Thermodynamic (specific heat, reversible magnetization, tunneling
spectroscopy) and transport measurements have been performed on high quality
(K,Ba)BiO$_3$ single crystals. The temperature dependence of the magnetic field
$H_{Cp}$ corresponding to the onset of the specific heat anomaly presents a
clear positive curvature. $H_{Cp}$ is significantly smaller than the field
$H_\Delta$ for which the superconducting gap vanishes but is closely related to
the irreversibility line deduced from transport data. Moreover, the temperature
dependence of the reversible magnetization present a strong deviation from the
Ginzburg--Landau theory emphasazing the peculiar nature of the superconducting
transition in this material.Comment: 4 pages, 4 figures, 28 reference

A. A. Abrikosov

A. Carrington

A. G. M. Jansen

A. Junod

A. P. Mackenzie

A. S. Alexandrov

A. Schilling

A. Sulpice

B. F. Woodfield

C. Marcenat

D. Hall

D. R. Nelson

F. Bouquet

F. Marsiglio

G. Blatter

I. Joumard

I. W. Sumarlin

J. E. Graebner

J. Marcus

L. N. Bulaevskii

M. Roulin

M. S. Osofski

M. Tinkham

P. De Gennes

P. F. Sullivan

P. H. Kes

P. Samuely

P. Szabo

R. G. Dias

S. Blanchard

T. Klein

U. Welp

V. F. Gantmakher

V. J. Emery

Y. N. Ovchinnikov

Z. Hao

English

arXiv

International audienceThermodynamic (specific heat, reversible magnetization, tunneling spectroscopy) and transport measurements have been performed on high quality K, Ba BiO3 single crystals. The temperature dependence of the magnetic field HCp corresponding to the onset of the specific heat anomaly presents a clear positive curvature. HCp is significantly smaller than the field HD for which the superconducting gap vanishes but is closely related to the irreversibility line deduced from transport data. Moreover, the temperature dependence of the reversible magnetization presents a strong deviation from the Ginzburg-Landau theory emphasizing the peculiar nature of the superconducting transition in this material

Blanchard, S.

Klein, Thierry

Marcus, J.

Joumard, I.

Sulpice, A.

Szabo, P.

Samuely, P.

G. M. Jansen, A.

Marcenat, C.

HAL: Hyper Article en Ligne

Anomalous Magnetic Field Dependence of the Thermodynamic Transition Line in the Isotropic Superconductor K,Ba BiO3

