The Bose-glass transition in underdoped Bi2Sr2CaCu2O8+x crystals with columnar defects

Physica C 369 (2002) 278±281 www.elsevier.com/locate/physc

The Bose-glass transition in underdoped Bi2Sr2CaCu2O8‡x crystals with columnar defects M. Li a,*, C.J. van der Beek b, M. Konczykowski b, P.H. Kes a a

Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, Netherlands b Laboratoire des Solides Irradi es, Ecole Polytechnique, 91128 Palaiseau, France

Abstract The Bose-glass transition in underdoped Bi2 Sr2 CaCu2 O8‡x single crystals heavy-ion irradiated at room temperature was investigated by using a local Hall probe magnetometer. It is shown that the introduction of columnar defects, not only signi®cantly shifts the Bose-glass lines to much higher ®elds, but also results in a drastic increase of Tc and decrease of the penetration depth k due to the modi®cation of the oxygen concentration during the irradiation. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: BSCCO single crystals; Bose-glass transition; Doping dependence

1. Introduction It is well known that in highly anisotropic Bi2 Sr2 CaCu2 O8‡x (Bi-2212) crystals the constitutive elements of the liquid state are distinct pancake vortices with no long-range phase order along the c-axis. Introduction of columnar defects (CDs) produced by heavy-ion irradiation could partially reestablish the c-axis correlations in the liquid phase [1±3]. At induction BFOT  B  Birr …T †, the localized vortices in a so-called Bose-galss (BG) state behave as disentangled lines [4]. Here BFOT is the ®eld at which in the pristine sample the ®rstorder lattice±liquid transition takes place and Birr …T † is the irreversibility ®eld. At Birr …T † the system undergoes the BG transition to an entan-

gled vortex liquid phase and the I…V † response becomes linear [5,6]. Anisotropy and the penetration depth k are two of the most important parameters to in¯uence the position of the BG transition [6]. Much work has been done on the the BG transition in the optimally doped and overdoped Bi-2212 crystals, but for the underdoped samples with higher anisotropy not much is known. The purpose of this paper is to study the BG transition in irradiated underdoped crystals with a wide range of matching ®elds by measuring the ac transmittivity. It is shown that the irradiation signi®cantly in¯uences the oxygen content between the CDs. This e€ect also in¯uences the BG line in the high-temperature regime. 2. Experiments

*

Corresponding author. E-mail address: [email protected] (M. Li).

Bi-2212 single crystals were grown by the traveling solvent ¯oating zone method [7]. In order to

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 1 2 5 8 - 8

M. Li et al. / Physica C 369 (2002) 278±281

get underdoped crystals the growth was performed at low oxygen partial pressures. To homogenize the oxygen content, the as-grown underdoped crystals were annealed for several days at 700 °C in ¯owing nitrogen gas. The Tc of the unirradiated reference sample is 74.5 K. Rectangle single crystals with dimensions 500  200  20 lm3 were cut from a large piece. After being checked magneto-optically to ensure the absence of extended defects, these crystals were irradiated at room temperature with 5.8 Gev Pb ions at GANIL in Caen, France, with the dose equivalent ®elds 2 mT 6 B/ 6 4 T. The ion beam was directed parallel to the c-axis of the sample. Each ion impact creates an amorphous columnar track traversing the sample along its entire thickness. In order to determine the irreversibility ®eld Birr (T), the ac transmittivity was measured using a local Hall probe magnetometer with a dimension of 10  10 lm2 . A small ac ®eld of amplitude hac 6 0:1 mT and frequency f ˆ 7:75 Hz was applied parallel to the c-axis of the sample resulting in a periodic electric ®eld gradient of magnitude 2pl0 hac f at the sample edge. Meanwhile the dc ®eld creates the vortices in the sample. From the measured ac Hall voltage Vac in the center of the sample, the ®rst and third harmonic components of the transmittivity are determined as TH0 …f ; T † ˆ Vac …f ; T † Vac …f ; T  Tc †Š=‰Vac …f ; T  Tc † Vac …f ; T  Tc †Š and TH 3 ˆ Vac …3f ; T †=‰Vac …f ; T  Tc † Vac …f ; T  Tc †Š, respectively. The in-phase component of the fundamental component, TH0 , can be straightforwardly related to the magnitude of the shielding current in the sample. The detection of a nonzero TH 3 implies the presence of a nonlinear I…V † response which is the result of ¯ux pinning. We de®ne an irreversibility line Tirr …H †, or alternatively Birr …T †, as the temperature at which the TH 3 signal ®rst becomes distinguishable from the background noise during ®eld cooling, i.e., at that temperature the working point enters the nonlinear regime of the sample's I…V † characteristics. We ignore a small di€erence between B and H. The linear extrapolation to zero of the ®rst harmonic component TH0 in zero dc ®eld is used to de®ne Tc .

