Ion-Size Effect on Superconducting Transition Temperature Tc in …Er, Dy, Gd, Eu, Sm, and Nd؍R1؊X؊Yprxcayba2cu3o7؊Z Systems „R Li-Chun Tung, J

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provided by National Tsing Hua University Institutional Repository PHYSICAL REVIEW B VOLUME 59, NUMBER 6 1 FEBRUARY 1999-II

Ion-size effect on superconducting transition temperature Tc in …Er, Dy, Gd, Eu, Sm, and Nd؍R1؊x؊yPrxCayBa2Cu3O7؊z systems „R Li-Chun Tung, J. C. Chen, M. K. Wu, and Weiyan Guan Department of Physics, National Tsing Hua University, Hsinchu, 300, Taiwan, Republic of China ͑Received 14 September 1998͒

We observed a rare-earth ion-size effect on Tc in R1ϪxϪyPrxCayBa2Cu3O7Ϫz ͑RϭEr, Dy, Gd, Eu, Sm, and Nd͒ systems which is similar to that in R1ϪxPrxBa2Cu3O7Ϫz systems in our previous reports. For fixed Pr and 3ϩ Ca concentration ͑fixed x and y͒, Tc is linearly dependent on rare-earth ion radius rR . For a fixed Pr concentration x, there exists a maximum of Tc (Tc,max)inTc vs Ca concentration y curves. Tc,max shifts to higher Ca concentration region for samples with larger R ion radius. The enhancement of Tc ͑⌬Tc,max ϭTc,maxϪTc,yϭ0 ; Tc,yϭ0 is the transition temperature Tc without Ca doping͒ increases with increasing R ion 3ϩ radius. We proposed an empirical formula for Tc (rR ,x,y) to fit our experimental data: Tc(x,y)ϭTc0 2 2 2 ϪA␤ (␣/xϩy/␤) ϪBx. All fitting parameters in this formula, Tc0 , B, ␤, ␣/␤, and A␤ , are rare-earth ion-size dependent. ͓S0163-1829͑99͒01506-4͔

I. INTRODUCTION tration x. It suggests that Pr ions are trivalent and localize, rather than fill, the mobile holes on CuO2 planes. The local- The substitution of Y by trivalent rare-earth elements in ization leads to the suppression of superconductivity and in- orthorhombic YBa2Cu3O7Ϫy ͑YBCO͒, yields a supercon- duces a metal-insulator transition. In fact, most experimental ducting phase with T identical to YBCO,1 except for Ce, results supporting hole filling would also support hole local- c 19 Tb, Pm, and Pr. It shows that the magnetic moments of the ization. Recently, Kao, Yu, and Guan measured the hole concentration p per unit cell by using iodometric titration lanthanide ions have a weak effect on the CuO2 sheets. The insensitivity of the superconducting properties to the substi- technique for (Gd1ϪxPrx)Ba2Cu3O7Ϫy (xϭ0.1– 0.9) and tution is presumably due to their layered structure and the (R0.8Pr0.2)Ba2Cu3O7Ϫy ͑RϭYb, Er, Dy, Gd, and Nd͒ nearly complete lack of interaction between rare-earth and samples. The chemical hole concentration p was compared to the Hall number n CuO sheets.2 H and Tc reported in literature. What is 2 most surprising is that the total carrier concentration p is Although crystallographically identical to all the other independent of Pr concentration and remains primarily rare-earth-based superconductors, PrBa Cu O ͑PrBCO͒ 2 3 7Ϫy constant even when the samples are not supercon- inhibits the superconducting and metallic behavior.3–5 The ducting in higher Pr concentration region (xу0.5) in Y1ϪxPrxBa2Cu3O7Ϫy system is particularly interesting since 19 (Gd1ϪxPrx)Ba2Cu3O7Ϫy . It should also be noted that the it is isostructural to YBCO, yet the superconductivity is total carrier concentration p remains primarily constant even strongly suppressed as a function of Pr concentration. when Tc is changed by almost 100% with the changing of R The suppression of T by Pr doping in Y Pr Ba 19 c 1Ϫx x 2 ions in (R0.8Pr0.2)Ba2Cu3O7Ϫy . The authors proposed that Cu3O7Ϫy has been attributed to several possible mechanisms. the total hole concentration p measured by iodometric tech- The first mechanism involves the filling of holes ͑hole fill- nique is not changed with Pr doping but the concentration of ing͒ in CuO sheets due to the substitution of Pr ions with its 2 mobile holes nH measured by the Hall effect is changed with valence greater than ϩ3 and, hence, implies the suppression Tc and Pr doping. It strongly suggests that Tc suppression of superconductivity and metallic behavior, arising from a appears to be caused by hole localization rather than hole reduced number of carriers ͑holes͒ in CuO2 sheets. Indeed, filling. magnetic susceptibility,4–6 Hall measurements,5 thermoelec- 7 8 The second mechanism for Tc suppression involves the tric power, muon spin resonance, neutron diffrac- spin-flip effect of the pairing electrons ͑pair breaking͒, being tion,9 specific-heat measurement,10 and x-ray-absorption 20 11 explained on the basis of Abrikosov-Gor’kov ͑AG͒ theory, spectroscopy are consistent with a Pr valence substanti- which has been used widely and successfully for interpreta- ally larger than 3ϩ. Superconductivity observed in a tion of conventional alloy superconductors with paramag- 12 Pr0.5Ca0.5Ba2Cu3O7Ϫy film strongly supports this mecha- netic doping. This model suggests Pr ion acts as a strong 13 nism. Based on the spin-polaron model, Wood obtained an magnetic pair breaker.6,21–23 AG theory predicts that a re- agreement with experimental data for a Pr concentration de- duced transition temperature Tc /Tc0 will be a universal func- pendence of T in the Y Pr Ba Cu O system. c 1Ϫx x 2 3 7Ϫy tion of the reduced concentration x/xcr , However, this idea was later questioned. X-ray-absorption near-edge spectroscopy,14 valence-band resonant photoemission,15 lattice constant16 and Raman spectrum17 in- ln͓Tc /Tc0͔ϭ⌿͑1/2͒Ϫ⌿͑1/2ϩ0.14xTc0 /xcrTc͒, ͑1͒ dicate a Pr valence close to 3ϩ. According to electron- 18 energy-loss spectroscopy measurement, the total number of where Tc0 is the Tc for ‘‘pure’’ material ͑without doping͒, holes on O sites was shown to be independent of Pr concen- xcr is the critical concentration for complete suppression of

