Upper critical field of four-CuO2-layer TlBa2Ca3Cu4O111d

single crystals

Lu Zhanga,* , J.Z. Liub, R.N. Sheltonb

aDepartment of Physics, California State University, Stanislaus, 801 West Monte Vista Avenue, Turlock, CA 95382, USAbDepartment of Physics, University of California, Davis, CA 95616, USA

Received 17 September 1998; accepted 17 December 1998 by S.G. Louie

Abstract

Measurements of magnetization in the reversible region were performed as a function of temperature on TlBa2Ca3Cu4O111d

single crystals in magnetic fields up to 5.5 T with the field direction applied along the crystallinec-axis. A linear temperaturedependence was observed between 70 and 116 K for the reversible magnetization and the slope,�dM�=�dT�, decreased withincreasing field strength. NearTc (128 K), the magnetization showed a rounding. Both the field-dependent dM/dT – values inthe linear region and the rounding behavior of the magnetization nearTc indicated that the upper critical field,Hc2, in theTlBa2Ca3Cu4O111d system might be very large. Therefore, the reversible magnetization was measured in the low field range, i.e.H p Hc2, and the traditional method used to obtain theHc2 value based on the Abrikosov formula nearHc2 was not applicable.By using the model of Hao et al. [Z. Hao, J.R. Clem, M.W. McElfresh, L. Civale, A.P. Malozemoff, F. Holtzberg, Phys. Rev. B43 (1991) 2844], the reversible magnetization data were analyzed to determine the Ginzburg–Landau parameterk and the slopeof the upper critical field atTc, (dHc2/dT)uTc

. It was found thatk � 109, andHc2(0)� 160 T in the TlBa2Ca3Cu4O111d crystalswith the field parallel to thec-axis.q 1999 Elsevier Science Ltd. All rights reserved.

Keywords:A. High-Tc superconductors

1. Introduction

The unusually high upper critical field is one of thecrucial properties of high-Tc superconductors (HTS).Typical values ofHc2 for HTS, such ast100 T for theYBa2Cu3O72d system, are much larger than the stron-gest static magnetic field attainable at present. Numer-ous applications of HTS in strong magnetic fieldsdepend on this property [1].

Upper critical field studies in HTS also give impor-tant information about parameters characterizing thenormal Fermi-liquid and superconducting states [2].

Hc2(T) is determined by diamagnetic pair breakingnear Tc. The possible presence of a Pauli limit atlower temperatures, i.e. the breaking of spin align-ments preferred by the superconducting state, allowsfor conclusions concerning the symmetry type ofthe superconducting order parameter. The slope ofHc2(T) at Tc, �dHc2�=dT�uTc

, is influenced by thequasiparticle band structure of the pure material andby impurities.

Traditionally, the temperature dependence of theupper critical field was determined from the super-conducting transition curve at various magnetic fieldsobtained from experiments of resistivity, a.c. suscept-ibility, calorimetry and others. However, the tradi-tional method is complicated in HTS by an unusual

Solid State Communications 109 (1999) 761–766

SSC 4579

0038-1098/99/$ - see front matterq 1999 Elsevier Science Ltd. All rights reserved.PII: S0038-1098(99)00018-6

PERGAMON

* Corresponding author. Tel.: 209-667-3774; fax: 209-667-3099E-mail: zhang@toto.csustan.edu (L. Zhang)

broadening of the superconducting transition in themagnetic field as a result of the strong influence offlux flow and flux creep phenomena. It is argued thatHc2(T) obtained by the transition curve from resistivityand a.c. susceptibility experiments may only representthe onset of flux line motion as the magnetizationcurve becomes irreversible at these points [3–5].However, the classical Abrikosov formula [6] usedto determine theHc2 value by an extrapolation of thelinear portion of the d.c. magnetization is not accuratebecause the Abrikosov formula is given at the fieldsnearHc2 and dM=dT is expected to be field indepen-dent. Recently, Hao et al. developed a model [7] toobtain the Hc2 value by analyzing the reversiblemagnetization versus temperature in the intermediatefield range ofHc1 , H , Hc2.

