Trapping mechanism of superconductivity suppression induced by Pr substitution in the Ho1−xPrxBa2Cu3O7−δ system

Physica C 320 Ž1999. 173–182

Trapping mechanism of superconductivity suppression induced by Pr substitution in the Ho 1yx Pr x Ba 2 Cu 3 O 7yd system Z. Tomkowicz

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Institute of Physics, Jagiellonian UniÕersity, Reymonta 4, 30-059 Krakow, ´ Poland Received 9 January 1999; received in revised form 30 March 1999; accepted 31 May 1999

Abstract Pr concentration dependence of the superconducting transition temperature Tc in the Ho 1yx Pr x Ba 2 Cu 3 O 7y d system is determined from measurements of DC electrical resistance. This dependence coincides with that for the parallely studied Y1yx Pr x Ba 2 Cu 3 O 7y d reference system. Both systems have the same value of the critical concentration x c s 0.58, in accordance with nearly equal ionic radii of Ho 3q and Y 3q ions. It has been shown that the Tc Ž x . curve can be described with a single mechanism based on a decreasing number of sheet holes trapped by Pr IV-ions, if one takes also into account that the number of these ions changes with x. q 1999 Published by Elsevier Science B.V. All rights reserved. PACS: 74.62.Dh; 74.72.Bk; 74.25.Fy Keywords: Superconductivity suppression; Pr substitution; Electrical resistivity; Metal–insulator transition

1. Introduction Superconductivity suppression by Pr substitution in the R 1y x Pr x Ba 2 Cu 3 O 7y d systems ŽR s rare earth or Y. is one of the most intensively studied problems in the field of high-Tc superconductivity. Three basic mechanisms of this suppression were considered w1x: Ži. hole filling due to possible near 4q valency of Pr-ion, Žii. magnetic pair-breaking, and Žiii. hole localization. However, recently, Zou et al. w2x succeeded in obtaining bulk superconductivity in PrBa 2 Cu 3 O 7y d crystals with the critical temperature Tc f 80 K. These crystals were grown by the travel-

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ing-solvent floating-zone ŽTSFZ. method. It is still not clear why the samples obtained by the TSFZ method are superconducting, whereas those obtained by other methods are not superconducting. Recognized so far features of TSFZ samples are: a larger c-axis lattice constant and a rapid increase of Tc with pressure Žup to ; 105 K at 10 GPa.. A possible cause of the superconductivity absence in PrBa 2 Cu 3 O 7y d might be an effect of Pr atoms in the Ba sublattice. Solubility of Pr in the Ba sublattice was studied for two cases: PrŽBa 2y x Pr x .Cu 3 O 7y d and RŽBa 2y x Pr x .Cu 3 O 7y d . It really takes place and is greater in the former case w3,4x. It has been shown in respect of superconductivity suppression that Pr on the Ba site behaves like all other trivalent R-ions w5x. Although in the case of PrBa 2 Cu 3 O 7y d , no interchange between Pr and Ba sites was observed

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 3 4 6 - 9

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Z. Tomkowiczr Physica C 320 (1999) 173–182

