves depending on the sweep rate (Hv/t) of the biased DC field (HDc) are

shown in Fig. 5. In Fig. 5(a) curves for four different

Hv/t are shown. Here, the time constant of the lock-in amplifier was typically 0.3 s at large Hv/t. The curves exhibit three characteristic fields which give a sharp rise near 50 Oe, a dip near 650 Oe when Hv/t is large, and a gradual increase of X" around 800 Oe when H v / t is small. A s shown in Fig. 5(b), the former two characteristic fields were almost independent both of measuring frequency ( f ) and A C amplitude ( h A c = 0.1 ~ 6 0 e ) . The sharp rise is the first penetration field [30], as you can see a similar behavior in d M / d H [see Fig. 2(b)]. The dip field

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Y. Yamaguchiet al. / Physica C 246 (1995) 216-222

Hm(AC) was very close to Hm(DC) of the DC magnetization curve. The gradual increase of X" started at Hk(AC) near Hk(DC) of the DC magnetization curve, although the Hk(AC) was not clear and rather frequency dependent. To clarify the origins of the observed AC loss, X'-X" diagrams [31] for the curves in Fig. 5(a) are shown in Fig. 6 with those of three loss models: (1) relaxation loss, (2) eddy-current or diffusive loss as the basis of TAFF (thermally-assisted flux-flow) model [32] and (3) hysteresis loss based on Bean's model [33]. The diagram shows that the loss at low field with high sweep rate to the relaxational loss and the loss at high field is attributable to diffusive loss. With increasing temperature above 45 K, the dip at Hm(AC) in the X" versus HDC curves disappeared and changed into a shoulder at Ht(AC) as 0.5

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-;( Fig. 6. The X'-X" diagrams correspondingto the X" vs. HDC curves in Fig. 5(a). The diagrams based on some typical models are also shown. The observedAC loss is a diffusivetype around - X '= 0 at high field, while it is a relaxational type around - X' = 1 at low field and large Hv/t. shown in Fig. 7(a). The field Ht(AC) decreased rapidly with further increasing temperature. The shoulder was observed only in the case of a large Hv/t (e.g. 25 Oe/s). In the case of a step-by-step sweep, the shoulder disappeared and the X" started to increase from the corresponding field. The field Ht(AC) depended a little both o n hAc and f. When hgc was large at low f, a slight kink at H k ( A C ) in the X" versus HDC curve was observed close to Hk(DC) as shown in Figs. 7(a) and (b). When hgc and Hv/t were sufficiently small or f was large, H k ( A C ) was defined as the field where the derivative (dx"/dHDc) took a maximum, since it was almost independent of hAc. The Hk(AC) thus defined was almost independent of f and very close to Hk(DC). The temperature dependence of Hk(DC), Hk(AC), Hm(DC), Hm(AC) and Ht(AC) are summarized in Fig. 8. These characteristic fields divide the H-T plane into several regions in addition to the Meissner state.

4. Discussion

4.1. Vortexphase transition The ratio MFc/MzFc ---=0.16 of the present annealed sample suggests that the flux pinning is rather

220

Y. Yamaguchi et al. /Physica C 246 (1995) 216-222

larger than that of an as-grown sample [25,26] which scarcely shows a second peak in DC magnetization and has a smaller n i r r compared with the present sample. The small kink at Hk(AC) in the X" versus HDC curve at low f and large hAc (Fig. 7) is attributable to an abrupt decrease of Jc in the hysteresis loss under the condition of full penetration of HDC in the specimen. The rapid increase of X" at Hk(AC) at a high frequency corresponds to an abrupt increase of flux depinning in the diffusive loss [32]. These behaviors are a reflection of an abrupt extinction of Jc ct AM at Hk(DC). Above 50 K, pinning potentials below Hk(DC) are supposed to be sufficiently large against a small driving AC field. The thermal activation below Hk(DC) is perhaps suppressed by collective pinnings [34] growing with decreasing driving forces (hAc), although the observed AC loss at a large hAc has a diffusive

