Evidence for a Two Step Vortex Matter Melting in Irradiated Bi2Sr2CaCu2O8+δ Single Crystals

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Physics Procedia 36 (2012) 669 – 674

Superconductivity Centennial Conference

Evidence for a two step vortex matter melting in irradiated Bi2Sr2CaCu2O8+δ single crystals V. Shaidiuk*, L. Ammor and A. Ruyter,a* Laboratory LEMA UMR 6157 CNRS-CEA, University of Tours, Tours, 37200, France

Abstract Vortex pinning mechanism has been studied in single crystals shaped as thick microbridges using a laser method. Current-Voltage characteristics V(I) have been recorded in the vicinity of the critical temperature Tc, and at very low magnetic field B (from 5.10-3 to 3.10-2 T) parallel to the columnar defects for the irradiated sample (matching field BΦ = 1.5T parallel to its c axis). Our results clearly show a two steps depinning mechanism of the vortices with two different critical current values (Ic1< Ic2): Ic1 for “interstitial” vortex, and Ic2 for strongly localized ones. Using the temperature dependence of the critical current values Ic1, we recover the irreversibility line BIRR(T/Tc) already determined by magnetization measurements. More, our results clearly evidence that, despite I > Ic1, the vortex matter (VM) remains partially localized on columnar defects (CDs) for I < Ic2. And, from Ic2(T), a new line BTL(T/TC) has been determined above which the VM is totally liquid and CD’s are no more efficient. Finally, we conclude that a composite vortex structure exists for very low filling factor (i.e. B/BΦ < 0.02) and for high enough temperature (i.e. T > 0.7 Tc) independently of the vortex dimensionality.

© Rogalla and © 2011 2012 Published Published by by Elsevier Elsevier Ltd. B.V.Selection Selectionand/or and/orpeer-review peer-reviewunder underresponsibility responsibilityof ofHorst the Guest Editors. Peter Kes. Keywords : melting, pinning, magnetotransport, columnar defects, critical current.

1. Introduction A large variety of theoretical, experimental and numerical simulation studies were done for irradiated superconductor samples. But, only a small part of these studies concerns a two steps melting process. L. Radzihovsky has proposed that, for B > Bĭ, and in contrast to B < Bĭ where vortices are strongly localized on columnar defects (CDs) [1], additional vortices can be weaker pinned due to vortex-

* Corresponding author. E-mail address: [email protected]

1875-3892 © 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Guest Editors. doi:10.1016/j.phpro.2012.06.265

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vortex interactions leading to a two steps melting process [2]. But, contrary to his predictions, our recent experiments did not give any evidence of a two steps melting process at very low temperature (T = 5K) [3]. But, at this temperature and for for B > Bĭ, the VM is already solid before irradiation. Concerning the high range of temperature, some interesting results [4, 5, 6, 7, 8] were obtained. Firstly, the existence of three principal types of VM has been evidenced: solid, solid with droplets of liquid and the liquid states. But for their approach, samples were partially irradiated and the study is based on the comparison between irradiated and unirradiated regions. In order to illustrate the two steps melting process for B > Bĭ at high temperature, Goldschmidt et al. have used a numerical simulation approach [6, 9]. Their results clearly show the possibility to have such a behavior of the VM in an uniformly irradiated sample. On another hand, for the case B << Bĭ, there exists only few articles. However, Taüber et al. have proposed a very interesting study which has to be taken into account for the present work [7]. They have shown that the density of CD pinning energies may split for low filling fractions (B < Bĭ), and for strong enough vortex-vortex interactions leading to a two stages melting process. We think that this splitting of the density of pinning energies can also be obtained at very low magnetic field (i.e. B << Bĭ), and high enough temperature due to both the large increase of λab(T) and the renormalization of the pinning energies themselves. In this article, our aim is to study the vortex depinning process, to clarify whether the melting is due to a one step or a two steps depinning process [2, 10]. But, in any case, determine the vortex dimensionality and localize the melting line in the phase diagram µ 0H - T for a virgin sample are two fundamental points to solve before starting with irradiated samples.

2. Sample preparation This experiment was performed on slightly overdoped crystals of Bi-2212, synthesized using the well known self-flux technique [11, 12, 13]. Two samples were extracted by cleavage, than shaped as thick micro-bridges using an excimer laser ablation method [3]. Finally, samples were post-annealed using an appropriate chemical treatment under an oxygen gas flow. Using this technique is very useful to get a good homogeneity of the current flow and to make magnetotransport measurements possible down to very low applied magnetic field, and from T = 5K to TC. Two different cross sections have been considered: a rectangular (width = 50 µm, length = 100 µm, and thickness 20 µm) and a triangular one (with the same cross section area), samples 1 and 2, respectively (Fig. 1 a and b).

a)

b)

c)

Fig 1. Illustration of the different thick microbridges with rectangular (a) and triangular (b) cross-sections. Electrical contacts configuration (flux transformer) (c).