using neutron diffraction w6x, polarized neutron diffraction study w7x showed the substitution of 8% of the Ba by Pr-ions. In the light of the above, the superconductivity absence in PrBa 2 Cu 3 O 7y d seems to be even more puzzling because the small amount of Pr on the Ba sites cannot fully suppress the superconductivity. On the other hand, it is known that a considerable hybridization of Pr4f and O2p orbitals in PrBa 2 Cu 3 O 7y d takes place, which can be responsible for the superconductivity suppression and the high Neel ´ temperature TN f 17 K of Pr sublattice. The determined magnetic structure of Pr sublattice w8x rather excludes the possibility that the magnetic anomaly, observed at ; 17 K comes from PrBaO 3 impurity w9x. In spite of the possibility of superconductivity appearance in PrBa 2 Cu 3 O 7y d , its suppression for low Pr doping in the R 1y x Pr x Ba 2 Cu 3 O 7y d mixed system can be a legitimate phenomenon. In this work, we present a novel model describing this superconductivity suppression by Pr substitution in the samples prepared by the ceramic method. This model is based on the Pr–O hybridization. A clear picture of Pr–O hybridization was provided by Fehrenbacher and Rice w10x ŽF–R.. They explained the lack of superconductivity in PrBa 2Cu 3 O 7y d through the localization of holes in hybridized Pr4f–O2p p orbitals ŽF–R states., where they are transferred from Zhang–Rice ŽZ–R. states w11x. According to F–R, there are two kinds of Pr-ions, Pr III and Pr IV , which appear in almost equal proportions. The first of them is a normal ionic state Pr 3q Ž4f 2 ., the second is a mixture of the ionic state Pr 4q Ž4f 1 . and Pr 3q Ž4f 2 L. state, where L denotes a hole residing on the ligand. The resulting hybridized state ŽF–R state. has the wave function of the form
PrBa 2 Cu 3 O 7y d , who found that there are free holes in the chains and their number is nearly the same as for YBa 2 Cu 3 O 7y d . According to Widder et al. w13x, who performed analogous studies, free carrier concentration in chains is weakly affected by Pr doping in Y1y x Pr x Ba 2 Cu 3 O 7y d Žstrictly speaking, it decreased by about 14%.. It should be noted that in the F–R model not only chains but also mixed valent Pr III –Pr IV planes should be conducting. The fact that PrBa 2 Cu 3 O 7y d is a semiconductor was explained by F–R with an assumption that the DC conductivity of this compound is extremely sensitive to defects. Wang et al. w14x modified the F–R model, which allowed us to describe the metal–insulator transition ŽM–I. in Y1y x Pr x Ba 2 Cu 3 O 7y d at x ; 0.5 as intrinsic rather than extrinsic, as it is the case for the F–R model. However, Biagini et al. w15x calculated the electronic structure of PrBa 2 Cu 3 O 7y d using the LSDAq U method supporting the view of an extrinsic character of the insulating state of this compound. Liechtenstein and Mazin w16x ŽL–M. presented new calculations ŽLDA q UPr . of electronic structure starting from the F–R ideas. In their model, an additional ligand band, a ppp band Žoriginating from F–R states., crosses the Fermi level and seizes the holes. The position of this band should depend on R-ion, which can explain the ion size effect w17x, i.e., the critical concentration x c vs. ionic radius of R element dependence in R 1y x Pr x Ba 2 Cu 3 O 7y d . An important difference between the model of Wang et al. and that of L–M is that in the latter model the holes are continuously seized from Z–R states upon increasing Pr concentration even above x c . In the former, all sheet holes are seized already for x ; 0.5, near the Pr concentration at which superconductivity disappears. On further Pr doping, chain holes too are transferred to the F–R states, until for x s 1, the chains are depleted from the holes. Thus, the number of F–R states in PrBa 2 Cu 3 O 7y d is, according to this model, greater in comparison with the original F–R model. The model of Wang et al. does not necessarily have to be in contradiction with the optical reflectivity studies, because the authors pointed to another possibility of interpretation of these results. The F–R model predicts mixed or fluctuating valency of Pr-ion. Both such valencies were also proposed based on experimental studies. Moolenaar

