Reversible magnetization and superconducting properties of the four-layered Ba2Ca3Cu4O8+y(F,O)2 superconductor with Tc∼90.6K

Solid State Communications 152 (2012) 1870–1873

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Reversible magnetization and superconducting properties of the four-layered Ba2 Ca3 Cu4 O8 þ y ðF,OÞ2 superconductor with T c  90:6 K Yong-Tae Kwon a, Heon-Jung Kim b,n, Akira Iyo c, Parasharam M. Shirage c, Young Cheol Kim a a

Department of Physics, Pusan National University, Busan 609-735, Republic of Korea Department of Physics, College of Natural Science, Daegu University, Gyeongbuk 712-714, Republic of Korea c National Institute of Advanced Industrial Science and Technology (AIST), Central 2, Tsukuba, Ibaraki 305-8568, Japan b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 February 2012 Received in revised form 5 June 2012 Accepted 17 July 2012 by S. Miyashita Available online 22 July 2012

Reversible magnetization of grain-aligned Ba2 Ca3 Cu4 O8 þ y ðF,OÞ2 (F-0234) with T c C 90:6 K, which is a member with n ¼4 in the new homologous series Ba2 Can1 Cun O2n ðF,OÞ2 was investigated using the Hao–Clem model and fluctuation theories. The almost temperature independence of the Ginzburg– Landau parameter (k) up to 0.9 T=T c and the crossover point in M(T) indicated less 2D character, suggesting no drastic decrease in interlayer coupling compared to other high-Tc cuprate superconductors. The relatively strong interlayer coupling results from the smallest thickness of the charge reservoir block among other multilayered systems. On the other hand, the lab ð0Þ and Hc ð0Þ values derived from the Hao–Clem analysis strongly suggest that the decrease in Tc is due to both the decrease in the carrier density and weakened pairing strength. & 2012 Elsevier Ltd. All rights reserved.

Keywords: High-Tc superconductor Reversible magnetization Ba2 Ca3 Cu4 O8 þ y ðF,OÞ2

1. Introduction Since the discovery of high-Tc cuprate superconductors (HTSCs), almost three decades ago [1], it is still one of the most important themes in condensed matter physics. The phenomenology, particularly on the generic phase diagram of a single CuO2 plane is relatively well understood due to the progress in experiments and theories [2]. On the other hand, the mechanism for the high transition temperature (Tc), the nature of the unconventional normal state, and a possible way to increase Tc are still elusive. The most interesting feature of the phase diagram for a single CuO2 plane is the sensitivity of the physical properties to the carrier density. In particular, Tc shows a dome shape with respect to the carrier density, where the maximum Tc is considered optimally doped. The carrier density divides the regions below and above the optimal doped state, which is called the underdoped and the overdoped region, respectively. Despite the lack of a complete understanding about the factors to determine Tc, it was found to increase with increasing number of CuO2 planes in a unit cell. For example, the Tc of HgBa2 Can1 Cun O2n þ 2 þ y [Hg-12(n  1)n] compounds increases with increasing n, reaching maximum T c  136 K at n ¼3 [3,4]. This suggests that strong interlayer coupling between CuO2 planes is one of the crucial factors to increase Tc. On the contrary to the naive

n

Corresponding author. E-mail address: [email protected] (H.-J. Kim).

0038-1098/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ssc.2012.07.016

expectation, Tc begins to decrease above n ¼3. The possible origin of this behavior is that multilayered HTSCs with n Z 3 have crystallographically different CuO2 planes: the outer CuO2 plane (OP) with pyramidal coordinates of oxygen and the inner plane (IP) with square coordinates. The oxygen doping state of IP and OP is inevitably different, resulting in a non-uniform carrier density distribution in the unit cell as well as the reduced Tc for n 4 3. An extensive nuclear magnetic resonance (NMR) study on Hg1245 [4,5]confirmed the IP and OP to be in antiferromagnetic and superconducting states, respectively. Carrier density of each kind of CuO2 planes was also measured directly by NMR in F-0234 [6]. According to this study, the T c of the present sample implies N(OP)¼0.189 and N(IP) ¼0.150, which are carrier density of outer and inner CuO2 planes, respectively. This carrier distribution affects the reversible magnetization profoundly. In particular, the thermal fluctuations become pronounced when the doping levels of OP and IP are quite different as observed in Hg-1234 [7] and Hg-1245 [8], shortening the longitudinal correlation length of a vortex. To clarify the link between the doping states of multilayered HTSCs and the properties in magnetization, it is necessary to investigate a new multilayered HTSC with known ones. The crystal structure of HTSC consists of an alternating stacking of a superconducting layer (SCL) and a charge reservoir block (CRB) [3]. Typically, the SCL contains CuO2 layers separated by Ca (or Sr, Y, etc), and CRB have a characteristic layer inserted between the two Ba(Sr)-O layers. The stability of the crystal structure and doping state is controlled by the degree of matching between SCL and CRB. This paper reports the results of the