0163-1829/99/59͑6͒/4504͑9͒/$15.00PRB 59 4504 ©1999 The American Physical Society PRB 59 ION-SIZE EFFECT ON SUPERCONDUCTING... 4505 superconductivity and ⌿ is a digamma function. For xϷ0, it the number of the generated holes. This indicates that doping gives an asymptotic form, with Ca ions has a counterbalance effect on the suppression of Tc . 2 2 TcϭTc0Ϫ͓͑␲/4kB͒N͑EF͒␶ ͑gϪ1͒ J͑Jϩ1͔͒x, ͑2͒ Ca doping is able to increase the Tc of the oxygen- deficient YBCO.35 The replacement of 20% Ca ions in te- where N(EF) is the density of state at Fermi level and g and tragonal YBa2Cu3O6 induces the superconductivity; whereas J, respectively, the Lande´ g factor and the total angular mo- the same amount of Ca, in fully oxygenated YBa2Cu3O7Ϫy , 36 mentum of Hund’s rules ground state of the Pr ion and ␶ is lowers Tc from 90 to 78 K. Yakabe et al. showed that there the exchange interaction parameter. exists a maximum of Tc about 90 K with the variation of the The close correspondence of Tc vs x data with results carrier density in single phase Y1ϪxCaxBa2Cu3O7Ϫy thin based on AG theory ͓Eq. ͑2͔͒ has been interpreted as an films up to 50% Ca concentration. Similar behavior was ob- 21–23 37 evidence for pair breaking. Spin-polarized electronic served in Y1ϪxCaxBa2Cu2.64Co0.36O7Ϫy , Y1ϪxCaxBa2 24 38 band-structure calculations for RBa2Cu3O7Ϫy ͑RϭY, Gd, Cu2.5Fe0.5O7, Y1ϪxCaxSr2Cu3ϪyM yO6ϩz ͑MϭTi, and R; and Pr͒ also confirms the pair-breaking mechanism. AG yϭ0.33 and 0.15͒, and Y1ϪxCaxSrBaCu3ϪyM yO6ϩz ͑M theory ͑pair-breaking model͒ successfully explained the ba- ϭAl, Co, Fe, and Ga, yϭ0, 0.4͒.39 These observations indi- sic features of experiments, but the theory is difficult to ex- cate that the substitution of Ca2ϩ for Y3ϩ in these com- plain the metal-insulator transition at larger Pr concentration pounds compensates the loss of the holes and restores the 3,4,6,21,25 in (Y1ϪxPrx)Ba2Cu3O7Ϫy . superconductivity. 26 Fehrenbacher and Rice proposed that the difference be- The Tc of Y1ϪxϪyPrxCayBa2Cu3O7Ϫz ͑Ref. 22͒ could be tween PrBa2Cu3O7Ϫy and other RBa2Cu3O7Ϫy comes from enhanced by Ca doping and there exists a maximum of Tc IV an enhanced stability of the Pr state due to the hybridiza- (Tc,max) for varying Ca concentration y. The Tc vs y curves tion with oxygen neighbors, involving the transfer of holes can be resolved into two parts: ͑1͒ the counteracting effects 2ϩ from primary planar O 2p␴ to 2p␲ states. A particularly of generation and filling of holes on the CuO2 sheets by Ca important unusual characteristic of Pr ions is its 4 f wave and Pr4ϩ ions, respectively, and ͑2͒ the depairing of super- function, while the other rare-earth ions are characterized by conducting electrons via exchange interaction of mobile more symmetric orbital. Hybridization could generate an ex- holes on the CuO2 sheets with local Pr magnetic moments. change interaction between the Pr magnetic moment and the Combining the features of both models, Neumeier et al.22 mobile holes on CuO2 planes, leading to hole localization suggested an empirical polynomial function, and/or pair breaking. Though this model has been widely used in discussion of Y1ϪxPrxBa2Cu3O7Ϫy , it could not ex- 2 TcϭTc0ϪA͑␣Ϫ␤xϩy͒ ϪBx, ͑3͒ plain the