Thermodynamic properties of five-layered HgBa2Ca4Cu5O12+y from equilibrium magnetization

Current Applied Physics 10 (2010) 1033–1036

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Thermodynamic properties of five-layered HgBa2Ca4Cu5O12+y from equilibrium magnetization Y.-T. Kwon a, M.-S. Park b, J.-D. Kim b, K.-Y. Choi c, M.H. Jung c, A. Iyo d, K. Tokiwa e, Y.C. Kim a, S.-I. Lee c,* a

Department of Physics, Pusan National University, Busan 609-735, Republic of Korea Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea c National Creative Research Initiative Center for Superconductivity and Department of Physics, Sogang University, Seoul 121-742, Republic of Korea d National Institute of Advanced Industrial Science and Technology (AIST), Central 2, Tsukuba, Ibaraki 305-8568, Japan e Tokyo University of Science, Noda, Chiba 278-8510, Japan b

a r t i c l e

i n f o

Article history: Received 10 August 2009 Received in revised form 2 December 2009 Accepted 21 December 2009 Available online 4 January 2010 Keywords: Hg1234 Thermodynamic properties Penetration depth Coherence length Equilibrium magnetization

a b s t r a c t By using the Hao–Clem model, we analyzed the equilibrium magnetization of the grain-aligned HgBa2Ca4Cu5O12+y (Hg1245) with T c ’ 108 K. We obtained thermodynamic parameters, such as the penetration depth ½kab ð0Þ and the coherence length ½nab ð0Þ from the thermodynamic critical field ½Hc  and the Ginzburg–Landau parameter ½j. Compared to the four layered superconductor HgBa2Ca3Cu4O10+y (Hg1234), the obtained penetration depth was slightly increased indicating that the Cooper pair density of Hg1245 was decreased, which was one of the reasons why the transition temperature ðT c Þ of the Hg1245 did not increase as compared to the Hg1234. The expected increase of T c for the material with the more CuO2 planes was not achieved because of the insufficient doping of the Cooper pairs while adding CuO2 planes. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction If we want to study the effect of the number of CuO2 planes (n) in a unit cell on superconductivity, the homologous HgBa2Can1 CunO2n+2+y [Hg12(n  1)n] cuprate is one of the best candidates. For n P 3, the Hg12(n  1)n consists of two types of CuO2 planes. The inner CuO2 plane (IP) has square coordinates of oxygen, while the outer CuO2 plane (OP) has pyramidal coordinates of oxygen. The doping level ðN h Þ between the IP and the OP, is inhomogeneous because of the crystallographic inequality [1–3]. For Hg1245, antiferromagnetism was observed at the IPs by using Nuclear Magnetic Resonance (NMR) [1,2] and the muon spin rotation [4]. This observation indicated that the antiferromagnetism at the IPs suppresses the superconductivity and weakened the interlayer coupling of the superconductivity between the OPs. It was apparent that the appearance of the antiferromagnetism affected the equilibrium magnetization. However, there has been no study on the thermodynamic parameters characterizing the basic superconductivity of Hg1245. The thermodynamic parameters of Hg12(n  1)n for 1 6 n 6 4 have already been investigated, as shown in Table 1 [5–8]. This equilibrium magnetization gives direct information on the thermodynamic parameters such as

* Corresponding author. Tel.: +82 2 705 8827; fax: +82 2 704 8832. E-mail address: [email protected] (S.-I. Lee). 1567-1739/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cap.2009.12.035

the Ginzburg–Landau parameter ðjÞ, the thermodynamic critical field ðHc Þ, the upper critical field ðHc2 Þ, the penetration depth ðkÞ, and the coherence length ðnÞ. Therefore, a study of equilibrium magnetization on the thermodynamic parameters for n ¼ 5 is urgently needed. In this paper, we present the thermodynamic parameters for the five-layer superconductor HgBa2Ca4Cu5O12+y (Hg1245) by using the Hao–Clem model and compare these parameters with the homogeneous series Hg12(n  1)n for 1 6 n 6 4. The penetration depth of Hg1245 was longer than that of Hg1234, indicating the reduction of the Cooper pair density of Hg1245. The suppression of the Cooper pair density of Hg1245 should be one of the reasons why the superconducting transition temperature ðT c Þ did not increase while adding more CuO2 planes. Even ðHcc2ð0Þ Þ was quite reduced for Hg1245. 2. Experiments Five layered HgBa2Ca4Cu5O12+y can be synthesized only at a high pressure in the few GPa range. This Hg1245 is a form of polycrystalline and should be grain aligned to study the directional dependence of the superconductivity [9]. We ground the polycrystalline Hg1245 into fine powders. We, then, sifted the powder to make sure that each of the grains was a single grain. The fine Hg1245 powder was thoroughly mixed with commercial epoxy