Y.-T. Kwon et al. / Solid State Communications 152 (2012) 1870–1873

reversible magnetization on Ba2 Ca3 Cu4 O8 þ y ðF,OÞ2 (F-0234) with T c C 90:6 K [9]. In F-0234, there are two Ba-(O,F) layers with no other layer between the CRB and the part of apical oxygens are substituted with fluorine. Compared to other multilayered HTSCs, F-0234 contains no heavy or toxic elements, which is why this phase is stabilized only under high pressure conditions. Moreover, the length between SCLs d with d ¼ 7:36 A˚ is smallest [9], which suggests that the interlayer coupling and doping mechanism may be different from other multilayered HTSCs. Therefore, F-0234 is a suitable system to address this issue by analyzing the reversible magnetization. An analysis of reversible magnetization, particularly one based on the Hao–Clem model [10,11], provides invaluable information such as the interlayer coupling, carrier density, and pairing strength, which can be applied successfully to a range of superconductors, such as HTSCs [12–14] and MgB2 [15,16].

2. Experiment The crystal structure was examined by X-ray diffraction (XRD, Rigaku). The field-dependent magnetization 4pMðTÞ in a zerofield-cooling (ZFC) and field-cooling (FC) state were obtained for magnetic fields up to 5 T using a SQUID magnetometer (Quantum Design). Polycrystalline F-0234 was synthesized under high pressure conditions as reported previously [9]. For magnetization measurements, the sample was aligned using the method reported by Farrel et al. [17]. In this method, the sample was ground into a fine powder and aligned along the c axis in a high magnetic field. The aligned sample showed only (00l) in the XRD pattern and a full width at half maximum of the (001) peak is less than 0:3J .

3. Results and discussion Fig. 1 shows the magnetization 4pMðTÞ mainly in the reversible region for HJc below H¼5 T. The inset in Fig. 1 shows a magnified 4pMðTÞ near Tc, revealing a crossover point at ðT n ,4pMn Þ ¼ ð88:7 K,1:6 GÞ. This suggests that the M(T) curves deviate strongly from a standard London behavior [18]. Indeed, this is a well-known signature of thermal fluctuations due to thermal distortion of the vortex lines. According to Koshelev [19], a crossover point occurs when the equation, Mn ¼m1 ðkB T n =f0 sÞ, holds, where m1 ¼0.346, f0 and kB are the flux quantum and

Fig. 1. Reversible magnetization 4pMðTÞ obtained from the various fields (H r 5 T) parallel to the c-axis. The inset shows the magnified view near Tc. The crossing point can be seen.

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Boltzmann constant, respectively, and s is the effective interlayer distance. Using the crossover point with Tn ¼88.7 K and ˚ Interestingly, 4pM n ðT n Þ ¼ 1:6 G, s was obtained to be  16:1 A. this value is larger than the length between the CuO2 layers ˚ and that between the SCLs (7.36 A), ˚ but quite similar to (3.19 A) ˚ This indicates that the the length of the half unit cell (16.9 A). pancake vortices are strongly coupled across the CuO2 planes in the SCL, and even in the adjacent SCLs along the c direction. This is quite different from Hg-1245 [8], where the effective interlayer distance is shorter than the distance between the SCLs, showing 2D vortex properties. For the understanding of reversible magnetization, the Hao–Clem model based on the Ginzburg–Landau free energy [10,11] was used. In principle, this model can be applicable when the positional fluctuations are not important. This can describe the reversible magnetization for the entire mixed state between Hc1 and Hc2, where Hc1 and Hc2 are the lower and upper critical fields, respectively. This model enables one to determine the superconducting parameters, such as the Ginzburg–Landau parameter k and thermodynamic critical field Hc. In addition, the fluctuation regions can be inferred from the temperature dependence of k, which exhibits an anomalous increase when the thermal fluctuations become significant [7,8,14]. In the Hao–Clem model, the reversible magnetization in the pffiffiffi dimensionless form, 4pM 0 ¼ 4ppffiffiffiM= 2Hc ðTÞ, is a universal function of the external field, H0 ¼ H= 2Hc ðTÞ, for a given value of k [11]. Therefore, the experimentally measured 4pM versus H data obtained at each temperature was fitted to the Hao–Clem model using Hc and k as parameters. If the fitting is successful, the 4pM 0 versus H0 data at different temperatures should lie on a single universal curve. Using this procedure, the k values of F-0234 at different temperatures was obtained, as shown in Fig. 2. k is almost temperature-independent up to 80 K (  0:9 T=T c ), above which k increases abruptly. This is a region where the Hao–Clem model fails due to the enhanced thermal fluctuations. The average value of k (kav ) for 40 r T r 80 is 102. The behavior of k in F-0234 was similar to YBa2Cu4O8 [20], which is a well-known 3D HTSC in that the anomalous increase in k begins above 0:9 T=T c . This is in strong contrast with other 2D multilayered HTSCs [21,7,8,14,13], where k begins to increase anomalously well below 0:9 T=T c or it