Z. Tomkowiczr Physica C 320 (1999) 173–182

et al. w18x proposed fluctuating valency from the Mossbauer effect on 141 Pr in PrBa 2 Cu 3 O 7y d with ¨ the mean valency of 3.4 " 0.1. Mixed valency in turn was proposed by van Ancum et al. w19x. Hilscher et al. w20x performed XANES studies of Pr L III and Pr L II edges in PrBa 2 Cu 3 O 7 , PrBa 2 Cu 3 O6 and related compounds. They found that there is an admixture of about 15% of tetravalent Pr in PrBa 2Cu 3 O 7y d . Booth et al. w21x performed K-edge X-ray absorption fine structure ŽXAFS. studies for PrBa 2 Cu 3 O 7y d , results of which also support the F–R model. They showed that most of the Pr–O ˚ but about nearest neighbours distances are 2.45 A, ˚ Žin a range 15–40% of them are distributed at 2.27 A ˚ .. The shorter from 2.27 y 0.12 to 2.27 q 0.03 A distance should correspond to the tetravalent Pr-ion. O1s electron energy loss spectroscopy studies w22x for Y1y x Pr x Ba 2 Cu 3 O 7y d showed that the number of holes does not change with Pr concentration. This result is in agreement with a iodometric titration study of Kao et al. w23x for Gd 1y x Pr x Ba 2 Cu 3 O 7y d . The authors found that the total hole concentration is almost constant as a function of Pr doping and equals 0.8 " 0.02. Recently, however, Chen et al. w24x using XANES were able Žin spite of polycrystalline material. to determine the hole distribution in the electronic and crystal structure of Dy1y x Pr x Ba 2 Cu 3 O 7y d and showed that some hole depletion takes place not only in the CuO 2 planes, but also in the CuO 3 ribbons Žhowever, the hole count increases elsewhere.. This conclusion was confirmed by thermoelectric power study of Dy1y xPr x Ba 2 Cu 3 O 7y d performed by Huang et al. w25x Žthe same group.. In this work, the Ho 1y x Pr x Ba 2 Cu 3 O 7y d system was studied, for which the Tc Ž x . dependence was carefully determined. Up to now, the concentration dependence of critical temperature Tc has been well determined only for Y1y x Pr x Ba 2 Cu 3 O 7y d w1,26, 27x. The very form of Tc Ž x . dependence for other systems with R / Y was not so exactly studied. We have determined Tc Ž x . dependence for the Ho 1y x Pr x Ba 2 Cu 3 O 7y d system with the aim to compare it with that for the Y1y x Pr x Ba 2 Cu 3 O 7y d system. This comparison seems to be particularly interesting because the ionic radius of Ho 3q-ion is nearly equal to the ionic radius of Y 3q-ion. Thus, a small difference in Tc Ž x . can give a hint as to the mecha-

175

nism of superconductivity suppression. We will show that the obtained dependence Tc Ž x . can be understood using the F–R concept assuming a change in the number of Pr IV -ions with concentration.

2. Experimental All samples of the R 1y x Pr x Ba 2 Cu 3 O 7y d system, where R s Ho or Y, were prepared by the solid state reaction method. The samples of the Ho 1y x Pr xBa 2 Cu 3 O 7y d system were more difficult to synthesize and many trials were undertaken for obtaining good homogeneous samples. The preparation conditions, which we give below, had to be specially optimized for this system. Appropriate amounts of dried high purity components Žoxides and BaCO 3 . were mixed, hand pressed into pellets and calcined in an alumina boat in air at 9008C for 24 h. Then the samples were crushed, ground, pressed into pellets under press and sintered at 9308C for 30 h under flowing oxygen and cooled. This process was repeated several times and each time the temperature of sintering was increased slightly. This sintering temperature was dependent on Pr concentration. It was higher for higher Pr concentration. For x ; 0.50, it was about 9458C. It was near the melting point, which probably has a minimum in this range of concentration. Sintering time was 30 h each time, but in the last process it was 48 h. Finally, the samples were cooled under oxygen with a rate of 1.58rmin and kept 6 h in oxygen stream at 4508C before cooling to room temperature. Intermediary grindings during preparation were necessary to avoid phase separation as double superconducting transitions were otherwise observed. Nearly all samples were of good quality, single phased and had a pronounced texture as checked by means of X-ray powder diffractometer. Preferred orientation of the c-axis was perpendicular to the surface of pellets. The oxygen content was not checked, but the oxygenation conditions were sufficient for obtaining the full degree of saturation. Most difficult to synthesize were samples of the Ho 1y x Pr x Ba 2 Cu 3 O 7y d system with x about 0.15– 0.20, and we did not succeed in obtaining quite homogeneous samples. For these samples, resistance

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Z. Tomkowiczr Physica C 320 (1999) 173–182

vs. temperature curves showed a small anomaly at ; 90 K. However, no anomaly was seen on AC magnetic susceptibility vs. temperature curves. Samples of the Y1y x Pr x Ba 2 Cu 3 O 7y d system were prepared similarly. These samples were easier to obtain. The density of samples was approximately 85% of the theoretical value. For most measurements, the samples were cut into bars of approximately 2.5 = 2 = 10 mm3 dimensions. The cutting was performed along the diameter of pellets. DC electrical resistance was measured by means of the four point method using reversible current direction. The lowest attainable temperature in these measurements was 4.2 K. Contacts were made by soldering with In–Au alloy and their resistance at room temperature was below 1 V. A middle point Žstrictly, inflection point obtained by differentiation. of the resistive transition was taken as Tc .