Y.-T. Kwon et al. / Current Applied Physics 10 (2010) 1033–1036

Table 1 Transition temperature T c , the Ginzburg–Landau parameter jav g ¼ kab =nab , the thermodynamic critical field Hc ð0Þ, the upper critical field at absolute zero in the caxis Hcc2 ð0Þ, the in-plane coherence length nab ð0Þ, and the in-plane penetration depth kab ð0Þ of HgBa2Ca4Cu5O12+d, derived from the reversible magnetization MðTÞ measurement.

T c (K)

Hg1201 [5]

Hg1212 [6]

Hg1223 [7]

Hg1234 [8]

Hg1245

95.6

116.8 115 0.84 170 13.9 191 12.6 [22]

134.5 141.2 1.08 201.6 12.0 ± 0.8 174 ± 5 15.8 [23]

125 102 1.12 205 12.7 157 18.9 [23]

108 82.2a 0.66b 111.2c 17.2c 170.7d 22.2 [24]

j av g Hc ð0Þ (T) Hcc2 ð0Þ (T) nab ð0Þ (Å) kab ð0Þ (nm) c-axis (Å) b c d

(a)

400 300 200 100 0

In the temperature range of 50 K 6 T 6 70 K. From the two-fluid theory. Assuming the BCS clean limit. From the empirical formula.

and then put in a magnetic field of 7 T. Then, each of the grains was aligned. This is called Farrell’s method [10]. Each grain of the both superconductors is homogeneous and optimally doped. We measured the low-field magnetization MðTÞ of the aligned Hg1245 by using a superconducting quantum interference device (SQUID, Quantum Design). The structure of the crystal was examined by using an X-ray diffractometer (XRD, Rigaku). The field-dependent magnetizations MðTÞ in the zero-field-cooling (ZFC) and the fieldcooling (FC) state were obtained for magnetic fields up to 5 T by using a SQUID magnetometer.

10

30

40 2θ (deg)

50

60

(b) -0.2

Tc=108 K

-0.4

FC

-0.6 ZFC

-0.8 -1.0

3. Results and discussion

0

20

40

60 80 T (K)

100

120

140

Fig. 1. (a) Only the (0 0 l) peaks were detected from the X-ray diffraction patterns. (b) The low-field susceptibility 4pvðTÞ of c-axis aligned HgBa2Ca4Cu5O12+d measured at H ¼ 10 mT parallel to c-axis. Zero-field-cooling (ZFC) magnetization characterized by the flux exclusion means diamagnetic shielding and field-cooling (FC) magnetization characterized by flux expulsion representing the Meissner effect.

0 -10

4πM (G)

Fig. 1a shows the X-ray diffraction patterns of grain-aligned Hg1245. Only (0 0 l) peaks were detected. Moreover, the full width at half maximum (FWHM) on the highest (0 0 l) peak was only 0.2°. This indicated that all of the grains were well aligned along the caxis. Fig. 1b shows the low-field susceptibility 4pvðTÞ of grainaligned HgBa2Ca4Cu5O12+y, using a static field of H ¼ 10 mT, parallel to the c-axis. At 5 K, the zero-field-cooled (ZFC) 4pvðTÞ for Hkc was 0.78, which had been corrected for the demagnetizing effect using an effective demagnetization factor D  1=3, as reasonable for the set of isolated spherical granules with nearly the same direction. The superconducting transition temperature ðT c Þ, defined as the onset of a diamagnetic transition, was 108 K. We measured the magnetization 4pMðTÞ for Hkc is measured for 0:3 T 6 H 6 5 T, as shown in Fig. 2. Only the reversible region was drawn. The magnetization curves crossed over at 104.7 K, reflecting the thermal distortion of the vortex lines [11]. We analyzed the equilibrium magnetization by using the Hao– Clem model [12,13] based on the Ginzburg–Landau (GL) theory. This model overcomes the limitation of the London model [14]. The London model treats vortex cores as singularities and then the free energy is calculated as a combination of both the magnetic flux density and the supercurrent density outside the vortex cores. However, the Hao–Clem model includes not only the electromagnetic energy outside the vortex cores but also the changes in the kinetic and the condensation energies originating from the suppression of the order parameter in the vortex cores. This model can describe the reversible magnetization for Hc1 < H < Hc2 , where Hc1 is the lower critical field. From the model, we can determine the thermodynamic parameters, such as j; Hc ð0Þ; nð0Þ; kð0Þ; and Hc2 ð0Þ. In the Hao–Clem model, the reversible magnetization is expffiffiffi pressed by a dimensionless form, 4pM 0  4pM= 2Hc ðTÞ with a giindependent. Here, the external field ven j, which is temperature pffiffiffi is defined as H0  H= 2Hc ðTÞ [13]. In order to describe reversible