Fig. 2. Temperature dependence of the Ginzburg parameter k calculated by the Hao–Clem model. This is almost temperature-independent up to 80 K (  0:9 T=T c ). The increase in k above 80 K signals the increased effect of thermal fluctuations. The inset shows pffiffiffi the curve of the 4pM versus H data at different temperatures scaled by 2Hc ðTÞ. The solid line represents the universal curve derived from the Hao–Clem model with kav ¼ 102.

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Fig. 3. Temperature dependence of the thermodynamic critical field Hc(T) (circle) derived from the Hao–Clem model together with the theoretical curves of the BCS theory (the dotted line) and the two-fluid model (the solid line).

increases continuously over the wide temperature regions. For example, in Hg-1234, k begins to increase at 0:8 T=T c [7]. Considering the same number of CuO2 planes in the structural unit, the result is rather unexpected and appears to be related to the short CRB in F-0234. The inset in Fig. 2 also shows the scaling form of the 4pM versus H data, which are all on a universal curve. This suggests that the fitting is reliable. Fig. 3 displays the temperature dependence of Hc from the Hao–Clem fitting. Hc ð0Þ was estimated using the Hc(T) of the twofluid model and that of the BCS theory. The Hc(T) of the two-fluid model and the BCS theory is given by Hc ðTÞ=Hc ð0Þ ¼ 1ðT=T c Þ2 [22] and Hc ðTÞ=Hc ð0Þ¼1:7367ð1T=T c Þ½10:2730ð1T=T c Þ0:0949 ð1T=T c Þ2  [23], respectively. In the temperature range, 40 r T r 80, both cases describe the data well, giving a similar extrapolated value of Hc ð0Þ ¼ 0:64 70:01 T. Since both formulae gave similar results, the two-fluid model was used to estimate Hc2 ð0Þ. dHc2 ðTÞ=dT9T ¼ T cp¼ffiffiffi0:877 T=K is acquired using the relation dHc2 ðTÞ=dT9T ¼ T c ¼ k 2dHc =dT9T ¼ T c . In order to obtain the Hc2 ð0Þ, we adopt the Werthamer–Helfand–Hohenberg (WHH) formula [24]. The WHH formula is given by Hc2 ð0Þ ¼ 0:5758ðk1 =kÞT c 9dHc2 =dT9T c , where k1 =k is 1.26 and 1.2 in the clean and the dirty limit, respectively. In both cases, Hcc2 ð0Þ was estimated to be 126 T. This 2 leads to xab ð0Þ ¼ 16:2 A˚ by using the relation Hcc2 ð0Þ ¼ f0 =2pxab ð0Þ, c where Hc2 ð0Þ is an upper critical field along the c-axis and xab ð0Þ is the coherence length in the ab-plane. The Hc(T) and kav obtained from the Hao–Clem modelpwere used ffiffiffi to calculate lab ðTÞ using the equation lab ðTÞ ¼ ð2 2pHc ðTÞ= kav f0 Þ1=2 , where f0 is the magnetic flux quantum and lab is the penetration depth in the ab-plane. Fig. 4 shows lab ðTÞ along with the theoretical curves. In the BCS theory [25], lðTÞ in the clean limit (x0 5 lð0Þ, where x0 is the BCS coherence length) can be expressed as follows: 2 31=2  Z 1 @f ðEÞ E 6 7 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dE5 lðTÞ ¼ lð0Þ412  , ð1Þ @E 2 2 0 ðE D Þ where f(E) is the Fermi function and D is the superconducting energy gap. On the other hand, in the dirty limit (l 5 x0 , where l is the electron mean free path), lðTÞ is given by the following equation:   DðTÞ DðTÞ 1=3 tanh lðTÞ ¼ lð0Þ , ð2Þ 2kB T Dð0Þ

Fig. 4. Temperature dependence of the penetration depth lab ðTÞ (circles). The lines are theoretical curves and the solid line is derived from the two-fluid model. The dotted and dashed lines are from the BCS theory in the clean and dirty limit, respectively.