Hal - Université Grenoble Alpes

Anomalous Magnetic Field Dependence of theThermodynamic Transition Line in the IsotropicSuperconductor K,Ba BiO3S. Blanchard, Thierry Klein, J. Marcus, I. Joumard, A. Sulpice, P. Szabo, P.Samuely, A. G. M. Jansen, C. MarcenatTo cite this version:S. Blanchard, Thierry Klein, J. Marcus, I. Joumard, A. Sulpice, et al.. Anomalous Mag-netic Field Dependence of the Thermodynamic Transition Line in the Isotropic Superconduc-tor K,Ba BiO3. Physical Review Letters, American Physical Society, 2002, 88, pp.177201.<10.1103/PhysRevLett.88.177201>. <hal-00959104>HAL Id: hal-00959104https://hal.archives-ouvertes.fr/hal-00959104Submitted on 13 Mar 2014HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.VOLUME 88, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 29 APRIL 2002Anomalous Magnetic Field Dependence of the Thermodynamic Transition Linein the Isotropic Superconductor K, BaBiO3S. Blanchard,1 T. Klein,1,2 J. Marcus,1 I. Joumard,1 A. Sulpice,3 P. Szabo,2,4P. Samuely,4 A. G. M. Jansen,5 and C. Marcenat61Laboratoire d’Etudes des Propriétés Electroniques des Solides, Centre National de la Recherche Scientifique,BP 166, F-38042 Grenoble Cedex 9,France2University Joseph Fourier, BP 53, F-38041 Grenoble Cedex 9, France3Centre de Recherche sur les Très Basses Températures, Centre National de la Recherche Scientifique,BP 166, 38042 Grenoble Cedex 9, France4Institute of Experimental Physics, Slovak Academy of Sciences, SK-04353 Kosˇice, Slovakia5Grenoble High Magnetic Field Laboratory, Max-Planck-Institut für Festkörperforschung andCentre National de la Recherche Scientifique, BP 166, F-38042 Grenoble Cedex 9, France6Commissariat à l’Energie Atomique–Grenoble, Département de Recherche Fondamentale sur la Matière Condensée,SPSMS, 17 rue des Martyrs, F-38054 Grenoble Cedex 9, France(Received 20 September 2001; published 11 April 2002)Thermodynamic (specific heat, reversible magnetization, tunneling spectroscopy) and transport mea-surements have been performed on high quality K, BaBiO3 single crystals. The temperature dependenceof the magnetic field HCp corresponding to the onset of the specific heat anomaly presents a clear positivecurvature. HCp is significantly smaller than the field HD for which the superconducting gap vanishesbut is closely related to the irreversibility line deduced from transport data. Moreover, the temperaturedependence of the reversible magnetization presents a strong deviation from the Ginzburg-Landau theoryemphasizing the peculiar nature of the superconducting transition in this material.DOI: 10.1103/PhysRevLett.88.177201 PACS numbers: 74.25.Bt, 74.25.Dw, 74.60.EcThe H-T phase diagram of high Tc superconducting ox-ides has been the focus of intense theoretical and experi-mental study during the past decade [1]. One of the mostinteresting phenomenon which has been observed is theexistence of a melting line TmH above which the vor-tex lattice melts into a liquid of entangled lines [1]. Thismelting has very important consequences for the physicsof vortices, since the free motion of the flux lines in theliquid state gives rise to a large dissipation and renders thesystem useless for applications. The presence of this liq-uid phase also hinders any direct determination of the up-per critical field Hc2 from standard magnetotransport data.Indeed, any resistive “critical” field HRT, defined as thefield for which the resistivity reaches some arbitrary valueR (e.g., 50% of the normal state resistivity), then presentsa positive curvature [2]. Similarly, the presence of strongthermal fluctuations also complicates the determination ofHc2 from thermodynamic measurements. These fluctua-tions lead to broad and smooth anomalies in specific heatmeasurements (Cp). Thus the field HCp (defined, for in-stance, by the inflection point of CpT) can present either apositive curvature in Y1Ba2Cu3O72d (YBCO) crystals [3],a linear dependence in Tl2Ba2CuO6 [4], or even almost nodependence with field in highly anisotropic systems suchas Bi2Sr2CaCu2O8 [5] and HgBa2Ca2Cu3O81d [6]. It isstill unclear whether this upper critical field still exists asa transition line or is just some smooth crossover betweenthe vortex liquid and the normal state.In order to shed light on this issue, we present thermo-dynamic (specific heat, magnetotunneling, reversible mag-netization) and transport measurements on high quality op-timally doped Kx, Ba12xBiO3 single crystals (x  0.4).This compound is interesting since thermal fluctuations areexpected to be small (the Ginzburg number Gi is only1024) due to its isotropic structure, a Tc  31 K, anda coherence length on the order of 30 Å. We show thatthe magnetic field HCp presents a strong positive curva-ture and is smaller than the field HD for which the super-conducting gap vanishes, indicating a very peculiar naturefor the thermodynamic superconducting transition in thissystem.These measurements were performed on new par-ticularly