rare-earth ion-size effect on Tc in the 27,28 R1ϪxPrxBa2Cu3O7Ϫy system. After systematic studies of the superconducting and where Tc0 is the maximum obtained value of Tc , A(␣ Ϫ␤xϩy)2 is an empirical term that represents the effect of normal-state properties of the R1ϪxPrxBa2Cu3O7Ϫy system, Guan and co-workers reported that the superconducting tran- hole generation by Ca ions and hole filling by Pr ions, Ϫ␣ is 27 an optimal hole concentration, ␤ is the deviation of the ef- sition temperature Tc , the magnetic ordering temperature 28 29,30 fective valence, ␯͑Pr͒, of Pr ions from ϩ3 ͓i.e., ␤ϭ␯(Pr) of Pr ions TN , the normal-state resistivity ␳, and the Ϫ3͔, ϪBx describes the overall depression of Tc with x due Hall number per unit cell nH in R1ϪxPrxBa2Cu3O7Ϫy ͑Ref. 30͒ are all R ion-size dependent. It was also reported that the to the pair-breaking mechanism. In this paper we study the effect of codoping of Pr and Ca Hall number nH of R0.9Ca0.1Ba2Cu3O7Ϫy ͑Ref. 31͒ and Tc of on Tc in R1ϪxϪyPrxCayBa2Cu3O7Ϫz ͑RϭEr, Dy, Gd, Eu, RBa2Cu3ϪxGaxO7Ϫy ͑Ref. 32͒ are also ion-size dependent. Sm, and Nd͒, and observe a rare-earth ion-size effect on Tc For a constant Pr concentration, Tc of R1ϪxPrx in these systems. For fixed Pr and Ca concentration, Tc is Ba2Cu3O7Ϫy linearly decreases with increasing R ion radius, 3ϩ and the c-axis per unit cell increases with increasing R ion linearly dependent on rare-earth ion radius rR . We pro- 3ϩ radius. One would expect the opposite trend based on the posed an empirical formula for Tc (rR ,x,y) to fit our ex- hybridization picture, since the average distance between perimental data. CuO2 plane becomes larger leading to a weaker Pr-CuO2 hybridization. Khomdskii33 suggested that Pr can induce a II. EXPERIMENTAL lattice distortion, especially the buckling of the CuO2 plane. It was established that the distance between Pr and its sur- Polycrystalline samples R1ϪxϪyPrxCayBa2Cu3O7Ϫz ͑R rounding oxygen, dPr-O , is less than dY-O .IfdPr-O keeps ϭEr, Dy, Gd, Eu, Sm, and Nd͒ were prepared by standard invariant in all R1ϪxPrxBa2Cu3O7Ϫy , one would expect a solid-state reaction method. Stoichiometry amounts of high- stronger buckling for R1ϪxPrxBa2Cu3O7Ϫy with larger R ion purity R2O3,Pr6O11, CaCO3, BaCO3, and CuO powders radius, leading to larger resistivity and stronger suppression were mixed, ground and calcined three times at 900, 910, of superconductivity. 920 °C, respectively, for 24 h followed by furnace cooling to Among all cation dopiness, Ca substitution for Y in room temperature. Each time the powders were ground and YBCO has attracted much attention.34–40 The valence state mixed before next firing for ensuring the homogeneity of of Ca2ϩ is lower than that of Y3ϩ. Such a substitution will samples. The resultant powders were reground and pressed 3 generate excess holes and Tc is suppressed by the overdop- under the pressure 40 kg/cm into pellets, which were sin- ing effect. On the other hand, it has been known that Ca tered in flowing oxygen at 930 °C for 30 h followed by a doping is likely to cointroduce oxygen vacancies, reducing slow cooling to 680 °C staying for 8 h, and then slowly 4506 LI-CHUN TUNG, J. C. CHEN, M. K. WU, AND WEIYAN GUAN PRB 59