The purpose of the present study is to investigatethe upper critical field properties of TlBa2Ca3-

Cu4O111d crystals and to obtain some important para-meters such ask andHc2(0). The TlBa2Ca3Cu4O111d

compound has a unique structure of four CuO2 layerswith a superconducting transition temperature of128 K [8], a critical current density of 1.6× 105 A/cm2 at 50 K [9] and a thermal activation energybarrier of 5 meV at 5 T [10]. The reversible magneti-zation versus temperature was measured on the TlBa2-Ca3Cu4O111d crystals in magnetic fields up to 5.5 Twith the field direction applied along the crystallinec-axis. The model of Hao et al. [7] was used in theanalysis of reversible magnetization data to obtainthe upper critical fieldHc2(T) and other superconduct-ing parameters.

2. Experimental

High quality TlBa2Ca3Cu4O111d single crystalswere prepared by a self-flux method. The crystal hasa tetragonal structure with a space group of P4/mmm,lattice parameters ofa � b � 0.384 nm andc �1.873 nm, and contains four CuO2 layers in eachunit cell. The superconducting transition temperatureis 128 K with a 10%–90% transition width of 8 Kmeasured by d.c. susceptibility. The details of thecrystal structure, sample preparation and characteriza-tion were reported in a previous publication [8].

A superconducting quantum interference device(SQUID) magnetometer was used in relaxationexperiments for TlBa2Ca3Cu4O111d crystals. The crys-tal was glued with GE-7031 varnish in a samplecapsule to insure that the crystal did not move andthat the magnetic field was applied along the crystal-line c-axis during the measurements. Before the startof each relaxation experiment, the sample was firstwarmed to 150 K (well aboveTc). The superconduct-ing magnet was reset such that the remnant field wasless than 1024 T. Once the field was quenched, thesample was zero-field-cooled to a desired tempera-ture. The crystal orientation with respect to theapplied field was checked by measuring the magneti-zation versus field at fields below the lower criticalfield, Hc1. The slope ofM(H) (H , Hc1) correspondedto 100% shielding and the demagnetization factor(degree of orientation) was determined to be around0.8 with 5% variation for all relaxation measurementsin the TlBa2Ca3Cu4O111d crystals. Then the magnetic

L. Zhang et al. / Solid State Communications 109 (1999) 761–766762

Fig. 1. The irreversibility line for field parallel to thec-axis of the TlBa2Ca3Cu4O111d crystal.

field was applied using the SQUID in the no-over-shoot mode. The scan length was set at 3.0 cm tominimize the variation in the magnetic field throughwhich the sample travels. An iterative regressionmode was used to calculate the magnetization of thesample.

In order to measure the reversible magnetization,the irreversible line was first determined in the TlBa2-

Ca3Cu4O111d crystals. The temperature,Tirr, whichwas defined as the low temperature limit of the rever-sible range, was measured at various fields [11]. TheTirr values decreased from 70 K at 0.4 T to 32 K at5.5 T, as shown in Fig. 1.

The reversible magnetization was measured under

the magnetic field up to 5.5 T and at temperaturesbetween 70 and 128 K. A normal state baseline wasobserved to be temperature independent fromTc to150 K which indicated that the background wascaused by the sample holder and could be subtractedfrom the data. Fig. 2 exhibits the resultant magnetiza-tion in the reversible region at different fields orientedparallel to thec-axis. In the reversible region, weobserved that the magnetization showed a nearlylinear temperature dependence except for the curva-ture found nearTc. The slope d�4pM�=dT varied from236 G/K at 0.4 T to27.7 G/K at 5.5 T and followeda logarithmic field dependence as shown in Fig. 3.

