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Defect-induced superconductivity in PrBa2Cu3O7
Physica C 314 Ž1999. 172–182
Defect-induced superconductivity in PrBa 2 Cu 3 O 7 Michihito Muroi ) , Robert Street Special Research Centre for AdÕanced Mineral and Materials Processing, Department of Physics, The UniÕersity of Western Australia, Nedlands, WA 6907, Australia Received 18 November 1998; received in revised form 11 December 1998; accepted 25 January 1999
Abstract The appearance of superconductivity in some PrBa 2 Cu 3 O y Ž y ; 7. single crystals and thin films can be accounted for on the assumption of the presence of disorder in the BarPr site occupancy. It is argued that Ba ions occupying the Pr site and Pr ions occupying the Ba site both weaken Pr–O hybridisation through local structural changes and lower the Madelung potential at the Cu site relative to that at the Pr site, thus favouring the CuIII oxidation state over the Pr IV oxidation state. Bulk superconductivity shows up when local superconducting regions, created near the defects, percolate through the sample. It is concluded that stoichiometric, defect-free PrBa 2 Cu 3 O 7 is insulating. q 1999 Published by Elsevier Science B.V. All rights reserved. Keywords: PrBa 2 Cu 3 O 7 ; Insulator–superconductor transition; Pr–O hybridisation; Substitution effects
1. Introduction Among the compounds of the type RBa 2 Cu 3 O 7 ŽR123., where R is Y or a rare-earth element except Ce, Pm and Tb, Pr123 is unique in that it is an insulator and does not show superconductivity while all the other R123s are superconductors with Tc s of about 90 K. A number of models have been proposed to explain this puzzling fact w1–10x. 1 Earlier explanations include ‘hole filling’ by Pr ions w1,2x, assumed to have a valence greater than 3 q , and ‘magnetic pair breaking’ by localised Pr 4f moments
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Corresponding author. Fax: q61-8-9380-1014; E-mail: [email protected] 1 For an extensive review on earlier studies on PrBa 2 Cu 3 O y and ŽR 1y x Pr x .Ba 2 Cu 3 O y , see Ref. w11x.
w3x. The hole filling model, however, was found to be inconsistent with the results of various spectroscopic studies w12–14x, which showed a valence close to 3 q for Pr; structural considerations w4x also pointed to trivalent Pr. The pair breaking model was questioned by the facts that other rare-earths such as Gd and Sm have larger 4f moments than Pr but do not suppress superconductivity, and that Pr123 is not only nonsuperconducting but also insulating. As a variant of the hole filling model, charge redistribution between the CuO 2 planes and the CuO chain layers has later been suggested w5x. However, an electron-energy-loss spectroscopy ŽEELS. study w14x shows that the density of unoccupied planar O 2p states remains unchanged with increasing x in Y1y x Pr x Ba 2 Cu 3 O 7 Ž0 F x F 1., while optical conductivity measurements on detwinned Y123 and Pr123 single crystals w15x indicate that the hole concentration in the CuO chain layer is similar in the
0921-4534r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 1 4 6 - X
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two compounds; both demonstrate clearly that the number of holes in the CuO 2 –R–CuO 2 block is little affected by the presence of Pr ions. Another explanation, which on the main point is most widely accepted, is the localisation of holes by Pr ions. Tang et al. w6x have argued that the strong Pr–O hybridisation, which results from the small energy difference between the Pr 3q:4f level and the Fermi energy EF , transforms the itinerant holes into small polarons, thereby suppressing superconductivity. Fehrenbacher and Rice ŽFR. w7x have shown through Hartree calculations that in R123, there are only two stable electronic configurations, one in which all the in-plane holes are in the CuIII oxidation state ŽCuIII state hereafter., i.e., in the hybridised Cu 3d–O 2p s orbitals, and the other in which all the in-plane holes are in the RIV oxidation state ŽRIV state hereafter., i.e., in the hybridised R 4f–O 2p p orbitals; that the energy level of the Pr 4f orbitals, combined with the local ionic arrangement of the 123 structure, favours the latter state to be realised in Pr123; and that the total probability of the 4f 1 Pr configuration is 0.15– 0.2 and holes spend most of their time on ligand O ions. This model ŽFR model. consistently explains a number of experimental observations, including the absence of a Tc between 0 and ; 90 K in the R123 series. Despite its success, the FR model does not seem to have been fully accepted. Criticisms on the FR model include the following: Ž1. the conclusion of the FR model that there are only two stable electronic configurations in R123 is inconsistent with the continuous decrease in Tc with increasing Pr concentration in Y1y x Pr x Ba 2 Cu 3 O 7 ŽYPr123. w8,9x; Ž2. treating the Pr–O hybridisation as a purely local phenomenon, the FR model fails to account for the R dependence of Tc suppression in RPr123 w8,9x; and Ž3. some Pr123 single crystals prepared by the travelling-solvent floating-zone ŽTSFZ. method w16–18x and epitaxial thin films w10,19x show bulk w16–19x or granular w10x superconductivity below 80–90 K, which implies that the insulating behaviour of Pr123 is not intrinsic but due to defects w10,19x. The first criticism depends on the assumption that the materials concerned are homogeneous, an assumption that has never been substantiated on rigorous grounds. In fact, a wide range of experimental observations on YPr123, including the variation of
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Tc with Pr concentration, has been consistently accounted for in terms of a percolation model w20,21x, in which coexistence of superconducting and insulating phases on a microscopic scale is assumed; this assumption is fully consistent with a 170 Yb Mossbauer study on Yb-doped YPr123 w22x, which ¨ provides conclusive evidence that Y1y x Pr x Ba 2 Cu 3 O 7 is inhomogeneous except for the end compounds Ž x s 0 and 1.. The second criticism also seems inadequate. The effects of substitution, not only on the R site but also on the Ba site in RPr123, have also successfully been explained within the framework of the percolation model w23–25x. The R dependence of Tc is compatible with the FR model. In addition, it is not evident whether the effect of Pr–O hybridisation is appropriately described by a band picture; the presence of distinct Pr–O bond lengths in Pr123 detected by X-ray absorption fine structure ŽXAFS. measurements w26x, as well as the Mossbauer results men¨ tioned above w22x, suggests that Pr–O hybridisation and the resultant hole localisation are local phenomena. Furthermore, the models proposed in Refs. w8,9x themselves seem to have the following major difficulties in explaining the R dependence of Tc . In Ref. w8x, the rate of Tc suppression is related with the R 4f energy level, which is expected to vary nonmonotonically, reflecting the nonmonotonic variation of the ionisation potential of R Žsee Fig. 2c.. The rate of Tc suppression, however, increases monotonically with decreasing atomic number of R, suggesting that the R dependence has little to do with the R 4f energy level but stems from the R ionic size. The argument in Ref. w9x depends on the assumption that substitutions with smaller ions result in weakening of Pr–O hybridisation. This assumption is valid for Sr-site substitutions but is highly unreasonable for R-site substitutions, as we have shown in previous papers w24,25x and substantiate further in this paper. Regarding the third criticism, an ‘oxygen’ model has been proposed w10x. This model ascribes the lack of superconductivity in polycrystalline Pr123 samples to Ba-site Pr impurities, which break Cooper pairs postulated to reside in the Cu–O chain layers and not in the CuO 2 planes. In a previous paper w24x, we have already shown that this model is highly unreasonable in many respects, and suggested that the local superconductivity observed in Pr123 thin
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films w10x could be due to defects such as Ba ions occupying the Pr site and excess O ions in the Cu–O chain layer. In this paper, we extend the discussions in Ref. w24x Ži. by comparing various sample preparation techniques from thermodynamical viewpoints, and Žii. by examining the crystal structure of the ‘superconducting Pr123’ and its effects on the electronic structure more in detail.