279

3. Results and discussion Fig. 1 shows Tc as function of B/ in comparison to the unirradiated reference sample. It is remarkable that Tc of these irradiation crystals increases after irradiation. The largest shift of Tc is seen for the sample with B/ ˆ 2 T. In the case of high irradiated doses (B/ ˆ 4 T), Tc decreases again, but is still 1 K higher than Tc of the pristine crystal. As will be discussed in detail in our future paper [7], the modi®cation of Tc is caused by oxygen ions which are expelled during the irradiation from the CDs into the crystal lattice. This gives rise to additional holes in the CuO2 planes of the matrix. We note that a similar e€ect in irradiated underdoped Bi2 Sr2 Can 1 Cun O2n‡4‡x …n ˆ 1; 2† thin ®lms has been reported by Pomar et al. [8]. Because of the parabolic relation between Tc and hole concentration in HTSC [9], the increased oxygen content leads to an enhancement of Tc in the underdoped regime, whereas for optimally and overdoped samples it yields a decrease of Tc . The latter has often been reported, because most studies about the e€ect of CDs in HTSC have been carried out on optimally and overdoped samples. The increase of Tc with irradiation doses and subsequent e€ect of heat treatments in our underdoped crystals can be explained by a simple di€usion model [7]. The decrease of Tc at very high doses may be due to the loss of e€ective superconducting area at the CDs [10].

Fig. 1. Tc versus B/ for underdoped Bi-2212 single crystals.

280

M. Li et al. / Physica C 369 (2002) 278±281

Fig. 3. Dependence of Birr …T † on B/ in comparison to the BFOT …T † of the pristine crystal.

Fig. 2. Fundamental transmittivity TH0 and TH00 and third harmonic amplitude jTH 3 j of the underdoped Bi-2212 single crystal with B/ ˆ 2 T. The dc ®eld values are indicated.

A typical ac transmittivity result of the fundamental and third harmonic amplitude is shown in Fig. 2 for the underdoped sample with B/ ˆ 2 T. The corresponding Birr …T † lines at which a third harmonic response is ®rst detected are plotted in Fig. 3 for the samples with 2 mT 6 B/ 6 2 T together with the BFOT line of the reference crystal [11]. It is seen that for very small densities of CDs, such as B/ ˆ 2 and 5 mT, the Birr …T † lines are monotonously shifted up from the BFOT …T † line. With increasing B/ (500 mT 6 B/ 6 2 T), the CDs produce a pronounced increase at low temperature similar to [6]. Three regimes can be distinguished: a low-temperature/high-®eld region in which Birr …T † depends exponentially on T, a region around Birr …T †  B/ =5 whose Birr drops much faster, and a high-temperature/low-®eld region whose Birr …T † decays exponentially again but much faster than in

the high ®eld regime. All the features are consistent with those of the optimally doped samples in [6]. However, the data for di€erent B/ in the hightemperature region do not coincide as they did for optimally doped Bi-2212. According to the description proposed by van der Beek et al. [6], the BBG …T † line in the hightemperature regime is given by     e0 s e0 s BBG ˆ BK exp kB T kB T 1 2

with BK ˆ U0 …k 1 ‡ …cs† † and kab2 …T † ˆ …1 T = Tc †kab2 …0†, c is the anisotropy parameter, e0 is the typical vortex energy scale e0 ˆ /20 =…4pl0 k2ab †, s   the distance between two CuO2 layers. For a 15 A

Fig. 4. Birr …T † for the irradiated underdoped Bi-2212 crystals with B/ ˆ 0:5, 1 and 2 T. The lines are ®tted to the data at high temperature.

M. Li et al. / Physica C 369 (2002) 278±281

®rst analysis we may ignore the cs term in BK because the anisotropy for these strongly underdoped samples is expected to be very large. As shown in Fig. 4, the ®t of the above expression for samples with B/ ˆ 0:5, 1 and 2 T yields: kab …0† ˆ 263, 252 and 241 nm, respectively. Note here that the higher the matching ®eld, the smaller the penetration depth indicating that the doping level of the lattice indeed increases with the matching ®eld. 4. Conclusion We studied the Bose-glass transition in underdoped Bi2 Sr2 CaCu2 O8‡x (Bi-2212) single crystals irradiated with heavy ions by using a local Hall probe. For the samples with higher doses, the introduction of CDs not only signi®cantly shifts the BG line to much higher ®eld due to vortex pinning in CDs, but also results in a drastic increase of Tc and a decrease of the penetration depth k. This is due to the modi®cation of doping level by the heavy-ion irradiation. During irradiation oxygen is expelled from the CD into the

281

crystal matrix. The average oxygen content follows a simple di€usion model [7].

Acknowledgements We are grateful for ®nancial support of the VORTEX program of the ESF (Europe Scienti®c Foundation) and NWO (Netherlandse Organisatie voor Wetenschappelijk Onderzoek).

References [1] N. Morozov et al., Phys. Rev. Lett. 82 (1999) 1008. [2] C.J. van der Beek et al., Phys.Rev.B 61 (2000) 4259; C.J. van der Beek et al., Phys. Rev. Lett. 74 (1995) 1214. [3] A.K. Pradhan et al., Phys. Rev. B 61 (2000) 14374. [4] D.R. Nelson, V.M. Vinokur, Phy. Rev. B 48 (1993) 13060. [5] W.S. Seow et al., Phys. Rev. B 53 (1996) 14611. [6] C.J. van der Beek et al., Phys. Rev. Lett. 86 (2001) 5136. [7] M. Li et al., in press. [8] A. Pomar et al., Phys. Rev. Lett. 85 (2000) 2809. [9] M.R. Presland et al., Physica C 176 (1991) 95. [10] Y. Zhu et al., Phys. Rev. B 48 (1993) 6436. [11] C.J. van der Beek et al., in press.