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character ( g " is as large as 0.4 in Fig. 7) due to a thermal activation of vortices. The abrupt decrease of Jc at Hk(AC) near Hk(DC) is a strong support of the presence of the exact H~, near Hk(DC), although the determination of n i r r from the M - H curve is sometimes ambiguous. The presence of a finite 6M and a sharp decrease of Jc at the same Hk(DC) are strong suggestions of a phase transition rather than gradual vortex depinning. The kink in the DC magnetization curve (Fig. 3) at a fixed temperature is another projection of the kink in the fixed-field magnetization at temperature sweep reported by Pastoriza et al. [10]. They have ascribed this transition (above 55 K) to first-order flux melting, although the magnetization hysteresis expected [40] for a first-order transition has not been observed. The present data on the magnetization jump (6M) above 55 K is consistent with their data. However, the ~M below 50 K is opposite to those above 55 K. The Clausius-Clapeyron equation (dHk/dT = dS/dM ~ 8Q/SM) conflicts with first-order melting, provided ~Q > 0. Therefore, the transition at Hk(DC) below 50 K may be a secondorder vortex/Bose-glass transition in favor of a large 6M or of a simple depinning line explicable from the TAFF model [24,25] in favor of a gradual behavior in AC susceptibility.

Y. Yamaguchiet al. / Physica C 246 (1995)216-222 4.2. Magnetic relaxation near second peak On the other hand, the dip at Hm(AC) below 40 K is due to an abrupt change in the magnetic relaxation as shown in Fig. 6. The relaxation time below Hm(AC) is suggested to be short enough compared with the time-scale of 1 / f (with f = 3.97 Hz) but long enough to give a transitional effect against the field sweep ( H v / t ) of 5 ~ 25 O e / s . Actually a large magnetic decay within one second has been reported [26,28,29]. The vortices barely settle after some tens of a second in such a strong pinning site to give a non-loss oscillation [35] for a small driving force (i.e. hAc = 60 mOe). The dip at Hm(AC) is caused by a difference in the relaxation before and after Hm(DC) at the very beginning time (t ,-, 0). As for the second peak itself, it has been attributed to various origins such as (1) the effect of a second-phase impurity [36], (2) a dimensional crossover of vortex dynamics [28], and (3) a matching effect due to dislocation networks [37]. However, the first origin, which expects a temperature dependence similar to that of the critical field of the second phase, is removed, because neither the peak field nor the Hr,(DC) has such a temperature dependence. In the crossover picture three-dimensionally (3D) coupled pancake vortices are supposed to change into a two-dimensional (2D) character at Bcr ~ ~0//S2/~ (S is the distance between the CuO 2 planes and F = mz/mx), and result in a change of the pinning properties of the vortices [38]. On the other hand, the matching effect is supposed to cause a strong shielding (like the Meissner effect) against the external field, and the AC loss is supposed to become very small at the matching field. The small value of the observed AC loss near above Hm(AC) seems to be attributable to this shielding by the matching effect. For a similar air-annealed Bi2Sr2CaCu208, there have been reported [39] some higher harmonics, which is not explained from the dimensional crossover. The matching effect may be alternatively pictured as a Mort insulator state in Bose-glass theory [4], although the calculation has been given for systems of columnar defects [4] or of twin boundaries [41]. If there is some network of pinning centers in this specimen, the Hm(DC) may be attributable to the

221

lower bound (Ha*) of the Mott insulator state. Moreover, the Ht(AC) which divides the phase with a different magnetic relaxation is a reminiscent of B *(T), which is a crossover field from individual pinning to collective pinning in the Bose-glass theory. The observed phase diagram resembles the theoretically expected one [4], although more quantitative experiments on critical exponents or anisotropy properties are necessary to verify this transition.

5. Conclusion Characteristic fields which divide the H - T plane into several regions are observed from magnetization measurements for H II c-axis of an air-annealed Bi2Sr2CaCu208 single crystal. In the M versus H curve a distinct kink is observed at H k, where the AC loss ( X " ) above 50 K indicates a rapid change in the critical current Jc being a measure of irreversible vortex pinnings. This is a strong suggestion of a vortex phase transition at the H k above 50 K. Below 40 K a sharp anomaly is observed at around 620 Oe both in the X" versus HDc curves and in the M - H curves. Above 45 K, this anomaly seems to merge into another crossover field in the magnetic relaxation. The observed phase diagram has been discussed in relation to a flux-melting and a possible vortex/Bose glass transition.

Acknowledgement The authors would like to thank K. Oka for his guide to the crystal growth.

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