where kB is the Boltzmann constant. In addition, we also employ the empirical formula, which is given by lðTÞ ¼ lð0Þ½1 ðT=T c Þ2 1=2 , to estimate lab ð0Þ and Tc. The solid line represents the fit obtained from the empirical formula, whereas the dotted and dashed lines are the fitted curves obtained from the BCS dirty and BCS clean limits, respectively. Among those, the fit to the formula in the BCS clean limit and the empirical formula provided the best results, both leading to lab ð0Þ  193 75 nm. In fact, it is known that in very clean HTSCs, line nodes in the gap give rise to a linear temperature dependence in lðTÞ, which is changed to T2 dependence in the dirty limit [26]. Since our sample is an aligned polycrystal, it is thought that it is in the dirty limit. In this case, the empirical formula describes lðTÞ over the entire temperature range below Tc [27]. Table 1 summarizes the thermodynamic parameters obtained from this study. The values of the other multilayered HTSCs with n¼3, 4, and 5 are also listed. This table shows a trend on the thermodynamic parameters of these HTSCs along with the distinguished features in F-0234. A first noticeable feature is the correlations of Tc with lab ð0Þ and Hc ð0Þ. According the London qto ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi expression for lab ð0Þ, lab ð0Þ is given by lab ð0Þ ¼ mnab =ð4m0 ns e2 Þ 1=2 pns , where mnab and ns are the in-plane component of the mass tensor and the Cooper pair density, respectively. While lab ð0Þ and Hc ð0Þ are different in the Ba2 Ca2 Cu3 O6 þ y ðF,OÞ2 (F-0223) [28] and Hg-1245, the Tc values of both compounds are similar. This suggests that Tc may be determined by two independent parameters, one of which is definitely the Cooper pair density ns. The other parameter is related to the pairing strength. Without full understanding for the mechanism of HTSC, the exact relation between the pairing strength and Hc ð0Þ is not known, but it seems that those parameters are strongly correlated. Therefore, although F-0223 and Hg-1245 have a similar Tc, there are different reasons why each has its own Tc. In the case of F-0223, the Cooper pair density is reduced considerably while the pairing strength is not. In contrast, the opposite is true for Hg-1245. From the above-mentioned observation, we can figure out a possible reason why F-0234 has an even lower Tc, based on the Cooper pair density and pairing strength. It can be inferred that the F-0234 has reduced Cooper pair density and weakened pairing strength, compared to F-0223 and Hg-1245. The importance of these parameters can be seen when F-0234 and CuBa2 Ca3 Cu4 O10 þ y (Cu-1234) [29] are compared. Although the lab ð0Þ of F-0234 is similar to that of Cu-1234, F-0234 still has a

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Table 1 Transition temperature Tc, Ginzburg–Landau parameter kav ¼ lab =xab , thermodynamic critical field Hc ð0Þ, upper critical field at absolute zero in the c-axis Hcc2 ð0Þ, in-plane coherence length xab ð0Þ, and in-plane penetration depth lab ð0Þ of Ba2 Ca3 Cu4 O8 þ y ðF,OÞ2 , derived from the reversible magnetization M(T) measurements. F-0223 [28]

Hg-1245 [8]

Hg-1234 [7]

Tl-1234a [13]

Cu-1234 [29]

F-0234

Hc ð0Þ (T) Hcc2 ð0Þ (T) ˚ xab ð0Þ (A)

108.8 160 0.81 232 11.9

108 82.2 0.66 111.2 17.2

125 102 1.12 205 12.7

128 99.7 1.02 207 12.6

117 127 0.9 196 12.8

90.6 102b 0.63c 126d 16.2d

lab ð0Þ (nm)

240

170.7 7.6

157 15.4

156 17.8

198

Tc (K)

kav

˚ f s (A)

–

–

219e 16.1

a

TlBa2 Ca3 Cu4 O10 þ y . In the temperature range of 40 K r T r 80 K. c From the two-fluid theory. d Assuming the BCS theory. e From the empirical formula. f Based on the theory of Koshelev [19]. b

lower Tc. This further decrease in Tc mainly results from the weakened pairing strength, which is reflected in a lower Hc ð0Þ. 4. Conclusions The reversible magnetization of the four-layered Ba2 Ca3 Cu4 O8 þ y ðF,OÞ2 , which has the shortest charge reservoir block was analyzed using the Hao–Clem model, and the thermodynamic parameters were determined. The Ginzburg–Landau paramter k was constant up to 0:9 T=T c , which indicates relatively less 2D behavior among the four-layered compounds. This was attributed to the smallest thickness of the charge reservoir block in Ba2 Ca3 Cu4 O8 þ y ðF,OÞ2 among other multilayered systems. Compared to the other four-layered high-Tc cuprate superconductors, this study showed that the carrier density and pairing strength are reduced, both of which result in a relatively larger decrease in Tc. These results are believed to be related to structural features of this compound.

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