2. Comparison of sample preparation methods The major premise of our discussions is that mutual substitution between the Ba and Pr sites is much more significant in the Pr123 samples that exhibit superconductivity than in ‘normal’ insulating Pr123 samples. Although the site occupancies of the ‘superconducting Pr123’ have not been determined and the reverse has been postulated w10,19x, there are strong indications that support the above premise. First, the c-lattice constants Ž c 0 . of superconducting Pr123 crystals are longer than those of insulating Pr123. The superconducting Pr123 crystals have been subjected to annealing in oxygen at lower temperatures Ž600 and 4008C. for a long time Ž100 h. w18x, and insufficient oxidation is an unlikely reason for the long c 0 . Since c 0 decreases with increasing x in PrBa 2y x Pr x Cu 3 O 7 w27x, as expected for a substitution with a smaller ion, the most likely explanation of the expanded c 0 is the occupation of Ba ions on the Pr site. Similar elongation of c 0 is observed in Y1y x Ca x Ba 2 Cu 3 O 7 as x increases w28x and in YBa 2 Cu 3 O 7 thin films as disorder in the Y and Ba site occupancy increases with decreasing substrate temperature w29x. Second, the TSFZ method yields superconducting Pr123 crystals only when the composition of the starting material is very rich in Ba w18x. In R123 with a larger R, including Pr123, R ions readily occupy the Ba site w12x, but the reverse is practically unknown in bulk polycrystalline samples, which may be accounted for as follows: since the Madelung potential at a cation site is always negative, substitution with a lower Žhigher. valence cation increases Ždecreases. the electrostatic energy of the crystal. Thus, in the substitution of Ba for Pr, the strain energy associated with the ionic size mismatch and
the electrostatic energy both increase, while in the substitution of Pr for Ba, the cost in strain energy is partly compensated by the gain in electrostatic energy. Moreover, in the latter case, the cost in strain energy could be further reduced and the gain in electrostatic energy could be further enhanced by introducing extra O ions in the adjacent Cu–O chain layers. A possible role of the excess Ba, then, is to increase the probability of the nucleation of Ba-rich Pr123, which is much less stable than Pr-rich Pr123. Third, in epitaxial-thin-film deposition and the TSFZ method, the techniques used to prepare the superconducting Pr123, crystals grow under nonequilibrium conditions in the presence of seed crystals. Epitaxial thin films are usually grown at a substrate temperature ŽTs . in the range 550–7508C, a few hundred degrees lower than the temperature required to form the 123 phase by conventional solid state reaction Ž900–9508C.. Under such conditions, the 123 phase is probably not the most stable phase. The 123 phase nevertheless forms, owing to the presence of seed crystals which favours the nucleation of the 123 phase over that of other competing phases such as BaCuO 2 and Pr2 BaCuO5 ; i.e., the 123 phase is kinetically, not thermodynamically, stabilised. In the ideal 123 structure, the R and Ba ions arrange in the ordered sequence –R–Ba–Ba–R–Ba–Ba– . . . along the c-axis. This means that to form the perfect 123 ˚ structure, a diffusion length of at least about 6 A Žhalf the c-lattice constant. is necessary for R ions. As Ts decreases, the diffusion length naturally decreases, and a certain degree of mixing between the R and Ba sites becomes inevitable. Blackstead et al. w10x claim that the use of a lower Ts minimises Pr occupation on the Ba site. This claim would be valid if the perfect 123 phase were formed before the constituent atoms arrive at the substrate. In reality, the atoms must rearrange themselves to form the 123 structure after arriving at the substrate. The lower the Ts , the more mixing between the R and Ba sites, which has been demonstrated clearly by a systematic study of Y123 thin films deposited at various substrate temperatures w29x. ŽIn view of the smaller ionic size difference between Pr and Ba than between Y and Ba, the mixing of R and Ba ions will occur still more easily in Pr123.. Bulk single crystal growth, on the other hand, takes place at a sufficiently high temperature near the melting point. The process is
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nonetheless nonequilibrium because crystal growth from liquid always involves a certain degree of supercooling, and the phaseŽs. formed is Žare. again determined not only by thermodynamics but also by kinetics. During crystal growth by the TSFZ method w16–18x, a large area of the molten zone, thin in the scan direction, is in contact with the seed crystals, thus favouring the nucleation of the 123 phase. It is possible then that the 123 structure is formed even when a local composition of the melt happens to be favourable for the formation of other competing phases, with the natural consequence of wrong site occupancies. ŽFluctuation in local composition on a microscopic scale, inevitably present in a multi-component liquid, will be particularly large when the relevant compound melts incongruently as is the case with R123.. Fourth, carefully prepared Pr123 polycrystalline samples show consistent structural, electrical and magnetic properties w4,30,31x, while the single crystals prepared by the TSFZ method exhibit large scattering in both structural and superconducting properties even within a single sample w17,18x. The fact that the crystal structure of the insulating portion of the TSFZ crystals is similar to that of polycrystalline samples w17,18x strongly suggests that it is the superconducting portion of the TSFZ crystals that is anomalous and the superconductivity is extrinsic in origin. It is true that R ions tend to occupy the Ba site in R123 with a larger R w12,32,33x, and it was, in fact, claimed that in the synthesis of polycrystalline Pr123 samples, the stoichiometric cation ratio ŽPr:Ba:Cus 1:2:3. of the starting material results in a mixture of BaCuO 2 and Pr1qx Ba 2yx Cu 3 O 7 w32,33x; later studies w4,30,31x have demonstrated, however, that stoichiometric Pr123 with no detectable Pr on the Ba site can be prepared by optimising the synthesis conditions. Note that in the case of polycrystalline samples, the level of Ba-site occupation by Pr can be estimated from the fraction of second phaseŽs. present; this is difficult for single crystals, since the starting composition is generally nonstoichiometric. Not being a one-shot process, solid state reaction, in principle, guarantees the thermodynamically most stable state to be realised in the end. The problem of long diffusion lengths required for phase formation, an inevitable consequence of large inhomogeneity in the starting mixture, can be overcome by extending
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the reaction time, by repeating firing and regrinding many times, and by choosing the appropriate synthesis conditions, such as temperature and oxygen partial pressure. Despite the ‘worship’ of single crystals widespread in the literature, we do not find any reason why polycrystalline samples are inherently more defected than single crystals or epitaxial thin films. It is inappropriate to justify the assumption that Pr123 polycrystalline samples contain more Basite Pr ions than epitaxial thin films w10,19x simply because significant Pr ions are present on the Ba site in some polycrystalline samples. ŽSmall amounts of Pr ions on the Ba site, if ever present, cannot explain the insulating behaviour of Pr123 anyway; a recent study on YBa 2y x R x Cu 3 O y ŽR s Pr,La. w34x shows that the decreases in Tc with Pr doping and La doping are similar and that superconductivity persists up to x ; 0.6..
3. Electronic structure of R123 and effects of Pr r Ba site disorder in Pr123 Before discussing the effect of disorder in the PrrBa site occupancy, we reexamine the electronic structure of R123 in terms of the FR model w7x. According to the model, the relative stability of the CuIII state Žsuperconducting solution. and the RIV state Žnonsuperconducting solution. is mainly determined by two factors: t pf , the hopping integral between R 4f zŽ x 2yy 2 . orbitals and O 2p p orbitals with the f symmetry ŽR 4f and O 2p p orbitals hereafter., and D PF , defined as D PF s ´ P y ´ F , where ´ P and ´ F are the energies of the localised CuIII and Pr IV states, respectively. A larger Žsmaller. t pf and a larger Žsmaller. D PF favour the RIV ŽCuIII . state. Transition between the two states is a crossover, and not a gradual change in electronic structure, as is incorrectly assumed in many theoretical considerations in the literature. We consider three parameters that are expected to control t pf and D PF : the R–O bond length Ž d R – O ., the O–R–O bond angle Ž u R . Žsee Fig. 1b. and D E h , defined as D E h s I3 ŽCu. q V M ŽCu.4 y I4ŽR. q VM ŽR.4 , where I k ŽX. is the k th ionisation potential of element X and VM ŽX. is the Madelung potential at
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Fig. 1. Ža. Crystal structure of Y123. The ions on the x s a 0r2 plane are drawn with bold lines, while the ions on the x s 0 Ž a0 . plane are drawn with thin lines. Structural data from Ref. w31x. Žb. Local ionic arrangement around an R ion in R123. Filled and open circles indicate Cu and O ions, respectively. Žc. Movement of O ions expected for a substitution of a larger divalent cation for R.
the X site. 2 d R – O and u R will determine t pf : the smaller the d R – O and the closer the u R to 109.48 Žthe value of u R for a perfect cube made of the eight O ions surrounding an R ion., the more overlap between the R 4f and O 2p p orbitals and hence, a larger t pf . We emphasise here that d R – O and u R should be treated on an equal footing, since the R 4f orbitals are directional. D E h represents the energy difference between the Cu and R sites in the ionic limit w24,25x and is expected to be a good measure of D PF . In Fig. 2a–c, the three parameters are plotted as functions of the R ionic radius Ž r R . for a series of R123 compounds; structural data were taken from Ref. w31x. It can be seen that as r R increases, d R – O increases and u R decreases away from 109.48. However, the data points for Pr123 are anomalous: d R – O is smaller and u R is larger than expected from the trends. This is a clear indication of a spontaneous lattice distortion that has occurred in Pr123 to achieve
2 In the calculation of V M , we assigned the formal ionic charges to all the sites except the O site in the Cu–O chain layer Žor NbO 2 layer in the case of NbBa 2 PrCu 2 O 8 .. The charge on that O site was adjusted to ensure the charge neutrality of the crystal. The error associated with this arbitrariness in charge assignment is negligibly small; e.g., the difference in DVR for Y123 calculated with three different charge assignments in the Cu–O chain layer, q3 to Cu and y2 to O, q2 to Cu and y1 to O, and q1 to Cu and 0 to O, is less than 0.05 eV, which is smaller than the size of the symbols used for the plots in Fig. 2f.
a better overlap between the Pr 4f and O 2p orbitals. The data presented in Fig. 2a and b thus indicate that the crystal structure of Pr123 is not ideal for Pr–O hybridisation and that the Pr–O hybridisation in Pr123 is enhanced at the cost of increased strain energy. The variation of D E h with r R ŽFig. 2c., on the other hand, is not monotonic, reflecting the nonmonotonic variation of I4 ŽR. with atomic number. Among all the R123s, only Pr123 has a positive D E h Ž0.77 eV., which is favourable for the Pr IV state to be realised w7x. The unique insulating behaviour of Pr123 is thus reasonably explained as resulting from a crossover from the CuIII state to the Pr IV state, which crossover must take place by going from Nd123 to Pr123. However, the difference in D E h between Pr123 Ž0.77 eV. and Nd 123 Žy0.64 eV. is relatively small Žthe difference would be still smaller if there were no spontaneous lattice distortion in Pr123, which increases VM ŽCu. –V M ŽR. and hence, D E h ., and judging from the overall trends in Fig. 2a and b, the crystal structure of Nd123 is probably more suitable for R–O hybridisation than that of Pr123. In fact, the Neel ´ temperature for Nd-sublattice ordering in Nd123 depends strongly on the oxygen content w37x, suggesting that the Nd–O hybridisation is relatively strong. It appears that Nd123 and Pr123 are located very close to the crossover point between the CuIII and RIV states. It might then be possible to induce transitions between the superconducting Žmetallic. and insulating states by applying external stresses. A metal Žsuperconductor. –insu-
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Fig. 2. Ža. Variations of d R – O , u R and D Eh with R ionic radius Ž r R . in R123. Structural data taken from Ref. w31x. Žd–f. Variations of d R – O , u R and D E h with doping level Ž x . in Y1yx Ca x Ba 2 Cu 3 O 7 Ždata from Ref. w28x., Y0.4 Pr0.6 Ba 2yx Sr x Cu 3 O 7 Ždata from Ref. w35x. and NbBa 2y x Sr x PrCu 2 O 8 Ždata from Ref. w36x..