FIG. 3. Temperature dependence of dc molar magnetization ͑ZFC and FC͒ for Dy0.9ϪyPr0.1CayBCO (yϭ0 – 0.2). The smaller pictures in the right column show the Tconset .

III. RESULTS AND DISCUSSION FIG. 1. X-ray powder-diffraction patterns for Gd0.8ϪyPr0.2CayBa2Cu3O7Ϫz (yϭ0 – 0.3). Si peaks are labeled by X-ray-diffraction patterns at room temperature show that symbol ‘‘s.’’ all samples have layered orthorhombic perovskitelike structure and no extra peaks arising from the impurity phases cooled to 450 °C for 30 h before a ﬁnal cool to room tem- within the experimental errors ͑Ͻ5%͒. As an example, perature. the x-ray powder-diffraction patterns of Gd0.8ϪyPr0.2Cay The structure of the samples were examined by Rigaku Ba2Cu3O7Ϫz are shown in Fig. 1. The additional peaks, la- Rotaﬂex rotating anode x-ray diffractometer using Cu K␣ beled by symbol ‘‘s’’, are arising from silicon, added as a radiation with a wavelengthϭ1.5406 Å. Differential thermal standard in order to determine the lattice parameters of our analysis was also carried out in several groups of samples to samples. These results indicate Ca doping (yр0.3) in RBCO does not yield impurity phases in bulk material. check the presence of other phases. Tc was determined from electrical resistivity measurement using a low-frequency ͑37 The lattice parameters a, b, and c of Er0.8ϪyPr0.2 Hz͒ four-lead technique. The measuring current is limited to CayBa2Cu3C7Ϫz are shown in Fig. 2. The c axis increases 20 ␮A. Electrical contacts to the samples were made by with increasing Ca concentration y. It is due to that the radius silver-paste epoxy. The dc magnetization was measured by a of Ca ions ͑99 pm͒ is much larger than that of Er ions ͑89 Quantum design superconducting quantum interference de- vice magnetometer.

FIG. 4. Temperature dependence of dc molar magnetization FIG. 2. Lattice constants a, b, and c vs Ca concentration y for ͑ZFC͒ for bulk and powder samples of Dy0.9ϪyPr0.1CayBCO (y Er0.8ϪyPr0.2CayBCO. ϭ0 – 0.2). PRB 59 ION-SIZE EFFECT ON SUPERCONDUCTING... 4507

FIG. 7. Temperature dependence of dc molar magnetization ͑ZFC͒ for bulk samples of Eu0.8ϪyPr0.2CayBCO (yϭ0 – 0.3).