3. Superconductivity suppression and its mechanism: results and discussion The temperature dependences of resistance for samples of the Ho 1y x Pr x Ba 2 Cu 3 O 7y d system are shown in Fig. 1. The samples with x - 0.60 show a superconducting transition. The width of the transi-

Fig. 1. Temperature dependences of electrical resistance for the Ho 1y x Pr x Ba 2 Cu 3 O 7y d system. The curves are normalized to the value of resistance at 290 K.

Table 1 Critical temperatures and some widths of transitions Žbetween 5% and 95% of transition. for the Ho 1y x Pr x Ba 2 Cu 3 O 7y d system x

Tc ŽK.

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.5 0.52 0.55 0.57 0.60

90.7 90.5 86.7 81.2 75.6 67.5 60.0 53.4 44.0 39.8 28.3 25.8 20.7 9.51 0

DTc ŽK. 1.5

2.0

4.4

5.6

10.4 13.5

tion increases with Pr concentration. However, this width does not decrease if samples are subjected to the additional preparation stage. Tc values and widths of transition are compiled in Table 1. The character of RŽT . curves is metallic for low x and high temperatures, but at low temperatures the semiconductor-like character begins to appear for x close to 0.6. The sample with x s 0.6 still shows a beginning of the transition. Above x s 0.6 the resistance is a decreasing function of temperature. The detailed characteristic of this function is the subject of another paper w28x. The Tc vs. x dependence obtained from RŽT . curves is shown in Fig. 2. A characteristic plateau is observed for low x, similarly as for the Y1y x Pr xBa 2 Cu 3 O 7y d system studied by Neumeier and Maple w26x. The obtained Tc Ž x . dependence agreed with that of Neumeier and Maple for the Y1yxPr x Ba 2 Cu 3 O 7y d system, except of that x c was 0.05 greater. It was important to check this result. To this end, we have prepared several samples of the Y1y x Pr x Ba 2 Cu 3 O 7y d system with x close to x c . Several additional samples were also prepared in order to check the agreement of Tc values in the remaining concentration region. A similar thermal treatment as for Ho 1y x Pr x Ba 2 Cu 3 O 7y d was used and the same method of data extraction. These newly obtained Tc values for Y1y x Pr x Ba 2 Cu 3 O 7y d matched the Tc Ž x . curve for Ho 1yx Pr x Ba 2 Cu 3 O 7y d

Z. Tomkowiczr Physica C 320 (1999) 173–182

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Žsupporting 4q valency of Pr. and hole generation by Ca-ions. As noted in Ref. w22x, this analysis is still tenable if one, instead of hole filling, assumes hole localization. According to this model, Tc is given by the expression 2

Tc Ž x , y . s Tc 0 y A Ž a y b x q y . y Bx ,

Fig. 2. Critical temperature vs. Pr concentration for Ho 1y x Pr x Ba 2 Cu 3 O 7y d and Y1yx Pr x Ba 2 Cu 3 O 7y d . The line is a polynomial fit through the points for Ho 1y x Pr x Ba 2 Cu 3 O 7y d to guide the eye. Vertical bars denote widths of transition for this system.

in the whole concentration range. The end part of this curve can be well fitted with the AŽ x c y x .1r2 function, which allows us to determine the exact value of x c equal to 0.58 " 0.004, the same for both systems. This means that the large magnetic moment of Ho 3q-ion has no influence on the superconductivity suppression induced by Pr-ions. Fig. 3 shows a comparison of the experimental Tc Ž x . curve ŽB. with the theoretical one being the best fit Žstarting from Tc0 s 90.7 K. to the magnetic pair-breaking theory of Abrikosov and Gorkov ŽAG. w29x. The difference of both curves is shown in the inset to Fig. 3. It is seen that the difference goes through a maximum at x ; 0.15 and saturates at about x ; 0.3. Neumeier et al. w30x measured Tc for the Y1y xyy Pr x Ca y Ba 2 Cu 3 O 7y d system as a function of x and y in the low concentration region, i.e., for x, y below 0.2. They observed that Ca substitution Žat constant x . increases initially Tc , which after passing through a maximum is decreasing. Ca, as is well known, supplies new holes which counteract the superconductivity suppression. The authors developed a phenomenological model describing Tc Ž x, y . data in the range x, y F 0.2. The model assigns Tc suppression with Pr doping to two mechanisms: change in the hole number and magnetic pair-breaking. The first one is a result of hole filling by Pr-ions