lator transition might occur in Nd123 under uniaxial pressure along the c-axis, which would shift all the three parameters to the directions favourable for the Nd IV state; similarly, an insulator–metal Žsupercon-
ductor. transition might be induced in Pr123 by applying biaxial pressure in the ab-plane. Because of the coupling between the electronic state and the crystal structure as discussed above, these transitions
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would be first-order ones, accompanied by discontinuous changes in structural parameters such as c 0 , d R – O and u R . We now discuss the effect of Ba ions incorporated in the Pr site of Pr123. Since structural data for Pr123 having Ba ions on the Pr site are not available, we have calculated d R – O , u R and D E h for Y1yx Ca x Ba 2 Cu 3 O 7 Ž x s 0, 0.1 and 0.2. w28x, which are plotted as functions of x in Fig. 2d–f. R ions are substituted by larger divalent cations in both cases, and changes in the three parameters with increasing doping level will be qualitatively similar. It can be seen that as the Ca concentration Ž x . increases, d R – O increases, u R decreases away from 109.48, and D E h decreases. The reasons for these changes, all favourable for the CuIII state, are twofold: geometric and electrostatic. As can be seen in Fig. 1a, where the crystal structure of Y123 is depicted, the arrangement of the planar O ions in the 123 structure is largely constrained by their close contact with the neighbouring R and Ba ions. Incorporation of a larger Ca2q ion ˚ . in place of a smaller Y 3q ion Ž r Y s Ž rCa s 1.12 A ˚ . will naturally expand the surrounding O 8 1.019 A cage, resulting in an increase in r R – O . The expansion of the O 8 cage will not be isotropic because the Cu–O bonds, having a significant covalent character, are stiffer and more reluctant to expand than the other bonds. As a consequence, the expansion along the c-axis dominates that in the ab-plane ŽFig. 1c., resulting in a decrease in u R . As the Cu–O and R–O bond lengths increase, VM ŽCu. and VM ŽR. both increase, since the contribution from the negatively charged O 2y ions, which dominates VM , decreases with increasing cation–anion distance. The increase in V M ŽCu., however, is smaller than that in V M ŽR. because of the difference in the oxygen coordination number ŽCN. ŽCN s 5 for Cu and CN s 8 for R.. Thus, V M ŽCu. y V M ŽR. and hence D Eh decrease with increasing x. The above effects, which are purely geometric in origin, are accentuated by the lower valence of Ca as compared with Y. In the 123 structure, the separation between two adjacent CuO 2 planes will be determined by the balance of the Coulomb repulsion between negatively charged CuO 2 planes Žnet charge of approximately y2. and the Coulomb attraction between the CuO 2 planes and positively charged R
layers Žnet charge of 3 y x .. As x increases, the former becomes progressively more dominant, and the separation between adjacent CuO 2 planes increases. d R – O increases and u R decreases, as a result. As the valence of the R site decreases with Ca doping, V M ŽCu. and VM ŽR. both decrease, but the decrease is greater for VM ŽCu. than for V M ŽR. because the nearest-neighbour R–Cu distance is smaller than the nearest-neighbour R–R distance. Thus, V M ŽCu. –V M ŽR. and hence, D E h decrease. The changes in d R – O , u R and D E h brought about by the Ba substitution for Pr in Pr123 will be much larger than those effected by the Ca substitution for Y in Y123 examined above, since the difference in ionic ˚ . and Pr Ž1.126 A˚ . is much radii between Ba Ž1.420 A ˚ . and Y Ž1.019 larger than that between Ca Ž1.120 A ˚ .. A To investigate the effect of Pr substitution for Ba in Pr123, we have calculated d R – O , u R and D E h for Y0.4 Pr 0.6 Ba 2y x Sr x Cu 3 O 7 Ž x s 0, 1. w35x and NbBa 2y x Sr x PrCu 2 O 8 Ž x s 0, 1, 2. w36x in which Ba ions are replaced by smaller Sr ions; NbBa 2 PrCu 2 O 8 is isostructural with Pr123 except that the Cu–O chain layers in Pr123 are replaced by NbO 2 layers. The results are plotted in Fig. 2d–f. The graphs show clear trends: d R – O increases while u R and D Eh decrease with increasing x. These changes are very similar to those observed in Y1y x Ca x Ba 2 Cu 3 O 7 , showing that in R123, the Ba-site substitution with a smaller cation is equivalent to the R-site substitution with a larger cation; in other words, the effects of ‘chemical pressure’ on the three parameters are opposite for the Ba-site and R-site substitutions. This is quite natural in view of the 123 structure ŽFig. 1a.. The R site is located in between two adjacent CuO 2 planes, and a larger cation incorporated in the R site pushes them away from the R site towards the Cu–O chain layers. The Ba site, on the other hand, is located between the CuO 2 plane and the nearestneighbour Cu–O chain layer, and a larger cation incorporated in the Ba site pushes the CuO 2 plane towards the R site. In the above calculation of D E h , the formal valence of q2 was assigned to the BarSr site, and the effect of the higher valence of Pr Žq3. was not taken into account. ŽIn the defected Pr123 we are considering, Ba2q ions are replaced by Pr 3q ions.. To take it into account, we have repeated calcula-
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tions of D Eh by assigning an ionic charge of 2 q xr2 to the BarSr site. The results, indicated by error bars in Fig. 2f, show that D E h is decreased further with this charge assignment. However, the additional decrease in D Eh is small as compared with the overall decrease with increasing x, suggesting that structural changes due to the substitution are more important in reducing D E h than the valence difference. It is thus likely that the incorporation of Pr in the Ba site in Pr123 changes all the three parameters to the directions unfavourable for the Pr–O hybridisation and favourable for the CuIII state. This is consistent with the experimental observation that the Neel ´ temperature for the Pr sublattice ordering decreases with increasing x in PrŽBa 2y x Pr.Cu 3 O 7 w27x. In the above considerations, we used information on the average crystal structure and assigned the same fractional ionic charge to the site containing substituted ions, regarding the crystal as homogeneous. In real crystals, however, the distribution of defects ŽPr-site Ba and Ba-site Pr. is not uniform but discrete and random. Accordingly, the three parameters, d R – O , u R and D E h , will vary in space, reflecting the statistical distribution of the defects. It is most likely that for a low defect density Ž a ., noticeable changes in the three parameters are confined in small local regions extending possibly no more than a few unit cells from the defects. ŽHere and in the following discussion, we define the defect density as a in ŽPr1y a Ba a .ŽBa 2y a Pra .Cu 3 O 7 , i.e., the density of Ba ŽPr. ions on the Pr ŽBa. site.. These local regions, in which the CuIII state is strongly favoured, will become superconducting if the CuO 2 planes within them are optimally doped. The condition of optimal doping, however, may not be satisfied because of the local charge imbalance Ža Ba-site Pr ion provides an extra electron and a Pr-site Ba ion an extra hole.. The extra electronrhole will be bound to the defect through Coulomb interaction, possibly inhibiting superconductivity. In fact, the Tc of Y123 thin films decreases with increasing disorder in the YrBa site occupancy w29x, suggesting that the order parameter is suppressed near the defects. As a increases, the fraction of local regions in which the CuIII state is favoured progressively increases. This increase will be faster than that of a , since the regions between the defects are also subject to structural changes that are favourable for the CuIII state as
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the separation between defects decreases. Superconductivity will then be set up in those regions in which the CuIII state is favoured and at the same time, no defects are present over a distance greater than the in-plane coherence length Ž j a b .. At a critical defect density Ž a c ., local superconducting regions percolate through the sample, and bulk superconductivity shows up. This transition at a c will be of first order because of the coupling between the electronic state and the crystal structure in Pr123. As a c is approached from below, it becomes energetically favourable to drive essentially all the holes into the CuIII state, thereby releasing the strain energy stored in part of the crystal to stabilise the Pr IV state. The transition at a c will thus accompany discontinuous changes in Tc and structural parameters including c 0 , as schematically depicted in Fig. 3. When a is close to a c , the transition may possibly be induced by external pressure: a crystal with a just above a c would show a metal Žsuperconductor. –insulator transition under uniaxial pressure along the c-axis, whereas a crystal with a just below a c would exhibit an insulator–metal Žsuperconductor. transi-
Fig. 3. Variations of the c-lattice constant Ž c 0 . and Tc with defect density in R123 ŽR sY, Pr.. ŽThe diagrams are schematic.. The defect density is defined as a in ŽR 1y a Ba a .ŽBa 2y a R a .Cu 3 O 7 .