FIG. 5. Temperature dependence of resistivity ␳ for the c axis increases progressively with decreasing oxygen Dy0.9ϪyPr0.1CayBCO (yϭ0 – 0.2). The smaller pictures in the right content. When the R ion radius is comparable to that of Ca column show the Tcmid . Two samples were sintered with the same ions in our R1ϪxϪyPrxCayBa2Cu3O7Ϫz samples, the c axis condition. does not increase apparently. ͑For example, in Eu0.8ϪyPr0.2CayBa2Cu3O7Ϫz , cϭ11.698 Å, when yϭ0 and 3ϩ pm͒. This increment is reduced in other cϭ11.707 Å, when yϭ0.2. rEu ϭ95 pm͒. Therefore, it is R1ϪxϪyPrxCayBa2Cu3O7Ϫz system where the R ion radius is reasonable to assume the oxygen content does not vary much larger. The lattice parameter b decreases and a increases in our samples. slightly with increasing Ca concentration y. These behaviors The temperature dependence of dc molar magnetization are similar to that reported in the Y1ϪxCaxBa2Cu3O7Ϫy M(T)ofR1ϪxϪyPrxCayBa2Cu3O7Ϫz was measured both in system.42 Yang et al.41 reported that the c axis of zero-field cooling ͑ZFC͒ and field-cooling ͑FC͒ over the R(Ba1ϪxCax)Cu3O7Ϫz ͑RϭY and Pr͒ decreases abruptly, temperature range 5–90 K in the magnetic field of 10 G. A where Ca ions occupy the Ba site and it is just opposite to the typical result for Dy0.9ϪyPr0.1CayBa2Cu3O7Ϫz is shown in observed result shown in Fig. 2. Therefore, we believe that Fig. 3. The M(T) curves demonstrate a superconducting the Ca ions replace the R site but not the Ba site in our transition with a ‘‘knee’’ in ZFC. It could be due to the R1ϪxϪyPrxCayBa2Cu3O7Ϫz samples. granular character of the sintered samples. The supercon- It was reported that in fully oxygenated YBCO, Ca dop- ducting transition of sintered pellets could be divided as a ing is accompanied by the loss of oxygen content,40 but it two-step process with first the transition of grains and fol- was also reported that the oxygen content does not change lowed by the transition of intergrain barriers or junctions at with Ca concentration in the Y 1ϪxϪyPrxCayBa2Cu3O7Ϫz lower temperatures. The ‘‘knee’’disappears when the sample system.22 It suggests that the loss of oxygen content, result- is ground and when the powder dc magnetization measure- ing from Ca doping, can be compensated by Pr doping. On ments are performed as shown in Fig. 4. the other hand, in oxygen-deficient YBCO,42 the length of Normal-state resistivity ␳(T) was measured in the tem-

FIG. 6. Temperature dependence of dc molar magnetization FIG. 8. Temperature dependence of resistivity ␳ for ͑ZFC͒ for bulk samples of Eu0.9ϪyPr0.1CayBCO (yϭ0 – 0.2). Eu0.9ϪyPr0.1CayBCO (yϭ0 – 0.2). 4508 LI-CHUN TUNG, J. C. CHEN, M. K. WU, AND WEIYAN GUAN PRB 59

FIG. 9. Temperature dependence of resistivity ␳ for Eu0.8ϪyPr0.2CayBCO (yϭ0 – 0.3). perature range between Tc and 290 K. All samples are ‘‘metallic’’ with linear temperature dependence before reaching the superconducting transition temperature. Typical resistivity vs temperature data ␳(T) for Dy0.9ϪyPr0.1CayBa2Cu3O7Ϫz are shown in Fig. 5. Tc is deﬁned as the temperature at which ␳ drops to 50% of its extrapolated normal-state resistivity. The M(T) and ␳(T)ofEu0.9ϪyPr0.1CayBa2Cu3O7Ϫz and