Ž 1.

where Tc0 is a maximum possible value of Tc , the second term represents hole generation by Ca-ions Ž y . and hole elimination Žfilling or localization. by Pr-ions Ž x ., a is an optimal hole concentration, b is the Pr valency in excess of 3q, Bx is the linear approximation Žvalid for low x . of the AG formula ŽEq. Ž2.. for Tc Ž x .. The best parameters obtained for the Y1y xyy Pr x Ca y Ba 2 Cu 3 O 7y d system were: Tc0 s 97 K, A s 425, a s 0.10, b s 0.95 " 0.20, and B s 96.5 K w30x. We performed analogous analysis for the Ho 1y x Pr x Ba 2 Cu 3 O 7y d system, but in the higher concentration range, up to x f 0.6. Therefore, we took the full implicit formula for Tc in the A–G theory ln

Tc 0

ž / ž Tc

sc

g

1 q 2

2p kTc

1

/ ž/ yc

2

,

Ž 2.

where Tc0 is the transition temperature in the absence of paramagnetic impurities, c is digamma function,

Fig. 3. Critical temperature vs. Pr concentration for Ho 1y xPr x Ba 2 Cu 3 O 7y d . The following are shown: experimental data, AG curves ŽA, C. and fit of the model, which takes into account the hole elimination and AG mechanism. Inset: a difference between the experimental dependence and the curve C Žsolid line is a guide to the eye..

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k is the Boltzmann constant, and g is a pair-breaking parameter assumed as proportional to the concentration of magnetic impurities. Both mechanisms were fitted to the experimental data in two following ways. According to the first, the hole-elimination contribution was stopped at some concentration x h preserving a constant value up to x f 0.6. Fits obtained in this way were not satisfactory. According to the second way, the hole-elimination contribution was stopped at x h and zero value for it was put for x ) x h . Only for x h - 0.25 fits were satisfactory Žsee Fig. 3.. The following values of parameters were obtained with x h s 0.20: Tc0 s 100.7, A s 441, a s 0.15, b s 0.82 " 0.20 and B s 119.9 " 5 Ž B s pgr4kx .. The difference with respect to the results of Neumeier et al. w30x originates mainly from the fact that the A–G contribution is in our case constrained by the high x part of the Tc Ž x . curve. The A–G curve, corresponding to the obtained values of Tc0 and B, is shown in Fig. 3, marked with the letter A. The existence of the specific point x h could mean that a valency change from 4q to 3q occurs at x h . In fact, a valency change with Pr doping was predicted by Lundqvist et al. w31x but taking place gradually in the whole x region. This is in contrast with Tomkowicz et al. w32x who found that the valency of Pr-ion is not greater than 3.2 in the low x region. Also, the magnetization study w33x supports the valency near 3q for low Pr doping. This moderately good description by two contributions, given above, seems to be a little artificial. Therefore, it would be of purpose to have an experimental evidence of the A–G contribution from an independent source. Some piece of evidence comes from the magnetization study of Y1y x Pr x Ba 2Cu 3 O 7y d , performed by Peng et al. w34x, who observed a bell shaped behavior of critical fields Ž Hc2 . vs. T. However, Hc2 ŽT . curves obtained for Gd 1y x Pr x Ba 2 Cu 3 O 7y d system by the resistive method showed no bell-like shape w35x. Thus, no definite conclusion about the presence of A–G mechanism can be drawn. Maple et al. w36x showed that the A–G mechanism cannot be the primary mechanism for the superconductivity suppression in the R 1y x Pr x Ba 2 Cu 3 O 7y d system. No fit improvement was obtained with a generalized A–G theory w37x, which takes into account an