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tion under in-plane biaxial pressure. These transitions would be similar to those predicted to occur in Nd123 and Pr123. An increase in a beyond a c will result in a decrease in Tc because of the increase in the fraction of nonsuperconducting regions created in the immediate vicinity of the defects; the behaviour of Pr123 for a ) a c will be qualitatively similar to that of Y123 ŽFig. 3.. Rigorous derivation of a c is difficult, but a rough estimate may be obtained by equating the average separation between defects, ˚ ., Ž2 x .y1 r2 a 0 Ž a 0 s in-plane lattice constant ; 3.9 A ˚ we obtain a c s 0.053. with j a b . For j a b s 12 A, This seems to be a reasonable level of PrrBa site disorder in view of the facts that an Y123 thin film deposited at ; 6108C has a similar value of a w29x and that local superconductivity was observed in a Pr123 thin film deposited at a slightly high temperature, 6508C w10x. We have so far assumed that the Žaverage. hole concentration in the CuO 2 plane remains optimal regardless of a . For higher values of a , however, the CuO 2 planes are most likely to be underdoped, since the superconducting Pr123 crystals have slightly Pr-rich compositions ŽPrrBa; 0.56. w18x and, furthermore, R ions occupying the Ba site tend to disrupt the Cu–O chains, thereby reducing the hole concentration in the CuO 2 plane w25x. This explains a large positive pressure effect on Tc Žup to 7.4 KrGPa. observed in Pr123 crystals prepared by the TSFZ method w17,38x; it is known that in materials having charge-reservoir layers, such as R123, the hole concentration in general increases under pressure and Tc shows a marked increase if the material is underdoped in the ambient pressure w39x. For example, large, positive pressure coefficients of Tc , in the range 7–10 KrGPa, have been reported for oxygen-deficient R123 ŽR s Y, Eu. w40–42x. It has been reported in Ref. w38x that Tc of a Pr123 crystal reaches 105 K under a hydrostatic pressure of 9.3 GPa. This value is much larger than that of Y123 Ž; 92 K. and has been considered anomalous w38x. We attribute the observed high Tc to the following two factors. First, the higher Tc of Pr123, as compared with that of Y123, is consistent qualitatively with the well-known trend that in the R123 series, the maximum Tc attainable ŽTc,max . tends to increase with increasing R ionic size, e.g., 90 K for Yb123 to 96 K for Nd123 w31x. Thus, a value of Tc near, if not
higher than, 100 K is expected for optimally doped Pr123. Second, mutual substitution between the Ba and Pr sites, likely to be present in superconducting Pr123 crystals, could affect Tc,max by modifying DVM Žs V M ŽO. y V M ŽCu.., where V M ŽO. and VM ŽCu., respectively, are the Madelung potentials at the in-plane O and Cu sites; as we have argued in Refs. w43,44x, DV M is one of the major factors controlling Tc,max with a smaller DVM corresponding to a higher Tc,max . To investigate this effect, we have calculated DV M for Pr123 Žthe structural data in Ref. w31x were used. for the following two types of charge assignment: Ži. the formal charge assignment, i.e., q3 to the Pr site and q2 to the Ba site, and Žii. q2.95 to the Pr site and q2.025 to the Ba site Žto simulate Pr123 with a s 0.05.. The results are 47.73 eV for case Ži. and 47.60 eV for case Žii.. ŽThe lower DVM for case Žii. is ascribed to the lower valence of the Pr site, which is favourable for a hole on the O site, since the Pr site is closer to the CuO 2 plane than the Ba site.. A higher Tc,max is thus expected for superconducting Pr123 containing defects. Rigorous justification of the above argument requires accurate structural data, including the atomic positions and site occupancies, for superconducting Pr123, and we just point out the following fact to support it; all the materials having crystal structures similar to that of R123 and high Tc s exceeding 100 K, e.g., TlBa 2 CaCu 2 O 7 , HgBa 2 CaCu 2 O6 and ŽPb,Tl.Sr2ŽCa,Y.Cu 2 O 7 , have divalent cations ŽCa2q . in place of R3q ions. Lowering the cation valence on the site closest to the CuO 2 plane is an effective way of increasing Tc,max w43x. ŽThis does not contradict the decrease in Tc with increasing Ca content, x, in Y1y x Ca x Ba 2 Cu 3 O y ; Tc,max is realised only when the whole CuO 2 plane is optimally doped..
4. Concluding remarks In this paper, we have argued that superconductivity in Pr123 observed in certain single crystals and thin films is induced by mutual substitution between the Pr and Ba sites; i.e., the superconductivity is extrinsic in origin. Both Pr-site Ba ions and Ba-site Pr ions change the crystal structure and modify the energy levels at the Cu and Pr sites in such a way as
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to be unfavourable for Pr–O hybridisation and favourable for holes in the CuIII oxidation state. These effects are local at low defect densities, and small superconducting regions are created near the defects. At a critical defect density, a c , local superconducting regions percolate through the sample and bulk superconductivity shows up. The transition at a c is predicted to be of first order, accompanying discontinuous changes in Tc and structural parameters. In this paper and in a series of previous publications w20,21,23–25x, we have discussed a wide range of experimental observations regarding the ‘Pr anomaly’. They include variations of Tc , T N and the hole concentration with Pr doping level in RPr123; their dependence on the R ionic size and on Ba-site substitution; decreases in the penetration depth and critical current density with increasing Pr doping level in YPr123; upturn in the resistivity vs. temperature curve near Tc observed for higher Pr doping level; qualitative changes in magnetoresistance with Pr doping level in YPr123; semiconductor–superconductor transition observed only in RPr123 having a larger R; coincidence of Tc Ž r s 0. with the temperature corresponding to the inflection point of the magnetisation vs. temperature curve; magneticflux trapping observed even for insulating compositions in YPr123; two-mode behaviour in the infrared reflectance spectra for RPr123 having a larger R; partial recovery of Tc by Ca doping in YPr123; suppression of specific heat anomaly at T N with decreasing Pr concentration in RPr123; its dependence on R; and superconductivity in Pr0.5 Ca 0.5Ba 2 Cu 3 O y . We have also provided a simple, clear criterion of whether or not Pr ions suppress superconductivity in a given host compound w24,25x, and explained the similarity and difference between the effects of Pr doping and Ce doping in Y123 w25x. What we would like to emphasise is consistency. All the experimental observations outlined above, many of them inexplicable in terms of models proposed by others, are accounted for, at least qualitatively, on the basis of a unified picture, namely, Pr–O hybridisation and the resultant localisation of holes, as formulated by Fehrenbacher and Rice w7x. This consistency, however, is achieved if, and only if, the following factors are properly taken into account. First, the materials concerned could be in-
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homogeneous. The inhomogeneity may not only be extrinsic, as in the case of superconducting Pr123, but also be intrinsic; any solid solution is inhomogeneous on a microscopic scale. Despite strong experimental evidence to support it, the concept ‘microscopically inhomogeneous electronic structure in an ideal solid solution’ is often dismissed without justification, but it is quite reasonable in view of the small coherence length of high-Tc materials Ž j a b ; 10 ˚ .. Treating RPr123 as a nanoscale mixture of suA perconducting and insulating regions is as reasonable as treating a mixture of submicron grains of Al Ž j ; 0.16 mm. and Al 2 O 3 as a composite of distinct superconducting and insulating materials. Second, Coulomb interaction is among the highest energyscale interactions in high-Tc materials, in which relatively covalent CuO 2 planes are embedded in strongly ionic crystals. Nevertheless, Coulomb interactions tend to be treated too casually, or even neglected altogether. Cation substitutions are often discussed only in relation with their effects on the hole concentration andror structural disorder. As we have been arguing, cation substitutions modify the Madelung potentials at various atomic sites, either directly through the valence effect or indirectly through structural changes, and have far-reaching influences on the electronic structure: the Madelung potential difference between the Cu and Pr sites is the major factor determining whether or not Pr ions interfere with superconductivity w24,25x, while that between the Cu and O sites is one of the main factors that control the maximum Tc in each cuprate superconductor w43,44x. We believe that proper considerations of inhomogeneity and Coulomb interaction are keys to understanding the properties not only of the R123-related compounds but also of the whole high-Tc materials.
References w1x A. Matsuda, K. Kinoshita, T. Ishii, H. Shibata, T. Watanabe, T. Yamada, Phys. Rev. B 38 Ž1988. 2910. w2x A.P. Gonc¸alves, I.C. Santos, E.B. Lopes, R.T. Henriques, M. Almeida, Phys. Rev. B 37 Ž1988. 7476. w3x A. Kebede, C.S. Jee, J. Schwelger, J.E. Crow, T. Mihalisin, G.H. Myer, R.E. Salomon, P. Schlottmann, M.V. Kuric, S.H. Bloom, R.P. Guertin, Phys. Rev. B 40 Ž1989. 4453.
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w4x M.E. Lopez-Morales, D. Rıos-Jara, J. Taguena, ´ ´ ¨ ˜ R. Escudero, S. La Placa, A. Bezinge, V.Y. Lee, E.M. Engler, P.M. Grant, Phys. Rev. B 41 Ž1990. 6655. w5x Y. Wang, H. Rushan, Z.-B. Su, Phys. Rev. B 50 Ž1994. 10350. w6x X.X. Tang, A. Manthiram, J.B. Goodenough, Physica C 161 Ž1989. 574. w7x R. Fehrenbacher, T.M. Rice, Phys. Rev. Lett. 70 Ž1993. 3471. w8x A.I. Liechtenstein, I.I. Mazin, Phys. Rev. Lett. 74 Ž1995. 1000. w9x G. Cao, Y. Yu, Z. Jiao, Physica C 301 Ž1998. 294. w10x H.A. Blackstead, J.D. Dow, D.B. Chrisey, J.S. Horwitz, M.A. Black, P.J. McGinn, A.E. Klunzinger, D.B. Pulling, Phys. Rev. B 54 Ž1996. 6122. w11x H.B. Radousky, J. Mater. Res. 7 Ž1992. 1917. w12x L. Soderholm, G.L. Goodman, J. Solid State Chem. 81 Ž1989. 121. w13x J.-S. Kang, J.W. Allen, Z.-X. Shen, W.P. Ellis, J.J. Yeh, B.W. Lee, M.B. Maple, W.E. Spicer, I. Lindau, J. Less Common Met. 148 Ž1989. 121. w14x J. Fink, N. Nucker, H. Romberg, M. Alexander, M.B. Maple, ¨ J.J. Neumeier, J.W. Allen, Phys. Rev. B 42 Ž1990. 4823. w15x K. Takenaka, Y. Imanaka, K. Tamasaku, T. Ito, S. Uchida, Phys. Rev. B 46 Ž1992. 5833. w16x Z. Zou, K. Oka, T. Ito, Y. Nishihara, Jpn. J. Appl. Phys. 36 Ž1997. L18. w17x Z. Zou, J. Ye, K. Oka, Y. Nishihara, Phys. Rev. Lett. 80 Ž1998. 1074. w18x K. Oka, Z. Zou, J. Ye, Physica C 300 Ž1998. 200. w19x T. Usagawa, Y. Ishimaru, J. Wen, T. Utagawa, S. Koyama, Y. Enomoto, Jpn. J. Appl. Phys. 36 Ž1997. L1583. w20x M. Muroi, R. Street, Physica C 208 Ž1993. 107. w21x M. Muroi, R. Street, Physica C 216 Ž1993. 345. w22x J.A. Hodges, G. le Bras, P. Bonville, P. Imbert, G. Jehanno, ´ Physica C 218 Ž1993. 283. w23x M. Muroi, R. Street, Physica C 228 Ž1994. 216. w24x M. Muroi, R. Street, Physica C 253 Ž1995. 205.