20

0.0

4πχ

a

100 20 ± 4 145 ± 9 9.5 [21]

500 Intensity (arb. unit)

1034

03T 0.3 0.5 0 5T 0.7 0 7T 1T 1.5 1 5T 2T 3T 4T 5T

-20 -30 -40 -50 -60 50

60

70

80

90 T (K)

100

110

120

Fig. 2. Zero-field-cooled magnetization 4pMðTÞ obtained from the various field ðH 6 5 TÞ parallel to c-axis.

magnetization using the Hao–Clem model, magnetizations 4pMðHÞ at each field should be constructed by selecting data at the same temperature. At a fixed temperature, the ratio of experimental 4pM i =Hi ði ¼ 1; 2; . . .Þ corresponds to 4pM 0 =H0 within pffiffiffi the theoretical magnetization curve with a given j. Thus, 2Hc ðTÞ can be determined by the ratio H0 =Hi for each i. Correctly chosen pffiffiffi j leads to 2Hc ðTÞ with the smallest standard deviation for each i.

Y.-T. Kwon et al. / Current Applied Physics 10 (2010) 1033–1036

In this process, the temperature dependence of the j is obtained as shown in the inset of Fig. 3. The increased jðTÞ for T P 70 K indicates that the thermal fluctuation of vortices, that is not included in Hao–Clem model, predominantly occurred [15]. Therefore, a temperature independent j of 82.2 is obtained by averaging the j values ðjav g Þ for 50 K 6 T 6 70 K. Using the obtained Hc ðTÞ, all experimental data are collapsed into the universal curve. This curve is produced by the chosen jav g as shown in Fig. 3. This indicates that the jav g and Hc ðTÞ, obtained from the Hao–Clem model are reasonable. The Hc ðTÞ and the jav g obtained from the Hao–Clem model are used pffiffiffi to calculate the kab ðTÞ by using the relation kab ðTÞ ¼ ð2 2pHc ðTÞ=jav g /0 Þ1=2 , where /0 is the magnetic flux quantum and kab is a penetration depth in the ab-plane. Fig. 4 shows the temperature dependence of kab marked with circles. In the framework of the BCS theory [16], kðTÞ in the clean limit ðl  n0 Þ, where n0 is the BCS coherence length) follows:

" kðTÞ ¼ kð0Þ 1  2

Z

1

0

#1=2   @f ðEÞ E dE  ; pffiffi 2 @E ðE  D2 Þ

ð1Þ

pffiffiffi Fig. 3. 4pM vs. H scaled by 2Hc ðTÞ. The solid line represents the universal curve derived from the Hao–Clem model with jav g ¼ 82:2: Inset: the temperature dependence of the Ginzburg–Landau parameter jðTÞ calculated by the Hao–Clem model. The averaged value of jðjav g Þ is 82.2 for 50 K 6 T 6 70 K.

260 Hc (kG)

6

λab (nm)

240

4 2 0

220

Hc(T) 20

40

60 80 T (K)

100 λab(T)