anisotropy of superconducting order parameter. By the way, this theory also gives a linear Tc Ž x . dependence for low x and, moreover, is valid for nonmagnetic impurities. It should be noted that theories of superconductivity suppression taking into account simultaneously disorder and Coulomb interaction w38,39x predict a linear Tc Ž x . dependence for a low concentration of impurities. The question arises if these theories can be used instead of the A–G theory for the description of the observed Tc Ž x . curve. In Ref. w28x 1, we show that at x close to 0.6, the CuO 2 planes become insulating. Because the A–G mechanism has nothing in common with M–I transition, it was important to find another mechanism that would be compatible with the existing M–I transition. Therefore, it was necessary to test the validity of the above theories for our case. Unfortunately, these theories predict Tc Ž x . dependence, which is inconsistent with experiment for higher x region, and it was not possible to change its character by varying parameters. Here, we propose another mechanism of superconductivity suppression based on the F–R model w10x of electronic structure of PrBa 2 Cu 3 O 7y d . It consists in hole depletion in CuO 2 planes as a result of their trapping at Pr-sites Žsee Section 1. and is in principle not much different from that described by the square term of Eq. Ž1.. However, we would like to extend this description to the whole superconductivity region x F 0.6. Taking into account the premise that the M–I transition and the disappearance of superconductivity take place nearly at the same Pr concentration we can disregard the A–G mechanism. Any assistance of the A–G mechanism would always cause an earlier disappearance of superconductivity before the M–I transition occurs. Let us look again at the Tc Ž x . curve in Fig. 4. Two parabolas, which are drawn through the points in a low x region, correspond to different number Õ 0

1 In this work, comparative studies of electrical transport in the nonsuperconducting part of the Ho 1y x Pr x Ba 2 Cu 3 O 7y d system and relative differently doped systems have been carried out. It has been obtained that the suppression of superconductivity in the Ho 1y x Pr x Ba 2 Cu 3 O 7y d system is connected with a M–I transition in the CuO 2 planes Žat x close to 0.6., but chains are still conducting and become insulating only in the limit of x s1.

Z. Tomkowiczr Physica C 320 (1999) 173–182

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Pr x Ba 2 Cu 3 O 7y d . Our consideration presumes that there is about 80–90% of Pr IV -ions in the low x region. Let us assume that the relative number Õ 0 b of trapping Pr IV -ions Žwith respect to the whole number of Pr-ions. changes with Pr concentration and this change is described by b parameter, normalized to 1 for x s 0. Thus, instead of Eq. Ž3., we come to the following equation:

½ ž

Tc s Tc 0 1 y

Fig. 4. Critical temperature vs. Pr concentration for Ho 1y xPr x Ba 2 Cu 3 O 7y d ; see text for details. Inset shows the concentration dependence of the relative number Õ 0 b of Pr IV -ions Žwith respect to all Pr-ions. corresponding to different values of Õ 0 from the main figure; Õ 0 b x denotes the relative number of Pr IV -ions Žwith respect to all R-ions. being equal to the number of trapped holes; 0.8y Õ 0 b x denotes the number of remaining mobile holes, which can be compared with the Hall number n H X shown as a function of x Žafter Ref. w40x., n H is the derivative of n H with respect to x; curve L shows the concentration dependence of Pr valency in excess of 3 Žafter Ref. w31x.. Dashed lines in the inset above x s 0.6 are hypothetical Žsee text..

of holes localized by one Pr-ion. General equation of these parabolas is Õ0

2

½ ž /5

Tc s Tc 0 1 y

n sh

x

,

Ž 3.

where n sh is the number of sheet holes Žper unit cell.. It is known, that there are n sh f 0.4 hole in CuO 2 planes to localize, so the disappearance of superconductivity after parabola at x f 0.5 is expected when each Pr localizes Õ 0 s 0.8 hole Žcurve labeled Õ 0 s 0.8 in Fig. 4. and the disappearance at x f 0.45 is expected when each Pr localizes Õ 0 s 0.9 hole Žcurve labeled Õ 0 s 0.9.. However, superconductivity persists up to x s 0.6. This could mean that not only the second suppressing mechanism should not exist, but to the contrary, there exists some factor supporting superconductivity in the higher x region. In the F–R model, every Pr IV –O hybrid traps one hole and the relative number of Pr IV -ions in PrBa 2 Cu 3 O 7y d is about half. Let this parameter be allowed to change with concentration in R 1y x-

Õ0 b Ž x . n sh

2

x

/5

.

Ž 4.