w25x M. Muroi, R. Street, Physica C 301 Ž1998. 277. w26x C.H. Booth, F. Bridge, J.B. Boyce, T. Claeson, Z.X. Zhao, P. Cervantes, Phys. Rev. B 49 Ž1994. 3432. w27x S.K. Malik, S.M. Pattalwar, C.V. Tomy, R. Prasad, N.C. Soni, K. Adhikary, Phys. Rev. B 46 Ž1992. 524. w28x G. Botter, I. Mangelschots, E. Kaldis, P. Fischer, Ch. Kruger, ¨ ¨ F. Fauth, J. Phys. Condens. Matter 8 Ž1996. 8889. w29x J. Ye, K. Nakamura, Phys. Rev. B 50 Ž1994. 7099. w30x J.J. Neumeier, T. Bjørnholm, M.B. Maple, J.J. Rhyne, J.A. Gotaas, Physica C 166 Ž1990. 191. w31x M. Guillaume, P. Allenspach, W. Henggler, J. Mesot, B. Roessli, U. Staub, P. Fischer, A. Furrer, V. Trounov, J. Phys. Condens. Matter 6 Ž1994. 7963. w32x B. Okai, M. Kosuge, H. Nozaki, K. Takahashi, M. Ohta, Jpn. J. Appl. Phys. 27 Ž1988. L41. w33x K. Kinoshita, A. Matsuda, H. Shibata, T. Ishii, T. Watanabe, T. Yamada, Jpn. J. Appl. Phys. 27 Ž1988. L1642. w34x D.H. Ha, Physica C 302 Ž1998. 299. w35x H. Song, G. Cao, Z. Xu, Y. Ren, Q. Zhang, Z. Phys. B 103 Ž1997. 29. w36x H. Michor, M. Vybornov, T. Holubar, W. Perthold, G. Schaudy, G. Hilscher, P. Rogl, Physica C 226 Ž1994. 1. w37x K.N. Yang, J.M. Ferreira, B.W. Lee, M.B. Maple, W.-H. Li, J.W. Linn, R.W. Erwin, Phys. Rev. B 40 Ž1989. 10963. w38x J. Ye, Z. Zou, A. Matsushita, K. Oka, Y. Nishihara, T. Matsumoto, Phys. Rev. B 58 Ž1998. R619. w39x J.S. Schilling, S. Klotz, in: D.M. Ginsberg ŽEd.., Physical Properties of High Temperature Superconductors III, World Scientific, Singapore, 1992, p. 59. w40x C.W. Chu, Z.J. Huang, R.L. Meng, L. Gao, P.H. Hor, Phys. Rev. B 37 Ž1988. 9730. w41x R. Benischke, T. Weber, W.H. Fietz, J. Metzger, K. Grube, T. Wolf, H. Wuhl, ¨ Physica C 203 Ž1992. 293. w42x I.V. Medvedeva, Y.S. Bersenev, B.A. Gizhevsky, N.M. Chebotaev, S.V. Naumov, G.B. Demishev, Z. Phys. B 81 Ž1990. 311. w43x M. Muroi, Physica C 219 Ž1994. 129. w44x M. Muroi, R. Street, Physica C 235–240 Ž1994. 1347.
Defect-induced superconductivity in PrBa 2 Cu 3 O 7 Michihito Muroi ) , Robert Street Special Research Centre for AdÕanced Mineral and Materials Processing, Department of Physics, The UniÕersity of Western Australia, Nedlands, WA 6907, Australia Received 18 November 1998; received in revised form 11 December 1998; accepted 25 January 1999
Abstract The appearance of superconductivity in some PrBa 2 Cu 3 O y Ž y ; 7. single crystals and thin films can be accounted for on the assumption of the presence of disorder in the BarPr site occupancy. It is argued that Ba ions occupying the Pr site and Pr ions occupying the Ba site both weaken Pr–O hybridisation through local structural changes and lower the Madelung potential at the Cu site relative to that at the Pr site, thus favouring the CuIII oxidation state over the Pr IV oxidation state. Bulk superconductivity shows up when local superconducting regions, created near the defects, percolate through the sample. It is concluded that stoichiometric, defect-free PrBa 2 Cu 3 O 7 is insulating. q 1999 Published by Elsevier Science B.V. All rights reserved. Keywords: PrBa 2 Cu 3 O 7 ; Insulator–superconductor transition; Pr–O hybridisation; Substitution effects
1. Introduction Among the compounds of the type RBa 2 Cu 3 O 7 ŽR123., where R is Y or a rare-earth element except Ce, Pm and Tb, Pr123 is unique in that it is an insulator and does not show superconductivity while all the other R123s are superconductors with Tc s of about 90 K. A number of models have been proposed to explain this puzzling fact w1–10x. 1 Earlier explanations include ‘hole filling’ by Pr ions w1,2x, assumed to have a valence greater than 3 q , and ‘magnetic pair breaking’ by localised Pr 4f moments
)
Corresponding author. Fax: q61-8-9380-1014; E-mail: [email protected] 1 For an extensive review on earlier studies on PrBa 2 Cu 3 O y and ŽR 1y x Pr x .Ba 2 Cu 3 O y , see Ref. w11x.
w3x. The hole filling model, however, was found to be inconsistent with the results of various spectroscopic studies w12–14x, which showed a valence close to 3 q for Pr; structural considerations w4x also pointed to trivalent Pr. The pair breaking model was questioned by the facts that other rare-earths such as Gd and Sm have larger 4f moments than Pr but do not suppress superconductivity, and that Pr123 is not only nonsuperconducting but also insulating. As a variant of the hole filling model, charge redistribution between the CuO 2 planes and the CuO chain layers has later been suggested w5x. However, an electron-energy-loss spectroscopy ŽEELS. study w14x shows that the density of unoccupied planar O 2p states remains unchanged with increasing x in Y1y x Pr x Ba 2 Cu 3 O 7 Ž0 F x F 1., while optical conductivity measurements on detwinned Y123 and Pr123 single crystals w15x indicate that the hole concentration in the CuO chain layer is similar in the
0921-4534r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 1 4 6 - X
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two compounds; both demonstrate clearly that the number of holes in the CuO 2 –R–CuO 2 block is little affected by the presence of Pr ions. Another explanation, which on the main point is most widely accepted, is the localisation of holes by Pr ions. Tang et al. w6x have argued that the strong Pr–O hybridisation, which results from the small energy difference between the Pr 3q:4f level and the Fermi energy EF , transforms the itinerant holes into small polarons, thereby suppressing superconductivity. Fehrenbacher and Rice ŽFR. w7x have shown through Hartree calculations that in R123, there are only two stable electronic configurations, one in which all the in-plane holes are in the CuIII oxidation state ŽCuIII state hereafter., i.e., in the hybridised Cu 3d–O 2p s orbitals, and the other in which all the in-plane holes are in the RIV oxidation state ŽRIV state hereafter., i.e., in the hybridised R 4f–O 2p p orbitals; that the energy level of the Pr 4f orbitals, combined with the local ionic arrangement of the 123 structure, favours the latter state to be realised in Pr123; and that the total probability of the 4f 1 Pr configuration is 0.15– 0.2 and holes spend most of their time on ligand O ions. This model ŽFR model. consistently explains a number of experimental observations, including the absence of a Tc between 0 and ; 90 K in the R123 series. Despite its success, the FR model does not seem to have been fully accepted. Criticisms on the FR model include the following: Ž1. the conclusion of the FR model that there are only two stable electronic configurations in R123 is inconsistent with the continuous decrease in Tc with increasing Pr concentration in Y1y x Pr x Ba 2 Cu 3 O 7 ŽYPr123. w8,9x; Ž2. treating the Pr–O hybridisation as a purely local phenomenon, the FR model fails to account for the R dependence of Tc suppression in RPr123 w8,9x; and Ž3. some Pr123 single crystals prepared by the travelling-solvent floating-zone ŽTSFZ. method w16–18x and epitaxial thin films w10,19x show bulk w16–19x or granular w10x superconductivity below 80–90 K, which implies that the insulating behaviour of Pr123 is not intrinsic but due to defects w10,19x. The first criticism depends on the assumption that the materials concerned are homogeneous, an assumption that has never been substantiated on rigorous grounds. In fact, a wide range of experimental observations on YPr123, including the variation of
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Tc with Pr concentration, has been consistently accounted for in terms of a percolation model w20,21x, in which coexistence of superconducting and insulating phases on a microscopic scale is assumed; this assumption is fully consistent with a 170 Yb Mossbauer study on Yb-doped YPr123 w22x, which ¨ provides conclusive evidence that Y1y x Pr x Ba 2 Cu 3 O 7 is inhomogeneous except for the end compounds Ž x s 0 and 1.. The second criticism also seems inadequate. The effects of substitution, not only on the R site but also on the Ba site in RPr123, have also successfully been explained within the framework of the percolation model w23–25x. The R dependence of Tc is compatible with the FR model. In addition, it is not evident whether the effect of Pr–O hybridisation is appropriately described by a band picture; the presence of distinct Pr–O bond lengths in Pr123 detected by X-ray absorption fine structure ŽXAFS. measurements w26x, as well as the Mossbauer results men¨ tioned above w22x, suggests that Pr–O hybridisation and the resultant hole localisation are local phenomena. Furthermore, the models proposed in Refs. w8,9x themselves seem to have the following major difficulties in explaining the R dependence of Tc . In Ref. w8x, the rate of Tc suppression is related with the R 4f energy level, which is expected to vary nonmonotonically, reflecting the nonmonotonic variation of the ionisation potential of R Žsee Fig. 2c.. The rate of Tc suppression, however, increases monotonically with decreasing atomic number of R, suggesting that the R dependence has little to do with the R 4f energy level but stems from the R ionic size. The argument in Ref. w9x depends on the assumption that substitutions with smaller ions result in weakening of Pr–O hybridisation. This assumption is valid for Sr-site substitutions but is highly unreasonable for R-site substitutions, as we have shown in previous papers w24,25x and substantiate further in this paper. Regarding the third criticism, an ‘oxygen’ model has been proposed w10x. This model ascribes the lack of superconductivity in polycrystalline Pr123 samples to Ba-site Pr impurities, which break Cooper pairs postulated to reside in the Cu–O chain layers and not in the CuO 2 planes. In a previous paper w24x, we have already shown that this model is highly unreasonable in many respects, and suggested that the local superconductivity observed in Pr123 thin
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films w10x could be due to defects such as Ba ions occupying the Pr site and excess O ions in the Cu–O chain layer. In this paper, we extend the discussions in Ref. w24x Ži. by comparing various sample preparation techniques from thermodynamical viewpoints, and Žii. by examining the crystal structure of the ‘superconducting Pr123’ and its effects on the electronic structure more in detail.