200

180

emperical formula BCS dirty limit BCS clean limit 40

50

60 T (K)

70

1035

f ðEÞ is the Fermi function and D is the superconducting energy gap. In the dirty limit ðl  n0 Þ, where l is the electron mean free path, kðTÞ is given by [17]:

kðTÞ ¼ kð0Þ

  DðTÞ DðTÞ 1=3 ; tanh 2kB T Dð0Þ

ð2Þ

where kB is the Boltzmann constant. In addition, we employ the empirical formula, given by kðTÞ ¼ kð0Þ½1  ðT=T c Þ2 1=2 , to estimate kab ð0Þ and T c . The solid line represents the fit obtained from the empirical formula, while the dotted line and the dashed line are the fitted curves obtained from the BCS dirty and the BCS clean limit, respectively. Among those, the empirical formula gives the best results and, thus, leads to kab ð0Þ  170:7 nm and T c  107:4 K. The BCS theory gives kab ð0Þ  181 nm and T c  109:1 K in the clean limit and kab ð0Þ  183:7 nm and T c  91:8 K in the dirty limit, respectively. The inset of Fig. 4 shows the Hc ðTÞ (open symbols) obtained from the Hao–Clem analysis. We apply the Hc ðTÞ to the two-fluid model given by Hc ðTÞ=Hc ð0Þ ¼ 1  ðT=T c Þ2 [18]. The solid line expresses the fit of the two-fluid model that produces Hc ð0Þ  0:66 T and T c  107:2 K. We determine the Hc2 ð0Þ by using the two-fluid model. Thus, following differentiating the Hc ðTÞ of the near two-fluid model, dHc =dT ¼ 12:3 mT/K p ffiffiffi T c is obtained. By using the relation dHc2 ðTÞ=dTjT¼T c ¼ j 2dHc =dTjT¼T c , dHc2 ðTÞ= dTjT¼T c ¼ 1:43 T/K is subsequently acquired. In order to obtain the Hc2 ð0Þ, we adopted the Werthamer–Helfand–Hohenberg (WHH) formula [19]. The WHH formula is given by Hc2 ð0Þ ¼ 0:5758ðj1 =jÞT c jdHc2 =dTjT c , where j1 =j is 1.26 and 1.2 in the clean and the dirty limit, respectively. The Hcc2 ð0Þ is 111.2 T in the clean limit leading to nab ð0Þ ¼ 17:2 Å by using the relation Hcc2 ð0Þ ¼ /0 =2pn2ab ð0Þ. Here, Hcc2 ð0Þ is an upper critical field along the c-axis and nab ð0Þ is a coherence length in the ab-plane. According to the previous NMR experiment [1,2], the IP is an antiferromagnetic state, not a superconducting state. This suppressed the interlayer coupling of the superconductivity between the two outer CuO2 planes [15]. If the two outer CuO2 planes are separated, then we expect that the Hg1245 might effectively act as two Hg1201, This is because, the c-axis lattice parameter of Hg1245 is approximately two times longer than that of Hg1201. However, the thermodynamic parameters of Hg1245 are not correlated with those of Hg1201, as described in Table 1. We also note that the T c is determined by both the interlayer coupling strength and the charge p carrier density [20]. From the ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi London expression for kab ð0Þ ¼ mab =ð4l0 ns e2 Þ, the k2ab ð0Þ / mab =ns , where mab is an electronic effective mass in the ab-plane and ns is a charge carrier density. The kab ð0Þ of Hg1245 is larger than that of Hg1234 indicating that the Cooper pair density is smaller if we assume that the electronic effective mass in the abplane is unchanged. In addition, the previous equilibrium magnetization analysis [15] has revealed that the interlayer coupling of Hg1245 is weaker than that of Hg1234. Therefore, the suppression of the T c of Hg1245 can be explained by an increase of kab ð0Þ and the weak interlayer coupling compared with Hg1234. Moreover, the Hc2 ð0Þ of Hg1245 is suppressed compared to that of Hg1234. This may have originated from the suppressed superconductivity due to the appearance of the antiferromagnetism in Hg1245. 4. Conclusions

80

Fig. 4. The temperature dependence of the penetration depth kab ðTÞ (circles) derived from Hc ðTÞ and jav g obtained from the Hao–Clem model. Inset: the circles denote the temperature dependent thermodynamic critical field Hc ðTÞ derived from the Hao–Clem model. The solid line represents the fit of Hc ðTÞ by the two-fluid model.