Then, the sample 2 was irradiated with a beam of Pb ions (5.8 GeV) parallel to its c-axis at the heavy-ion facility GANIL (Caen – France). The density of irradiated defects corresponds to a matching

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field BΦ = 1.5T, corresponding to an average distance dΦ ≈ 360Å between the tracks. The magnetic field was aligned at T/TC = 0.5 with the ion tracks using B = 0.6T, and the well known dip feature occurring in dissipation for vortices parallel to the columnar defects. It must be pointed out that both these samples do not exhibit any geometrical barrier as it was shown by Majer et al. [14] for virgin ones, and A. E. Koshelev and V. M. Vinokur [15] for irradiated ones. For this work, two kinds of measurements were performed: magnetization ones using a commercial SQUID powered by Quantum Design, and magnetotransport ones using a homemade system. Note that a flux transformer configuration has been used for magnetotransport measurements [16], and that electrical contacts exhibit low resistance values of about 1ȍ (Fig. 1 c). Applying a standard dc fourprobe method, T – V were measured with a resistance resolution of about 5µΩ, and I – V characteristics with a voltage resolution of 1 nV, and a temperature stability better than 5 mK.

3. Results The irreversibility line (IL) is often considered to separate a pinned vortex solid from an unpinned vortex liquid and is commonly identified with the vortex melting line but the effect of geometrical barriers have to be taken into account particularly for virgin samples [14]. Consequently, to locate the position of the intrinsic location of the melting line and to establish the vortex dimensionality we used a thick microbridge with a triangular cross section as proposed by Majer et al. [14]. Using this shape, vortices can easily cross sample edges [14, 17]. The other possibility could have been to use a Corbino geometry [18] but our approach gives a better homogeneity of the current flow. Thus, the melting line (ML) is determined based on the jump of V/I versus T which can be considered as a signature of a firstorder transition (Fig. 2a). More, the decoupling line (DL) has simultaneously been obtained using the flux transformer configuration (Fig. 2b). 1.10

101 100

10-2

10-4

TMelt.(0.05T)

TMelt.(0.01T)

50

60 T(K)

70

1.05

b)

10-1 10-2

1.00

10-3 10-4

0.95

10-5 10-3

10-5

V/I (V/A)

10-1 10-3

100 d(V/I)/dT

V/I

a)

Top. / Bot.

10-1 10-2

102

101

100

TDec.(0.1T)

TDec.(0.02T)

10-6

0.90 30

40

50

60

70

80

90

T (K)

Fig 2. (a) V/I vs. T (filled symbols) and dV/dT vs. T (open symbols) for µ 0H = 0.05 and 0.01T. (b) Vtop/I and Vbot/I vs. T (open symbols) and Vtop/Vbot vs. T (filled symbols) for µ 0H = 0.02 and 0.1T.

Both these two lines are drawn in figure 3. One can see that ML is different from the one obtained by SQUID measurements using M(T) cycles, and that ML matches DL up to 0.03T.

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3D

Liqu

id

2D Liquid

0

μ H, T

10-1

10-2

3D Solid 10-3 0.5

0.6

0.7

0.8

0.9

1.0

t=T/Tc

Fig 3. Phase diagram for virgin samples : melting line (filled squares), decoupling line (filled circles) and irreversibility line (filled triangles) obtained by SQUID.

Now, that these intrinsic properties of the virgin sample have been determined, effects of CDs on pinning and depinning processes can be investigated. Because it has been shown that the presence of CDs suppress geometrical barriers effects [19], a thick microbridge with a rectangular cross section can be used. Such a uniform thickness is fundamental to avoid inhomogeneity in the pinning process. At high temperature and very low applied field (B << Bĭ), we obtained three typical I-V characteristics as shown at figure 4. At ‘low temperatures’, we obtained two steps with two critical currents (Fig. 4a) which could be the signature of a two steps melting process. According to this idea, one can observe that Ic1 = 0 for intermediate temperatures. We attribute this to a partial melting of the VM because Ic2 is still finite (Fig. 4b). Finally, at high temperatures both critical currents are zero Ic1 = Ic2 = 0. So, we can affirm that the VM is then a liquid (Fig. 4c). It must be noticed that these results are independent of the vortex dimensionality.