2. Comparison of sample preparation methods The major premise of our discussions is that mutual substitution between the Ba and Pr sites is much more significant in the Pr123 samples that exhibit superconductivity than in ‘normal’ insulating Pr123 samples. Although the site occupancies of the ‘superconducting Pr123’ have not been determined and the reverse has been postulated w10,19x, there are strong indications that support the above premise. First, the c-lattice constants Ž c 0 . of superconducting Pr123 crystals are longer than those of insulating Pr123. The superconducting Pr123 crystals have been subjected to annealing in oxygen at lower temperatures Ž600 and 4008C. for a long time Ž100 h. w18x, and insufficient oxidation is an unlikely reason for the long c 0 . Since c 0 decreases with increasing x in PrBa 2y x Pr x Cu 3 O 7 w27x, as expected for a substitution with a smaller ion, the most likely explanation of the expanded c 0 is the occupation of Ba ions on the Pr site. Similar elongation of c 0 is observed in Y1y x Ca x Ba 2 Cu 3 O 7 as x increases w28x and in YBa 2 Cu 3 O 7 thin films as disorder in the Y and Ba site occupancy increases with decreasing substrate temperature w29x. Second, the TSFZ method yields superconducting Pr123 crystals only when the composition of the starting material is very rich in Ba w18x. In R123 with a larger R, including Pr123, R ions readily occupy the Ba site w12x, but the reverse is practically unknown in bulk polycrystalline samples, which may be accounted for as follows: since the Madelung potential at a cation site is always negative, substitution with a lower Žhigher. valence cation increases Ždecreases. the electrostatic energy of the crystal. Thus, in the substitution of Ba for Pr, the strain energy associated with the ionic size mismatch and
the electrostatic energy both increase, while in the substitution of Pr for Ba, the cost in strain energy is partly compensated by the gain in electrostatic energy. Moreover, in the latter case, the cost in strain energy could be further reduced and the gain in electrostatic energy could be further enhanced by introducing extra O ions in the adjacent Cu–O chain layers. A possible role of the excess Ba, then, is to increase the probability of the nucleation of Ba-rich Pr123, which is much less stable than Pr-rich Pr123. Third, in epitaxial-thin-film deposition and the TSFZ method, the techniques used to prepare the superconducting Pr123, crystals grow under nonequilibrium conditions in the presence of seed crystals. Epitaxial thin films are usually grown at a substrate temperature ŽTs . in the range 550–7508C, a few hundred degrees lower than the temperature required to form the 123 phase by conventional solid state reaction Ž900–9508C.. Under such conditions, the 123 phase is probably not the most stable phase. The 123 phase nevertheless forms, owing to the presence of seed crystals which favours the nucleation of the 123 phase over that of other competing phases such as BaCuO 2 and Pr2 BaCuO5 ; i.e., the 123 phase is kinetically, not thermodynamically, stabilised. In the ideal 123 structure, the R and Ba ions arrange in the ordered sequence –R–Ba–Ba–R–Ba–Ba– . . . along the c-axis. This means that to form the perfect 123 ˚ structure, a diffusion length of at least about 6 A Žhalf the c-lattice constant. is necessary for R ions. As Ts decreases, the diffusion length naturally decreases, and a certain degree of mixing between the R and Ba sites becomes inevitable. Blackstead et al. w10x claim that the use of a lower Ts minimises Pr occupation on the Ba site. This claim would be valid if the perfect 123 phase were formed before the constituent atoms arrive at the substrate. In reality, the atoms must rearrange themselves to form the 123 structure after arriving at the substrate. The lower the Ts , the more mixing between the R and Ba sites, which has been demonstrated clearly by a systematic study of Y123 thin films deposited at various substrate temperatures w29x. ŽIn view of the smaller ionic size difference between Pr and Ba than between Y and Ba, the mixing of R and Ba ions will occur still more easily in Pr123.. Bulk single crystal growth, on the other hand, takes place at a sufficiently high temperature near the melting point. The process is
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nonetheless nonequilibrium because crystal growth from liquid always involves a certain degree of supercooling, and the phaseŽs. formed is Žare. again determined not only by thermodynamics but also by kinetics. During crystal growth by the TSFZ method w16–18x, a large area of the molten zone, thin in the scan direction, is in contact with the seed crystals, thus favouring the nucleation of the 123 phase. It is possible then that the 123 structure is formed even when a local composition of the melt happens to be favourable for the formation of other competing phases, with the natural consequence of wrong site occupancies. ŽFluctuation in local composition on a microscopic scale, inevitably present in a multi-component liquid, will be particularly large when the relevant compound melts incongruently as is the case with R123.. Fourth, carefully prepared Pr123 polycrystalline samples show consistent structural, electrical and magnetic properties w4,30,31x, while the single crystals prepared by the TSFZ method exhibit large scattering in both structural and superconducting properties even within a single sample w17,18x. The fact that the crystal structure of the insulating portion of the TSFZ crystals is similar to that of polycrystalline samples w17,18x strongly suggests that it is the superconducting portion of the TSFZ crystals that is anomalous and the superconductivity is extrinsic in origin. It is true that R ions tend to occupy the Ba site in R123 with a larger R w12,32,33x, and it was, in fact, claimed that in the synthesis of polycrystalline Pr123 samples, the stoichiometric cation ratio ŽPr:Ba:Cus 1:2:3. of the starting material results in a mixture of BaCuO 2 and Pr1qx Ba 2yx Cu 3 O 7 w32,33x; later studies w4,30,31x have demonstrated, however, that stoichiometric Pr123 with no detectable Pr on the Ba site can be prepared by optimising the synthesis conditions. Note that in the case of polycrystalline samples, the level of Ba-site occupation by Pr can be estimated from the fraction of second phaseŽs. present; this is difficult for single crystals, since the starting composition is generally nonstoichiometric. Not being a one-shot process, solid state reaction, in principle, guarantees the thermodynamically most stable state to be realised in the end. The problem of long diffusion lengths required for phase formation, an inevitable consequence of large inhomogeneity in the starting mixture, can be overcome by extending
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the reaction time, by repeating firing and regrinding many times, and by choosing the appropriate synthesis conditions, such as temperature and oxygen partial pressure. Despite the ‘worship’ of single crystals widespread in the literature, we do not find any reason why polycrystalline samples are inherently more defected than single crystals or epitaxial thin films. It is inappropriate to justify the assumption that Pr123 polycrystalline samples contain more Basite Pr ions than epitaxial thin films w10,19x simply because significant Pr ions are present on the Ba site in some polycrystalline samples. ŽSmall amounts of Pr ions on the Ba site, if ever present, cannot explain the insulating behaviour of Pr123 anyway; a recent study on YBa 2y x R x Cu 3 O y ŽR s Pr,La. w34x shows that the decreases in Tc with Pr doping and La doping are similar and that superconductivity persists up to x ; 0.6..
3. Electronic structure of R123 and effects of Pr r Ba site disorder in Pr123 Before discussing the effect of disorder in the PrrBa site occupancy, we reexamine the electronic structure of R123 in terms of the FR model w7x. According to the model, the relative stability of the CuIII state Žsuperconducting solution. and the RIV state Žnonsuperconducting solution. is mainly determined by two factors: t pf , the hopping integral between R 4f zŽ x 2yy 2 . orbitals and O 2p p orbitals with the f symmetry ŽR 4f and O 2p p orbitals hereafter., and D PF , defined as D PF s ´ P y ´ F , where ´ P and ´ F are the energies of the localised CuIII and Pr IV states, respectively. A larger Žsmaller. t pf and a larger Žsmaller. D PF favour the RIV ŽCuIII . state. Transition between the two states is a crossover, and not a gradual change in electronic structure, as is incorrectly assumed in many theoretical considerations in the literature. We consider three parameters that are expected to control t pf and D PF : the R–O bond length Ž d R – O ., the O–R–O bond angle Ž u R . Žsee Fig. 1b. and D E h , defined as D E h s I3 ŽCu. q V M ŽCu.4 y I4ŽR. q VM ŽR.4 , where I k ŽX. is the k th ionisation potential of element X and VM ŽX. is the Madelung potential at
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Fig. 1. Ža. Crystal structure of Y123. The ions on the x s a 0r2 plane are drawn with bold lines, while the ions on the x s 0 Ž a0 . plane are drawn with thin lines. Structural data from Ref. w31x. Žb. Local ionic arrangement around an R ion in R123. Filled and open circles indicate Cu and O ions, respectively. Žc. Movement of O ions expected for a substitution of a larger divalent cation for R.