The obtained b Ž x . dependences, describing the deviation of the experimental Tc Ž x . curve from the parabolas in Fig. 4, are shown in the inset to Fig. 4 in the form of Õ 0 b Ž x . curves. Unfortunately, our model does not predict the value of Õ 0 b for x above 0.6. The dashed line in the inset for x ) 0.6 is a hypothetical dependence. It is noted that in our model, Õ 0 b Ž1. should be equal to the number of trapped holes in PrBa 2 Cu 3 O 7y d , which after Wang et al. w14x should be equal to the number of all holes, thus, is greater than after F–R Žwe recall that the value of Õ 0 b Ž1. expected after F–R is about 0.5.. It will be shown in Ref. w28x 1 that only the model of Wang et al. is compatible with transport properties for x ) 0.6. Thus, we take the value of Õ 0 b Ž1. equal ; 0.8. 2 If the value of Õ 0 b Ž1. really equals 0.8, according to F–R, the total probability of Pr4f 1 configuration is roughly 0.2. Some recent experimental studies dealing with mixed or fluctuating valency give averaged value of valency of Pr-ion in PrBa 2Cu 3 O 7y d close to 3.4 Žsee Refs. w18,21,41x. in a relatively good agreement with our predictions. Our result for the concentration dependence of the relative number Õ 0 b of Pr IV -ions is compared in the inset with results of other authors. We show the derivative of the concentration dependence of the Hall number taken from Ref. w40x. The very concentration dependence of the Hall number is also

2 It is assumed after Kao et al. ŽRef. w23x. that the overall number n t of holes in the R 1yx Pr x Ba 2 Cu 3 O 7y d system is ; 0.8: 0.4 sheet hole plus 0.4 chain hole. This value of n t does not change with x ŽRefs. w22,23x.. The full agreement with the model of Wang et al. needs n t s1.

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Z. Tomkowiczr Physica C 320 (1999) 173–182

shown. 3 The Pr valency in excess of 3, obtained by Lundqvist et al. w31x, is shown by open circles Žcurve L; qualitative agreement with results of Lundqvist et al. can be obtained for low x under assumption that the weight of Pr4f 1 configuration in the F–R state is high.. The inset to Fig. 4 shows also the product Õ 0 b x. This quantity has interpretation of the relative number of Pr IV -ions with respect to all rare earth ions, or of the number of holes trapped by F–R states. It is interesting to compare it with that obtained by L–M w16x. In our case, all sheet holes are trapped already at x f 0.6. Above this concentration, the holes transferred from chains are trapped too until x s 1. In the case of the L–M model, sheet holes are still trapped above x f 0.6. It is worth to note that the ionic size effect Žsee Section 1. can now be easily understood with varying depth and position of the minimum in Õ 0 b Ž x .. The minimum value of Õ 0 b Ž x . in the inset to Fig. 4 is 0.65 at x s 0.53. A comparison of Õ 0 b Ž x . for different R 1y x Pr x Ba 2 Cu 3 O 7y d systems would be interesting in this aspect. In the case of the Nd 1y x Pr x Ba 2 Cu 3 O 7y d system the value of x c is reported in limits 0.30–0.40 w3,4,42x. Such a low value can be hardly obtained with our model. However, the presence of some Nd atoms at Ba sites can be an additional suppressing factor. Looking at the inset in Fig. 4, one can speculate that if Õ 0 b Ž x . curve instead to go up for x G 0.5 would go down approaching a value below 0.4 for x s 1, the compound PrBa 2 Cu 3 O 7y d would be superconducting. Thus, the superconductivity suppression in the Ho 1y x Pr x Ba 2 Cu 3 O 7y d system is understood by the hole localization at Pr IV -ions, the relative number of which changes with the concentration. The M–I transition in CuO 2 planes at x f x c is the natural consequence of trapping all sheet holes. If an additional suppressing mechanisms would contribute, or