15

10-6 10-7

10

10-8 5

10-9

T = 65.5 K

10-3

b)

8

10-4 10-5

6

10-6 4

10-7 10-8

2

10-9

10-10

0 0.1

1 I (mA)

10

10-10 0.1

10-2

10

6

T = 68.8 K

c)

5

10-4 4

10-5 10-6

3

10-7

2

10-8 1

10-9

0 1 I (mA)

10

10-10 0.1

d logV/d log I

20

10-5 V (V)

10-3

V (V)

a)

10-2

d logV/d log I V (V)

10

25

T = 62.2 K

-4

d logV/d log I

10-3

0 1

10

I (mA)

Fig 4. Typical I – V and I – dlogV/dlogI curves: (a) Ic1  0 and Ic2  0, (b) Ic1  0 and Ic2 = 0, and (c) Ic1 = Ic2 = 0 for B = 0.03T.

Now, we can focus on the second aim of this paper: the depinning process. According to the I-V curves aspect at low temperature, and because of similarities with critical phenomena, we fit the velocity close to the threshold of the depinning with the well known power law V ~ (I - Ic)ȕ where β is a constant [20]. More, we propose to fit the two steps depinning process with a sum of two independent responses : V(I) = V1(I) + V2(I) where V1(I) = C1 (I - Ic1)ȕ1 and V2(I) = C2 (I - Ic2)ȕ2, where Ic1 < Ic2, and C1, C2 are constants. This approach is based on the hypothesis that the density of pinning energies can split at very

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low magnetic field (i.e. B << Bĭ) if the temperature is high enough to induce a renormalization of the pinning energies themselves. Figure 5 shows a set of calculated data which perfectly fits the measured ones confirming the validity of our approach. 10-3 10-4

V (V)

10-5 10-6 10-7 10-8

Ic2

Ic1

10-9 2

4

6

8

10

12

14

16

18

20

I (mA)

Fig. 5. Measured I-V curve (open squares) and calculated one (filled circles) for B = 0.03T at T = 64K (V1(I) – solid line and V2(I) – dashed line).

These results confirm that two kinds of vortices have to be considered. Even if it does not confirm that less pinned vortices are interstitial, this proves that the VM exhibits a composite nature [4, 5, 6, 10, 14, 15]. Vortices can be classified in two different families with two different average pinning energies and then two critical current values Ic1 and Ic2 with Ic1 < Ic2. The temperature dependence of both these critical current are shown in figure 6a. From these curves which have been extrapolated to zero, we extracted (Tirr, µ 0H) couples in order to obtain the two associated irreversibility lines : IL1 and IL2 (Fig. 6b). Two fundamental informations are so given. Firstly, IL1 merges the irreversibility line obtained for irradiated samples using magnetization measurements (SQUID). This means that this type of measurement allow us to know when some vortices start to move even if the others are still pinned. Secondly, the melting process is a two steps depinning one. The VM, which is solid at low temperature, partially melts leading to an intermediate state made of both solid and liquid before a true liquid as the temperature increases independently of the vortex dimensionality. 0.016

μ H (T)

0.008

0

Ic

10

-1

10-2

0.006 0.004

Tirr1(Ic1=0)

a)

0.002 0.000 56

58

60

62

64

66 T, K

68

70

72

74

Tirr2(Ic2=0)

2D Liquid d ui iq +L

0.010

2D Solid

lid So

0.012

2D

Ic1 0.01T Ic2 0.01T Ic1 0.07T Ic2 0.07T

0.014

3D Solid

b) 10-3 0.5

0.6

0.7

0.8

0.9

1.0

t=T/Tc

Fig 6. (a) Temperature dependence of critical currents: Ic1 vs. T and Ic2 vs. T. (b) Phase diagram ȝ0H vs. t where t = T/Tc : melting line (filled squares), decoupling line (open circles), irreversibility line (open triangles) obtained by SQUID (filled circles), first and second irreversibility lines obtained by magnetotransport IL1 (open triangles) and IL2 (filled diamonds)

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4. Conclusions In summary, at high enough temperature and when columnar defects strongly outnumber vortices, we observed a two steps melting process of the vortex matter melting independently of the vortex dimensionality. Current-voltage characteristics are interpreted as the sum of two independent responses with two different values of the critical current. From this set of critical current points two irreversibility lines have been determined separating the phase diagram in three domains. A new vortex matter was found between the solid and the liquid ones. This new composite phase is a mixed phase in which droplets of liquid can move in between islands of solid.

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