We presented an equilibrium magnetization analysis of fivelayered HgBa2Ca4Cu5O12+y by using the Hao–Clem model. We determined basic thermodynamic parameters are determined. The obtained penetration depth ðkab ð0ÞÞ of Hg1245 is slightly increased compared to that of Hg1234 indicating that the charge carrier density of Hg1245 decreased. One of the reasons for the

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Y.-T. Kwon et al. / Current Applied Physics 10 (2010) 1033–1036

suppressed T c in Hg1245 may have originated from the decrease of Cooper pairs compared to Hg1234. Acknowledgment This work is supported by the Ministry of Science and Technology of Korea through the Creative Research Initiative Program and special fund of Sogang University. References [1] H. Kotegawa, Y. Tokunaga, Y. Araki, G.-q. Zheng, Y. Kitaoka, K. Tokiwa, K. Ito, T. Watanabe, A. Iyo, Y. Tanaka, H. Ihara, Phys. Rev. B 69 (2004) 014501. [2] H. Mukuda, M. Abe, Y. Araki, Y. Kitaoka, K. Tokiwa, T. Wananabe, A. Iyo, H. Kito, Y. Tanaka, Phys. Rev. Lett. 96 (2006) 087001. [3] H. Kotegawa, Y. Tokunaga, K. Ishida, G.-q. Zheng, Y. Kitaoka, H. Kito, A. Iyo, K. Tokiwa, T. Watanabe, H. Ihara, Phys. Rev. B 64 (2001) 064515. [4] K. Tokiwa, S. Ito, H. Okumoto, W. Higemoto, K. Nishiyama, A. Iyo, Y. Tanaka, T. Watanabe, Physica C 388 (2003) 243. [5] J. Hofer, J. Karpinski, M. Willemin, G.I. Meijer, E.M. Kopnin, R. Molinski, H. Schwer, C. Rossel, H. Keller, Physica C 297 (1998) 103. [6] M.-S. Kim, Ph.D. Thesis, Department of Physics, ChungBuk National University, 1997. [7] C.G. Kim, H. Kim, J.H. Lee, J.S. Chae, Y.C. Kim, Solid State Commun. 142 (2007) 54.

[8] M.-S. Kim, S.-I. Lee, S.-C. Yu, I. Kuzemskaya, E.S. Itskevich, K.A. Lokshin, Phys. Rev. B 57 (1998) 6121. [9] K. Tokiwa, A. Iyo, T. Tukamoto, H. Ihara, Czech. J. Phys. 46 (1996) 1491. [10] D.E. Farrell, B.S. Chandrasekhar, M.R. EdGuire, M.M. Fang, V.G. Kogan, J.R. Clem, D.K. Finnemore, Phys. Rev. B 36 (1987) 4025. [11] J.R. Clem, Phys. Rev. B 43 (1991) 7837. [12] Z. Hao, J.R. Clem, Phys. Rev. Lett. 67 (1991) 2371. [13] Z. Hao, J.R. Clem, M.W. Mcelfresh, L. Civale, A.P. Malozemoff, F. Holtzberg, Phys. Rev. B 43 (1991) 2844. [14] A.A. Abrikosov, Zh. Eksp. Teor. Fiz. 32 (1957) 1442; A.A. Abrikosov, Sov. Phs. JETP 5 (1957) 1174. [15] M.-S. Park, J.-D. Kim, K.-H. Kim, Y.-T. Kwon, Y.C. Kim, A. Iyo, K. Tokiwa, S.-I. Lee, Phys. Rev. B 77 (2008) 024519. [16] M. Tinkham, Introduction to Superconductivity, McGraw-Hill, New York, 1980. p 43. [17] J.R. Clem, Ann. Phys. (New York) 40 (1966) 286. [18] C.J. Gorter, H.B.G. Casimir, Physica (Amsterdam) 1 (1934) 306. [19] N.R. Werthamer, E. Helfand, P.C. Hohenberg, Phys. Rev. 147 (1966) 295. [20] S.L. Cooper, K.E. Gray, Physical Properties of High Temperature Superconductors, vol. IV, World Scientific, Singapore, 1994. 61pp. [21] A. Bertinotti, V. Viallet, D. Colson, J.-F. Marucco, J. Hammann, G. Le Bras, A. Forget, Physica C 268 (1996) 257. [22] S.N. Putilin, E.V. Antipov, M. Marezio, Physica C 212 (1993) 266. [23] K.A. Lokshin, I.G. Kuzemskaya, L.F. Kulikova, E.V. Antipov, E.S. Itskevich, Physica C 279 (1997) 11. [24] K.A. Lokshin, D.A. Pavlov, M.L. Kovba, E.V. Antipov, I.G. Kuzemskaya, L.F. Kulikova, V.V. Davydov, I.V. Morozov, E.S. Itskevich, Physica C 300 (1998) 71.