if some threshold number of sheet holes 4 is necessary for superconductivity to occur, then small concentration difference between x c and x for M–I transition will appear. Xiong et al. w43x suggest, based on Hall angle measurements for Y1y x Pr xBa 2 Cu 3 O 7y d that not only decreasing number of holes, but also their mobility contributes to superconductivity suppression. It is also worth mentioning the isotope effect, which nearly absent for the optimally doped YBa 2 Cu 3 O 7y d , appears with Pr substitution w44–46x. Taking all that into account, it seems that not only change in the hole number, but also some modification of the pairing mechanism takes place in the superconductivity suppression process with Pr doping. Therefore, a small concentration difference between the superconductivity disappearance and M–I transition in CuO 2 planes is expected Ži.e., 0.58 against 0.65 w28x.. The A–G mechanism cannot be completely excluded, at least for higher x. It was shown by magnetic measurements w47x that the sample Y0.95Pr0.05 Ba 2 Cu 3 O 7y d shows paramagnetism for T ) Tc . However, magnetization hysteresis loops of Y1y x Pr x Ba 2 Cu 3 O 7y d obtained at 5 K, show no paramagnetic contribution for x - 0.1 in magnetic fields up to 5 T. Nehrke and Pieper w48x proposed a nonmagnetic state of Pr-ion in PrBa 2 Cu 3 O 7y d . Although it has appeared not very probable w49,50x, nevertheless, it can occur for low Pr doping. In this case, Pr would be nonmagnetic because of a singlet crystal-field ground state, very distant from the first excited level. With higher Pr doping Pr-ions could become magnetic and the A–G mechanism could be operative if hybridization of the Pr4f and CuO 2 states were considerable. A high degree of this hybridization for x R 0.3 follows from the fact that Tc is strongly depressed by pressure in Y1y x Pr xBa 2 Cu 3 O 7y d for x G 0.3 w51,52x. However, the authors were not able to establish if the pair-breaking parameter B changes with pressure. Instead, they established that the number of holes localized per Pr-ion increases with pressure. The other possibility was proposed by Xu and Guan w53x. Here, Pr would

3

Chains are expected not to contribute to n H . Although there is some problem with calibration of n H , it is believed that n H should scale with the number of holes. It is worth to note that no anomaly is seen on n H Ž x . curve at x s 0.23, where according to Jiang et al. wPhys. Rev. B 55 Ž1997. R3390x chains become insulating.

4

According to Wood wPhys. Rev. Lett. 66 Ž1991. 829x, superconductivity does not occur until n sh s 0.07.

Z. Tomkowiczr Physica C 320 (1999) 173–182

be nonmagnetic for low x, because very quick fluctuations average Pr magnetic moment to zero Žthis scenario assumes an enhanced hybridization for low x .. It would be very desirable to solve the problem of the ground state magnetic moment both for low Pr doping, as well as for PrBa 2 Cu 3 O 7y d , to determine conditions for the appearance of superconductivity in this compound. 4. Concluding remarks Superconducting properties of the Ho 1y x Pr x Ba 2Cu 3 O 7y d system were studied by measurements of DC electrical resistance. The obtained concentration dependence of critical temperature for Ho 1y xPr x Ba 2 Cu 3 O 7y d does not essentially differ from that for the Y1y x Pr x Ba 2 Cu 3 O 7y d system. Both systems have the same critical concentration for the superconductivity disappearance. The mechanism of superconductivity suppression, which was proposed, is based on the hole trapping. For low Pr concentration, nearly all Pr-ions are the trapping Pr IV -ions. With increasing Pr concentration, the relative number of trapping Pr IV -ions decreases. In this mechanism, CuO 2 planes become insulating at x f 0.6 as a natural consequence of the trapping all sheet holes. Acknowledgements Thanks are due to M. Balanda for performing AC susceptibility measurements. J. Spałek and K. Tomala are acknowledged for discussion. References w1x H.B. Radousky, J. Mater. Res. 7 Ž1992. 1917, Review article. w2x Z. Zou, J. Ye, K. Oka, Y. Nishihara, Phys. Rev. Lett. 80 Ž1998. 1074. w3x K. Zhang, B. Dabrowski, C.U. Segre, D.G. Hinks, I.K. Schuller, J.D. Jorgensen, M. Slaski, J. Phys. C: Solid State Phys. 20 Ž1987. L935. w4x A. Suzuki, E.V. Sampathkumaran, K. Kohn, T. Shibuya, A. Tohdake, M. Ishikawa, Jpn. J. Appl. Phys. 27 Ž1988. L792. w5x M.J. Kramer, K.W. Dennis, D. Falzgraf, R.W. McCallum, S.K. Malik, W.B. Yelon, Phys. Rev. B 56 Ž1997. 5512. w6x A.K. Ganguli, C.N.R. Rao, A. Sequeira, H. Rajagopal, Z. Phys. B: Condens. Matter 74 Ž1989. 215.

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