Eu0.8ϪyPr0.2CayBa2Cu3O7Ϫz are shown in Figs. 6–9. 3ϩ FIG. 11. Tc vs ionic radius of R for R0.8ϪyPr0.2CayBCO ͑R Both M(T) and ␳(T)ofEu0.8ϪyPr0.2CayBa2Cu3O7Ϫz ex- hibit that T is raised by Ca doping before y reaches 0.2 and ϭEr, Y, Dy, Gd, Eu, and Nd; yϭ0 – 0.3͒ systems. Tc of c Y Pr Ca BCO were taken from Ref. 22. then decreases with more Ca doping due to the overdoping 0.8 0.2 y effect. There is a distinct maximum (Tc,max)inTc vs Ca Y Pr Ca Ba Cu O ,22 ͑⌬T Ϸ2.5 K at yϭ0.1͒. concentration y. The enhancement of Tc ͑⌬Tc,maxϭTc,max 0.8Ϫy 0.2 y 2 3 7Ϫz c,max For Pr concentration xϭ0.1, the substitution of 5% Ca does ϪTc, yϭ0Ϸ11 K at yϭ0.2, Tc, yϭ0 is the transition tempera- not change T substantially and when y is increased to 0.1, ture Tc without Ca doping͒ is much larger than that in c Tc is decreased by 5.3 K indicative of Tc,max located in the region 0ϽyϽ0.05. Superconducting transition temperatures Tc as a function 3ϩ of R ion radius rR for R1ϪxϪyPrxCayBa2Cu3O7Ϫz are shown in Fig. 10 (xϭ0.1) and Fig. 11 (xϭ0.2), which demonstrate that Tc decreases approximately linearly with in- 3ϩ creasing rR . The solid lines in the ﬁgures are the linear ﬁtting. The observed rare-earth ion size effect on Tc in R1ϪxϪyPrxCayBa2Cu3O7Ϫz systems is similar to that in

3ϩ 3ϩ FIG. 10. Tc vs ionic radius of R for R0.9ϪyPr0.1CayBCO ͑R FIG. 12. Ϫ(dTc /drR ) vs Ca concentration y for ϭY, Dy, Gd, Eu, Sm, and Nd; yϭ0 – 0.2͒ systems. Tc of R1ϪxϪyPrxCayBCO. The lines drawn through the data are guides to Y0.9Pr0.1CayBCO were taken from Ref. 22. the eyes. PRB 59 ION-SIZE EFFECT ON SUPERCONDUCTING... 4509

FIG. 15. Tc vs Ca concentration y for Dy1ϪxϪyPrxCayBCO. Tc are obtained from resistivity measurements with the error bars defined by the transition width. The solid lines drawn through the data represent the fitting curves of Eq. ͑4͒. FIG. 13. Tc vs Ca concentration y for R0.9ϪyPr0.1CayBCO ͑R ϭDy, Gd, Eu, Sm, and Nd͒. The lines drawn through the data are guides to the eyes. 3ϩ concentration y. For xϭ0.1, the ϪdTc /drR decreases with increasing Ca concentration y in the region 0ϽyϽ0.1, but 27–31 R1ϪxPrxBa2Cu3O7Ϫz systems in our previous reports. saturates at about yϭ0.15. These results imply that the rare- The negative slope of the solid lines in Figs. 10 and 11, earth ion size dependence of Tc is weaker in 3ϩ R Pr Ca Ba Cu O for increasing Ca concentration y ϪdTc /drR , are plotted in Fig. 12. For xϭ0.2, the 1ϪxϪy x y 2 3 7Ϫz ϩ 3 and that the trend of rare-earth ion size effect on Tc for ϪdTc /drR decreases monotonically with increasing Ca Ca-doped RBCO is opposite to that for Pr-doped RBCO.27–31 Tc of R1ϪxϪyPrxCayBa2Cu3O7Ϫz for xϭ0.1 and xϭ0.2 as a function of Ca concentration y are shown in Figs. 13 and 14, respectively. In the case of Pr concentration xϭ0.1 ͑Fig. 13͒, the monotonic decrease of Tc with increasing Ca concentration y for samples with a smaller R ion ͑Dy and Gd͒ implies that the Tc,max , possibly, locates in the region 0Ͻy Ͻ0.05. For Pr concentration xϭ0.2 ͑Fig. 14͒,aTc,max is clearly visible in each series. For a sample with a larger R ion radius, Tc,max in Tc vs y curves shifts to higher Ca concentration y, which reveals that a larger number of Ca ions are required to compensate the reduction of the mobile holes. Figure 14 indicates that the enhancement of Tc (⌬Tc,max) becomes larger for sample with a larger R ion radius. In order to make a quantitative analysis for Tc(x,y), we 2 fit our data using the Eq. ͑3͒, TcϭTc0ϪA(␣Ϫ␤xϩy) ϪBx. Typical results of fitting for Dy1ϪxϪyPrxCayBa2Cu3O7Ϫz and Gd1ϪxϪyPrxCayBa2Cu3O7Ϫz are shown in Figs. 15 and 16. The symbols represent the Tc , obtained from resistivity measurements, associated with the vertical bars indicating the transition width. The resultant parameters of fitting for R1ϪxϪyPrxCayBa2Cu3O7Ϫz ͑RϭY, Dy, Gd, Eu, and Nd͒ are shown in Table I. Some parameters, for example, A and ␣, seem scattered with respect to R ion radius. It is inconsistent 3ϩ with the results that Tc(rR ,x,y) itself depends on the R ion