the X site. 2 d R – O and u R will determine t pf : the smaller the d R – O and the closer the u R to 109.48 Žthe value of u R for a perfect cube made of the eight O ions surrounding an R ion., the more overlap between the R 4f and O 2p p orbitals and hence, a larger t pf . We emphasise here that d R – O and u R should be treated on an equal footing, since the R 4f orbitals are directional. D E h represents the energy difference between the Cu and R sites in the ionic limit w24,25x and is expected to be a good measure of D PF . In Fig. 2a–c, the three parameters are plotted as functions of the R ionic radius Ž r R . for a series of R123 compounds; structural data were taken from Ref. w31x. It can be seen that as r R increases, d R – O increases and u R decreases away from 109.48. However, the data points for Pr123 are anomalous: d R – O is smaller and u R is larger than expected from the trends. This is a clear indication of a spontaneous lattice distortion that has occurred in Pr123 to achieve
2 In the calculation of V M , we assigned the formal ionic charges to all the sites except the O site in the Cu–O chain layer Žor NbO 2 layer in the case of NbBa 2 PrCu 2 O 8 .. The charge on that O site was adjusted to ensure the charge neutrality of the crystal. The error associated with this arbitrariness in charge assignment is negligibly small; e.g., the difference in DVR for Y123 calculated with three different charge assignments in the Cu–O chain layer, q3 to Cu and y2 to O, q2 to Cu and y1 to O, and q1 to Cu and 0 to O, is less than 0.05 eV, which is smaller than the size of the symbols used for the plots in Fig. 2f.
a better overlap between the Pr 4f and O 2p orbitals. The data presented in Fig. 2a and b thus indicate that the crystal structure of Pr123 is not ideal for Pr–O hybridisation and that the Pr–O hybridisation in Pr123 is enhanced at the cost of increased strain energy. The variation of D E h with r R ŽFig. 2c., on the other hand, is not monotonic, reflecting the nonmonotonic variation of I4 ŽR. with atomic number. Among all the R123s, only Pr123 has a positive D E h Ž0.77 eV., which is favourable for the Pr IV state to be realised w7x. The unique insulating behaviour of Pr123 is thus reasonably explained as resulting from a crossover from the CuIII state to the Pr IV state, which crossover must take place by going from Nd123 to Pr123. However, the difference in D E h between Pr123 Ž0.77 eV. and Nd 123 Žy0.64 eV. is relatively small Žthe difference would be still smaller if there were no spontaneous lattice distortion in Pr123, which increases VM ŽCu. –V M ŽR. and hence, D E h ., and judging from the overall trends in Fig. 2a and b, the crystal structure of Nd123 is probably more suitable for R–O hybridisation than that of Pr123. In fact, the Neel ´ temperature for Nd-sublattice ordering in Nd123 depends strongly on the oxygen content w37x, suggesting that the Nd–O hybridisation is relatively strong. It appears that Nd123 and Pr123 are located very close to the crossover point between the CuIII and RIV states. It might then be possible to induce transitions between the superconducting Žmetallic. and insulating states by applying external stresses. A metal Žsuperconductor. –insu-
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Fig. 2. Ža. Variations of d R – O , u R and D Eh with R ionic radius Ž r R . in R123. Structural data taken from Ref. w31x. Žd–f. Variations of d R – O , u R and D E h with doping level Ž x . in Y1yx Ca x Ba 2 Cu 3 O 7 Ždata from Ref. w28x., Y0.4 Pr0.6 Ba 2yx Sr x Cu 3 O 7 Ždata from Ref. w35x. and NbBa 2y x Sr x PrCu 2 O 8 Ždata from Ref. w36x..
lator transition might occur in Nd123 under uniaxial pressure along the c-axis, which would shift all the three parameters to the directions favourable for the Nd IV state; similarly, an insulator–metal Žsupercon-
ductor. transition might be induced in Pr123 by applying biaxial pressure in the ab-plane. Because of the coupling between the electronic state and the crystal structure as discussed above, these transitions
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would be first-order ones, accompanied by discontinuous changes in structural parameters such as c 0 , d R – O and u R . We now discuss the effect of Ba ions incorporated in the Pr site of Pr123. Since structural data for Pr123 having Ba ions on the Pr site are not available, we have calculated d R – O , u R and D E h for Y1yx Ca x Ba 2 Cu 3 O 7 Ž x s 0, 0.1 and 0.2. w28x, which are plotted as functions of x in Fig. 2d–f. R ions are substituted by larger divalent cations in both cases, and changes in the three parameters with increasing doping level will be qualitatively similar. It can be seen that as the Ca concentration Ž x . increases, d R – O increases, u R decreases away from 109.48, and D E h decreases. The reasons for these changes, all favourable for the CuIII state, are twofold: geometric and electrostatic. As can be seen in Fig. 1a, where the crystal structure of Y123 is depicted, the arrangement of the planar O ions in the 123 structure is largely constrained by their close contact with the neighbouring R and Ba ions. Incorporation of a larger Ca2q ion ˚ . in place of a smaller Y 3q ion Ž r Y s Ž rCa s 1.12 A ˚ . will naturally expand the surrounding O 8 1.019 A cage, resulting in an increase in r R – O . The expansion of the O 8 cage will not be isotropic because the Cu–O bonds, having a significant covalent character, are stiffer and more reluctant to expand than the other bonds. As a consequence, the expansion along the c-axis dominates that in the ab-plane ŽFig. 1c., resulting in a decrease in u R . As the Cu–O and R–O bond lengths increase, VM ŽCu. and VM ŽR. both increase, since the contribution from the negatively charged O 2y ions, which dominates VM , decreases with increasing cation–anion distance. The increase in V M ŽCu., however, is smaller than that in V M ŽR. because of the difference in the oxygen coordination number ŽCN. ŽCN s 5 for Cu and CN s 8 for R.. Thus, V M ŽCu. y V M ŽR. and hence D Eh decrease with increasing x. The above effects, which are purely geometric in origin, are accentuated by the lower valence of Ca as compared with Y. In the 123 structure, the separation between two adjacent CuO 2 planes will be determined by the balance of the Coulomb repulsion between negatively charged CuO 2 planes Žnet charge of approximately y2. and the Coulomb attraction between the CuO 2 planes and positively charged R
layers Žnet charge of 3 y x .. As x increases, the former becomes progressively more dominant, and the separation between adjacent CuO 2 planes increases. d R – O increases and u R decreases, as a result. As the valence of the R site decreases with Ca doping, V M ŽCu. and VM ŽR. both decrease, but the decrease is greater for VM ŽCu. than for V M ŽR. because the nearest-neighbour R–Cu distance is smaller than the nearest-neighbour R–R distance. Thus, V M ŽCu. –V M ŽR. and hence, D E h decrease. The changes in d R – O , u R and D E h brought about by the Ba substitution for Pr in Pr123 will be much larger than those effected by the Ca substitution for Y in Y123 examined above, since the difference in ionic ˚ . and Pr Ž1.126 A˚ . is much radii between Ba Ž1.420 A ˚ . and Y Ž1.019 larger than that between Ca Ž1.120 A ˚ .. A To investigate the effect of Pr substitution for Ba in Pr123, we have calculated d R – O , u R and D E h for Y0.4 Pr 0.6 Ba 2y x Sr x Cu 3 O 7 Ž x s 0, 1. w35x and NbBa 2y x Sr x PrCu 2 O 8 Ž x s 0, 1, 2. w36x in which Ba ions are replaced by smaller Sr ions; NbBa 2 PrCu 2 O 8 is isostructural with Pr123 except that the Cu–O chain layers in Pr123 are replaced by NbO 2 layers. The results are plotted in Fig. 2d–f. The graphs show clear trends: d R – O increases while u R and D Eh decrease with increasing x. These changes are very similar to those observed in Y1y x Ca x Ba 2 Cu 3 O 7 , showing that in R123, the Ba-site substitution with a smaller cation is equivalent to the R-site substitution with a larger cation; in other words, the effects of ‘chemical pressure’ on the three parameters are opposite for the Ba-site and R-site substitutions. This is quite natural in view of the 123 structure ŽFig. 1a.. The R site is located in between two adjacent CuO 2 planes, and a larger cation incorporated in the R site pushes them away from the R site towards the Cu–O chain layers. The Ba site, on the other hand, is located between the CuO 2 plane and the nearestneighbour Cu–O chain layer, and a larger cation incorporated in the Ba site pushes the CuO 2 plane towards the R site. In the above calculation of D E h , the formal valence of q2 was assigned to the BarSr site, and the effect of the higher valence of Pr Žq3. was not taken into account. ŽIn the defected Pr123 we are considering, Ba2q ions are replaced by Pr 3q ions.. To take it into account, we have repeated calcula-
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tions of D Eh by assigning an ionic charge of 2 q xr2 to the BarSr site. The results, indicated by error bars in Fig. 2f, show that D E h is decreased further with this charge assignment. However, the additional decrease in D Eh is small as compared with the overall decrease with increasing x, suggesting that structural changes due to the substitution are more important in reducing D E h than the valence difference. It is thus likely that the incorporation of Pr in the Ba site in Pr123 changes all the three parameters to the directions unfavourable for the Pr–O hybridisation and favourable for the CuIII state. This is consistent with the experimental observation that the Neel ´ temperature for the Pr sublattice ordering decreases with increasing x in PrŽBa 2y x Pr.Cu 3 O 7 w27x. In the above considerations, we used information on the average crystal structure and assigned the same fractional ionic charge to the site containing substituted ions, regarding the crystal as homogeneous. In real crystals, however, the distribution of defects ŽPr-site Ba and Ba-site Pr. is not uniform but discrete and random. Accordingly, the three parameters, d R – O , u R and D E h , will vary in space, reflecting the statistical distribution of the defects. It is most likely that for a low defect density Ž a ., noticeable changes in the three parameters are confined in small local regions extending possibly no more than a few unit cells from the defects. ŽHere and in the following discussion, we define the defect density as a in ŽPr1y a Ba a .ŽBa 2y a Pra .Cu 3 O 7 , i.e., the density of Ba ŽPr. ions on the Pr ŽBa. site.. These local regions, in which the CuIII state is strongly favoured, will become superconducting if the CuO 2 planes within them are optimally doped. The condition of optimal doping, however, may not be satisfied because of the local charge imbalance Ža Ba-site Pr ion provides an extra electron and a Pr-site Ba ion an extra hole.. The extra electronrhole will be bound to the defect through Coulomb interaction, possibly inhibiting superconductivity. In fact, the Tc of Y123 thin films decreases with increasing disorder in the YrBa site occupancy w29x, suggesting that the order parameter is suppressed near the defects. As a increases, the fraction of local regions in which the CuIII state is favoured progressively increases. This increase will be faster than that of a , since the regions between the defects are also subject to structural changes that are favourable for the CuIII state as
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the separation between defects decreases. Superconductivity will then be set up in those regions in which the CuIII state is favoured and at the same time, no defects are present over a distance greater than the in-plane coherence length Ž j a b .. At a critical defect density Ž a c ., local superconducting regions percolate through the sample, and bulk superconductivity shows up. This transition at a c will be of first order because of the coupling between the electronic state and the crystal structure in Pr123. As a c is approached from below, it becomes energetically favourable to drive essentially all the holes into the CuIII state, thereby releasing the strain energy stored in part of the crystal to stabilise the Pr IV state. The transition at a c will thus accompany discontinuous changes in Tc and structural parameters including c 0 , as schematically depicted in Fig. 3. When a is close to a c , the transition may possibly be induced by external pressure: a crystal with a just above a c would show a metal Žsuperconductor. –insulator transition under uniaxial pressure along the c-axis, whereas a crystal with a just below a c would exhibit an insulator–metal Žsuperconductor. transi-
Fig. 3. Variations of the c-lattice constant Ž c 0 . and Tc with defect density in R123 ŽR sY, Pr.. ŽThe diagrams are schematic.. The defect density is defined as a in ŽR 1y a Ba a .ŽBa 2y a R a .Cu 3 O 7 .