3. Results and discussion

The reversible magnetization data were used in theupper critical field studies of the TlBa2Ca3Cu4O111d

crystals based on the model of Hao et al. [7]. Somedetails of the model and three non-linear equationsused for Hc2 analysis were described in Ref. [13].From the reversible magnetization versus field at agiven temperature, ak -value can be obtained fromthe smallest deviation of the value of

��2p

Hc�T�where k is the Ginzburg–Landau parameter andHc2�T� � k

��2p

Hc�T�. The data points used in theanalysis to obtaink andHc2(T) were from the rever-sible linear magnetization in the range 0.4 T, H ,5.5 T. Thek -value was found to be 109̂ 10 for thetemperatures between 70 and 116 K, which wasexpected to be temperature independent from the

L. Zhang et al. / Solid State Communications 109 (1999) 761–766 763

Fig. 2. Magnetization vs. temperature for fields parallel to thec-axis of the TlBa2Ca3Cu4O111d crystal.

Fig. 3. The slope of2d(4pM)/dT as a function of fields in the linearregion of magnetization vs. temperature of the TlBa2Ca3Cu4O111d

crystal.

model of Hao et al. The largek -value suggests thatthe TlBa2Ca3Cu4O111d system is an extreme-type-IIsuperconductor, which is consistent with theYBa2Cu3O72d [7] and Bi1.7Pb0.3Sr2CaCu2O8 [12]systems. TheHc2(T) has a linear temperature depen-dence with dHc2/dTuTc

being21.8 T/K for the TlBa2-Ca3Cu4O111d crystals (Fig. 4).

Generally, there are two major mechanisms forpair breaking: orbital pair breaking and Paulilimiting. Both mechanisms lead to the destructionof the superconductivity at upper critical fields.The Pauli limit occurs because of the influenceof magnetic field on the electrons in the super-conducting state. The Pauli paramagnetic limitingfield, Hpo, in the absence of spin–orbit scatteringwas given by Clogston [13]

Hpo �0� � 1:84Tc:

Usually orbital pair breaking takes place at lowmagnetic fields and determines the initial slope ofthe upper critical field atTc. One can obtain the orbitalcritical field asT! 0, Hc2*(0), from an extreme-type-II electron-spin effect theory of Werthamer, Helfandand Holhenverg (WHH) [14]:

Hc2* �0� � 0:693 2:dHc2

dTuTc

� �Tc:

The values ofHpo(0) andHc2*(0) in the TlBa2Ca3-

Cu4O111d crystals were estimated to be 240 and 160 T,respectively. AsHc2*(0) , Hpo(0), it can be concludedthat the upper critical field is limited by the orbital pairbreaking andHc2(0) � 160 T.

Another formula for the upper critical field fromFetter and Hohenberg (FH) [2] is

Hc2�0� � 0:5758k1�0�k

2:dHc2

dTuTc

� �Tc;

wherek1�0�=k equals 1.20 and 1.26 in the dirty andclean limits, respectively. The WHH formula yieldsthe sameHc2(0) values as the FH formula does in thedirty limit. However, the FH formula yields theHc2

values within 5% between the dirty and clean limits.For HTS, the experimental uncertainly caused by ther-mal fluctuation is relatively high and thek -valuesobtained by the model of Hao et al. usually vary byabout 10%. Therefore, the difference in theHc2(0)value between the clean and dirty limits is not signifi-cant for HTS.

Among manyHc2(0) values obtained by using thesame model of Hao et al. [7], aHc2(0)-value as high as

L. Zhang et al. / Solid State Communications 109 (1999) 761–766764

Fig. 4. The upper critical field vs. the applied magnetic field for the field orientation in thec-axis of the TlBa2Ca3Cu4O111d crystal.