FIG. 14. Tc vs Ca concentration y for R0.8ϪyPr0.2CayBCO ͑R radius linearly for ﬁxed x and y as shown in Figs. 10 and 11. ϭEr, Y, Dy, Gd, Eu, and Nd͒. Tc of Y0.8Pr0.2CayBCO were taken This discrepancy might be due to the fact that Ca ions do not from Ref. 22. The lines drawn through the data are guides to the contribute an equal number of holes to CuO2 planes for eyes. samples with different R ion radius. 4510 LI-CHUN TUNG, J. C. CHEN, M. K. WU, AND WEIYAN GUAN PRB 59

FIG. 16. Tc vs Ca concentration y for Gd1ϪxϪyPrxCayBCO. Tc are obtained from resistivity measurements with the error bars deﬁned by the transition width. The solid lines drawn through the data represent the ﬁtting curves of Eq. ͑4͒.

31 Ϫ1 Guan et al. reported that the Hall number nH ͑cell ͒ of R0.9Ca0.1Ba2Cu3O7Ϫz ͑RϭTm, Ho, Gd, and Nd͒ increases with decreasing R ion radius. In Nd0.9Ca0.1Ba2Cu3O7Ϫz and Ϫ1 Tm0.9Ca0.1Ba2Cu3O7Ϫz systems, nH ͑cell ͒ at 100 K is about 0.5 and 2.0, respectively. For pure RBCO, nH at 100 K 4,25 is about 0.4 in NdBa2Cu3O7Ϫz and 0.6 in YBa2Cu3O7Ϫz . It should be noticed that the difference of nH between FIG. 17. The fitting parameters of the Eq. ͑4͒, Tc0 ͑K͒, B ͑K͒, ␤, Nd0.9Ca0.1Ba2Cu3O7Ϫz and Tm0.9Ca0.1Ba2Cu3O7Ϫz is much 2 3ϩ ␣/␤, and A␤ ͑K͔͒ vs ionic radius of R for R1ϪxϪyPrxCayBCO larger ͑about 7 times͒ than that between NdBa2Cu3O7Ϫz and ͑RϭY, DY, Gd, Eu, and Nd͒ systems: The solid lines represent the YBa2Cu3O7Ϫz . It suggests that Ca ions contribute much linear fitting. more mobile holes to CuO2 sheets in Tm0.9Ca0.1Ba2Cu3O7Ϫz than in Nd0.9Ca0.1Ba2Cu3O7Ϫz . On the other hand, the re- established that all parameters, T , A␤2, B, ␣/␤, and ␤, ported n is about 0.3 in Nd Pr Ba Cu O ͑Ref. 30͒ and c0 H 0.8 0.2 2 3 7Ϫz depend on the R ion radius linearly. 0.4 in Y Pr Ba Cu O .43 The difference of n between 0.8 0.2 2 3 7Ϫz H The parameter B increases with increasing R ion radius, them is also as small as that between NdBa Cu O and 2 3 7Ϫz indicating a stronger pair-breaking effect due to Pr doping YBa Cu O . We suggest that the Eq. 3 should be modi- 2 3 7Ϫz ͑ ͒ for a sample with larger R ion radius, which is consist- fied to following form: ent with the R ion-size effect observed in 27–31 2 2 R1ϪxPrxBa2Cu3O7Ϫz . Tc͑x,y͒ϭTc0ϪA␤ ͑␣/␤Ϫxϩy/␤͒ ϪBx, ͑4͒ Tc0 increases slightly with increasing R ion radius. This where A␤2(␣/␤Ϫxϩy/␤)2 is equivalent to A(␣Ϫ␤x result is in accordance with the earlier results for pure 2 1 ϩy) in Eq. ͑3͒, Ϫ␣/␤ is an optimal hole concentration, and RBa2Cu3O7Ϫz . ␣/␤ is positive and decreases with in- 1/␤ is the number of holes contributed by a Ca ion to CuO2 creasing R ion radius, indicating that the pure and fully oxy- 2 planes. The parameters in Eq. ͑4͒, Tc0 , B, ␤, ␣/␤, and A␤ , genated RBa2Cu3O7Ϫz are all in the overdoped region. as a function of R ion radius are shown in Fig. 17. Our data ␤ increases with increasing R ion radius, indicating that