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tion under in-plane biaxial pressure. These transitions would be similar to those predicted to occur in Nd123 and Pr123. An increase in a beyond a c will result in a decrease in Tc because of the increase in the fraction of nonsuperconducting regions created in the immediate vicinity of the defects; the behaviour of Pr123 for a ) a c will be qualitatively similar to that of Y123 ŽFig. 3.. Rigorous derivation of a c is difficult, but a rough estimate may be obtained by equating the average separation between defects, ˚ ., Ž2 x .y1 r2 a 0 Ž a 0 s in-plane lattice constant ; 3.9 A ˚ we obtain a c s 0.053. with j a b . For j a b s 12 A, This seems to be a reasonable level of PrrBa site disorder in view of the facts that an Y123 thin film deposited at ; 6108C has a similar value of a w29x and that local superconductivity was observed in a Pr123 thin film deposited at a slightly high temperature, 6508C w10x. We have so far assumed that the Žaverage. hole concentration in the CuO 2 plane remains optimal regardless of a . For higher values of a , however, the CuO 2 planes are most likely to be underdoped, since the superconducting Pr123 crystals have slightly Pr-rich compositions ŽPrrBa; 0.56. w18x and, furthermore, R ions occupying the Ba site tend to disrupt the Cu–O chains, thereby reducing the hole concentration in the CuO 2 plane w25x. This explains a large positive pressure effect on Tc Žup to 7.4 KrGPa. observed in Pr123 crystals prepared by the TSFZ method w17,38x; it is known that in materials having charge-reservoir layers, such as R123, the hole concentration in general increases under pressure and Tc shows a marked increase if the material is underdoped in the ambient pressure w39x. For example, large, positive pressure coefficients of Tc , in the range 7–10 KrGPa, have been reported for oxygen-deficient R123 ŽR s Y, Eu. w40–42x. It has been reported in Ref. w38x that Tc of a Pr123 crystal reaches 105 K under a hydrostatic pressure of 9.3 GPa. This value is much larger than that of Y123 Ž; 92 K. and has been considered anomalous w38x. We attribute the observed high Tc to the following two factors. First, the higher Tc of Pr123, as compared with that of Y123, is consistent qualitatively with the well-known trend that in the R123 series, the maximum Tc attainable ŽTc,max . tends to increase with increasing R ionic size, e.g., 90 K for Yb123 to 96 K for Nd123 w31x. Thus, a value of Tc near, if not
higher than, 100 K is expected for optimally doped Pr123. Second, mutual substitution between the Ba and Pr sites, likely to be present in superconducting Pr123 crystals, could affect Tc,max by modifying DVM Žs V M ŽO. y V M ŽCu.., where V M ŽO. and VM ŽCu., respectively, are the Madelung potentials at the in-plane O and Cu sites; as we have argued in Refs. w43,44x, DV M is one of the major factors controlling Tc,max with a smaller DVM corresponding to a higher Tc,max . To investigate this effect, we have calculated DV M for Pr123 Žthe structural data in Ref. w31x were used. for the following two types of charge assignment: Ži. the formal charge assignment, i.e., q3 to the Pr site and q2 to the Ba site, and Žii. q2.95 to the Pr site and q2.025 to the Ba site Žto simulate Pr123 with a s 0.05.. The results are 47.73 eV for case Ži. and 47.60 eV for case Žii.. ŽThe lower DVM for case Žii. is ascribed to the lower valence of the Pr site, which is favourable for a hole on the O site, since the Pr site is closer to the CuO 2 plane than the Ba site.. A higher Tc,max is thus expected for superconducting Pr123 containing defects. Rigorous justification of the above argument requires accurate structural data, including the atomic positions and site occupancies, for superconducting Pr123, and we just point out the following fact to support it; all the materials having crystal structures similar to that of R123 and high Tc s exceeding 100 K, e.g., TlBa 2 CaCu 2 O 7 , HgBa 2 CaCu 2 O6 and ŽPb,Tl.Sr2ŽCa,Y.Cu 2 O 7 , have divalent cations ŽCa2q . in place of R3q ions. Lowering the cation valence on the site closest to the CuO 2 plane is an effective way of increasing Tc,max w43x. ŽThis does not contradict the decrease in Tc with increasing Ca content, x, in Y1y x Ca x Ba 2 Cu 3 O y ; Tc,max is realised only when the whole CuO 2 plane is optimally doped..
4. Concluding remarks In this paper, we have argued that superconductivity in Pr123 observed in certain single crystals and thin films is induced by mutual substitution between the Pr and Ba sites; i.e., the superconductivity is extrinsic in origin. Both Pr-site Ba ions and Ba-site Pr ions change the crystal structure and modify the energy levels at the Cu and Pr sites in such a way as
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to be unfavourable for Pr–O hybridisation and favourable for holes in the CuIII oxidation state. These effects are local at low defect densities, and small superconducting regions are created near the defects. At a critical defect density, a c , local superconducting regions percolate through the sample and bulk superconductivity shows up. The transition at a c is predicted to be of first order, accompanying discontinuous changes in Tc and structural parameters. In this paper and in a series of previous publications w20,21,23–25x, we have discussed a wide range of experimental observations regarding the ‘Pr anomaly’. They include variations of Tc , T N and the hole concentration with Pr doping level in RPr123; their dependence on the R ionic size and on Ba-site substitution; decreases in the penetration depth and critical current density with increasing Pr doping level in YPr123; upturn in the resistivity vs. temperature curve near Tc observed for higher Pr doping level; qualitative changes in magnetoresistance with Pr doping level in YPr123; semiconductor–superconductor transition observed only in RPr123 having a larger R; coincidence of Tc Ž r s 0. with the temperature corresponding to the inflection point of the magnetisation vs. temperature curve; magneticflux trapping observed even for insulating compositions in YPr123; two-mode behaviour in the infrared reflectance spectra for RPr123 having a larger R; partial recovery of Tc by Ca doping in YPr123; suppression of specific heat anomaly at T N with decreasing Pr concentration in RPr123; its dependence on R; and superconductivity in Pr0.5 Ca 0.5Ba 2 Cu 3 O y . We have also provided a simple, clear criterion of whether or not Pr ions suppress superconductivity in a given host compound w24,25x, and explained the similarity and difference between the effects of Pr doping and Ce doping in Y123 w25x. What we would like to emphasise is consistency. All the experimental observations outlined above, many of them inexplicable in terms of models proposed by others, are accounted for, at least qualitatively, on the basis of a unified picture, namely, Pr–O hybridisation and the resultant localisation of holes, as formulated by Fehrenbacher and Rice w7x. This consistency, however, is achieved if, and only if, the following factors are properly taken into account. First, the materials concerned could be in-
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homogeneous. The inhomogeneity may not only be extrinsic, as in the case of superconducting Pr123, but also be intrinsic; any solid solution is inhomogeneous on a microscopic scale. Despite strong experimental evidence to support it, the concept ‘microscopically inhomogeneous electronic structure in an ideal solid solution’ is often dismissed without justification, but it is quite reasonable in view of the small coherence length of high-Tc materials Ž j a b ; 10 ˚ .. Treating RPr123 as a nanoscale mixture of suA perconducting and insulating regions is as reasonable as treating a mixture of submicron grains of Al Ž j ; 0.16 mm. and Al 2 O 3 as a composite of distinct superconducting and insulating materials. Second, Coulomb interaction is among the highest energyscale interactions in high-Tc materials, in which relatively covalent CuO 2 planes are embedded in strongly ionic crystals. Nevertheless, Coulomb interactions tend to be treated too casually, or even neglected altogether. Cation substitutions are often discussed only in relation with their effects on the hole concentration andror structural disorder. As we have been arguing, cation substitutions modify the Madelung potentials at various atomic sites, either directly through the valence effect or indirectly through structural changes, and have far-reaching influences on the electronic structure: the Madelung potential difference between the Cu and Pr sites is the major factor determining whether or not Pr ions interfere with superconductivity w24,25x, while that between the Cu and O sites is one of the main factors that control the maximum Tc in each cuprate superconductor w43,44x. We believe that proper considerations of inhomogeneity and Coulomb interaction are keys to understanding the properties not only of the R123-related compounds but also of the whole high-Tc materials.
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