Table 1List of the upper critical field parameters for some HTS compoundsand two conventional commercial superconductors.Tc is the super-conducting transition temperature measured by d.c. susceptibility.dHC2=dTuTc

is the slope of the upper critical field atTc. All of theHTS data are obtained from single crystal studies for the fieldapplied parallel to thec-axis

Compound Tc (K) 2dHC2=dTuTc�T=K� Hc2(0)

TlBa2Ca3Cu4O111d 128 1.8 160 TBi1.7Pb0.3Sr2CaCu2O8 96 1.5 90 TYBa2Cu3O72d 94 1.65 89 TNb–Ti 9 11 T (4 K)Nb3Sn 18 22 T (4 K)

300 T was reported in thec-axis-oriented Bi2Sr2Ca2-Cu3O10 polycrystals assuming orbital pair breakingwas the dominant mechanism [15]. However, usingthe data given in the same publication, the Pauliparamagnetic limiting field,Hpo(0), can be calculatedto be 198 T. Therefore, the upper critical field mightbe lower than 300 T if Pauli limiting or the spin–orbital interaction mechanism as found in the heavyfermion systems is responsible for pair breaking inthat case.

Table 1 lists some upper critical field data for HTS.The Hc2(0) values were about 90 T for both double-CuO2-layer materials YBa2Cu3O72d [7] andBi1.7Pb0.3Sr2CaCu2O8 [12], compared with 160 T inthe four-CuO2-layer TlBa2Ca3Cu4O111d compound.Similar to Tc, the Hc2(0) value increases with thenumber of CuO2 layers, which might be caused by ahigher carrier concentration in the materials with alarger number of CuO2 layers. However, theHc2(T)value is about 92 T at 77 K, which is much larger thanthose of conventional commercial superconductors.For Nb–Ti, theTc is 9 K andHc2(4 K) is 11 T, andfor Nb3Sn it is 22 T withTc � 18 K. Therefore, HTSare not only conceptually interesting in understandingthe microscopic magnetism, but also practicallyimportant with respect to strong magnetic fieldapplications.

The phase diagram of a conventional supercon-ductor is determined by the ratio of the penetrationdepth to the coherence length. The penetration depth,l , is defined as the characteristic length scale overwhich the magnetic field varies within the material.The coherence length,j , is the characteristic lengthused to measure the variation of the order parameter.These superconducting parameters can be determinedby upper critical field studies. The coherencelength at zero temperature,j0, can be determined

from the equation

Hc2�0� � F0

2pj20

;

whereF0 � 2.07 × 10215 T m2 is the flux quantum.j0 � 1.4 nm was calculated assuming the clean limit.The penetration depth,l , can be determined fromk �l /j andl0� 150 nm was obtained for the TlBa2Ca3-Cu4O111d crystals. In comparison (see Table 2),the Ginzburg–Landau parameterk was 53 inYBa2Cu3O72d compared with 92 and 109 inBi1.7Pb0.3Sr2CaCu2O8 and TlBa2Ca3Cu4O111d , respec-tively. This indicates that the extreme anisotropicsuperconductors (such as Bi2Sr2CaCu2O8 and TlBa2-

Ca3Cu4O111d ) might have higherk values than thosein very anisotropic superconductors (such asYBa2Cu3O72d).

4. Conclusion

In conclusion, we have used the reversible, lineartemperature dependence of the d.c. magnetization ofTlBa2Ca3Cu4O111d crystals to determine the equili-brium upper critical fields of this material. Theupper critical field slope,�dHc2=dT�uTc

, of TlBa2Ca3-Cu4O111d crystals is found to be21.8 T/K for thec-direction. Using the WHH formalism, the zerotemperature orbital upper critical field is 160 T. Theassociated coherent length and London penetrationdepth are 1.4 and 150 nm, respectively.

Acknowledgements

This research is supported by the National ScienceFoundation under grant numbers DMR-95-32-085and DMR-97-01735.

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L. Zhang et al. / Solid State Communications 109 (1999) 761–766 765

Table 2List of superconducting parameters for some HTS superconductors.k is the Ginzburg–Landau parameter.j0 andl0 are the coherencelength and the penetration depth in theabplane at zero temperature,respectively

Compound k j0 (nm) l0 (nm)

TlBa2Ca3Cu4O111d 109 1.4 150Bi1.7Pb0.3Sr2CaCu2O8 92 2.0 178YBa2Cu3O72d 57 1.75 102

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