2 TABLE I. The ﬁtting parameters of equation ͑by the least-squares method͒: TcϭTc0ϪA(␣Ϫ␤xϩy)ϪBxϭTc0ϪA␤ (␣/␤Ϫxϩy/␤) ϪBx for R1ϪxϪyPrxCayBa2Cu3O7Ϫ␦.

2 R ␣␤A͑K͒B͑K͒Tc0͑K͒A␤xcϭ␣/␤ Y 0.11 0.89 256 93.8 96.4 203 0.124 Dy 0.14 1.18 172 115 97.0 238 0.119 Gd 0.175 1.90 141 162 99.6 509 0.092 Eu 0.089 1.38 325 132 94.3 619 0.065 Nd 0.18 2.10 164 261 101 723 0.086 PRB 59 ION-SIZE EFFECT ON SUPERCONDUCTING... 4511

3ϩ Finally, an overall Tc as a function of rR , x, and y in R1ϪxϪyPrxCayBa2Cu3O7Ϫz is proposed. All parameters in 2 Eq. ͑4͒, Tc0 , A␤ , B, ␣/␤, and ␤, depend on the R ion radius linearly ͑see Fig. 17͒:

3ϩ 3ϩ 3ϩ Tc͑rR ,x,y͒ϭ͑55ϩ0.46rR ͒Ϫ͑56rR Ϫ4800͓͒0.47Ϫ3.9 Ϫ3 3ϩ 3ϩ 2 ϫ10 rR Ϫxϩy/͑0.11rR Ϫ8.9͔͒ 3ϩ 3ϩ ϩ͑17rR Ϫ1400͒x, for rR у84 pm. ͑5͒

3ϩ In conclusion, we observed a rare-earth ion-size effect on FIG. 18. Hall number nH at 150 K vs 1/(0.11r Ϫ8.9) for R T in R Pr Ca Ba Cu O ͑RϭEr, Dy, Gd, Eu, Sm, R0.9Ca0.1BCO systems. ͑RϭTm, Ho, Gd, and Nd͒. c 1ϪxϪy x y 2 3 7Ϫz and Nd͒ systems which is similar with that in R Pr Ba Cu O systems in our previous reports.27–31 the number of holes contributed by Ca ions decreases with 1Ϫx x 2 3 7Ϫz For fixed Pr and Ca concentration ͑fixed x and y͒, Tc is increasing R ion radius. ␤ could be fitted by a linear relation, 3ϩ 3ϩ linearly dependent on rare-earth ion radius rR . We pro- ␤ϭϪ8.9ϩ0.11rR . 3ϩ 31 Ϫ1 posed an empirical formula for Tc (rR ,x,y) to fit our ex- Guan et al. reported that the Hall number nH ͑cell ͒ of perimental data. All fitting parameters in this formula, Tc0 , R0.9Ca0.1Ba2Cu3O7Ϫz ͑RϭTm, Ho, Gd, and Nd͒ increases 2 3ϩ 2ϩ 2 B, ␤, ␣/␤, and A␤ , are rare-earth ion-size dependent. linearly with respect to (rR ϪrCa ) . Especially noteworthy are that 1/␤ is the number of holes contributed by a Ca ion to CuO planes and it should be related to mobile holes, n .As 2 H ACKNOWLEDGMENTS illustrated in Fig. 18, the measured nH ͑Ref. 31͒ is, indeed, 3ϩ proportional to 1/(0.11rR Ϫ8.9). It strongly supports the The authors wish to acknowledge the assistance of S. R. validity of Eq. ͑4͒. Sheen and H. F. Lai with the measurements. We also thank The parameter A␤2 increases with increasing R ion ra- D. H. Chen for the analysis of the x-ray data and S. H. Cheng dius, suggesting a sharper carrier concentration dependence for his useful discussion. This study was supported by Na- of Tc for sample with larger R ion radius. tional Science Council, R.O.C.

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