homogeneous single crystals presenting verysharp superconducting transitions in both transport(DTc  0.15 K) and ac susceptibility (DTc  0.2 Kfor hac , 0.01 G) measurements. The specific heat wasmeasured by an ac technique [7] which allows us tomeasure small samples (here a few 1022 mm3) with highsensitivity (typically 1 part in 104). Heat was supplied tothe sample at a frequency v on the order of a few Hz bya light emitting diode via an optical fiber. The inducedtemperature oscillations were measured by a chromel-constantan thermocouple that was calibrated in situ usinga very pure silver single crystal as a reference. These mea-surements are only relative and were renormalized usingthe data from Ref. [8]. Figure 1 displays the temperaturedependence of the specific heat at various magnetic fieldsup to 5 T. The 7 T curve is equal to the normal statespecific heat above T  TcH  7 T  20 K and hasbeen used as a base line in Fig. 1.177201-1 0031-90070288(17)177201(4)$20.00 © 2002 The American Physical Society 177201-1VOLUME 88, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 29 APRIL 2002FIG. 1. Temperature dependence of the specific heat anomalyin a K, BaBiO3 single crystal. DCp  CpH , T 2 CpH 7 T, T . Inset: magnetic field dependence of the tunneling spec-tra at T  20 K and HT  0, 1, 2, 3, 4, 5, 6,7 (bold curve),8, 9, 10.The unusually high quality of our crystals is attested toby the narrow width of the transition, which is on the orderof 1 K in zero magnetic field, and by the amplitude of thespecific heat jump, DCpTcTc  4 5 mJ mol21 K22.This ratio is 2 and 5 times larger than that of Refs. [8]and [9], respectively, which are the only prior reports of aspecific heat anomaly at Tc in this system. This allowedus to study the magnetic field dependence of the specificheat anomaly in much greater detail. As shown in Fig. 1,this anomaly remains well defined in magnetic fields. TheTCp H curve corresponding to any characteristic pointof the transition (e.g., the onset, midpoint, or maximum)presents a clear positive curvature. This can be seen inFig. 2, where TCp corresponds to the onset of the peak.The shaded area represents the temperature differencebetween the onset and the midpoint of the transition.A very similar upward curvature has been obtained intwo other samples. A positive curvature was alreadyobtained by transport [10] and magnetic measurements[11]. However, in nonclassical superconductors, there isan ambiguity in defining Hc2 using those techniques.Another striking feature of the specific heat anomaly isthe rapid collapse of its height with field. Such behaviorwas previously observed in high Tc materials [5,6] andis usually attributed to the presence of highly field-dependent thermal fluctuations. The observation of a simi-lar collapse in K, BaBiO3 remains a puzzling issue.Geometrical arguments based on entropy conservationimply that this reduction must be accompanied by arapid, anomalous, increase of the specific heat at low0.4 0.5 0.6 0.7 0.8 0.9 1024681012T/Tcµ 0H (T)TvgTCp T∆FIG. 2. H-T phase diagram of the K, BaBiO3 system.Squares [HCp T ]: onset of the specific heat anomaly (seeFig. 1; the shaded area represents the temperature differencebetween the onset and the midpoint of the anomaly), circlesHvgT: “vortex-glass transition” line deduced from transportmeasurements (R ! 0); triangles: HDT defined as the linefor which the superconducting gap measured by tunnelingspectroscopy vanishes. The different characteristic temperaturesat 3T (arrows) are as shown in Fig. 3.temperature for fields much smaller than the upper criticalfield of 30 T deduced from transport data. The datafrom Ref. [8] also suggest such behavior.The specific heat measurements are in striking contrastwith our previous magnetotunneling [12] data which sug-gested that HD presents a classical Werthamer-Helfang-Hohenberg (WHH) dependence. We have thus performedsimilar magnetotunneling measurements on the sampleused in the specific heat experiments. The inset of Fig. 1shows the evolution of the tunneling spectra near the nor-mal state at T  20 K with increasing magnetic fields. Asshown by the bold curve, at H  HCp 20 K  7 T, a gapis still well developed and it closes at about 10 T. Asshown in Fig. 2, in agreement with our previous data, thecurvature is much less pronounced for HD and surprisinglyHCp , HD. Note that, even though the difference betweenTCp and TD is quite large, the resistivity reaches about95% of its normal state value (RN) at TCp and smoothlyincreases up to 100% for T  TD (see Fig. 3). The spe-cific heat anomaly thus defines a fundamental boundarybelow which the resistivity drops rapidly towards zero butsuperconductivity is only completely destroyed at T  TDfor which R  RN and the superconducting gap is com-pletely suppressed. Note that the difference between TDand TCp is not due to sample homogeneities since heavyion irradiation leads to an increase of TCp which then tendstowards TD [13]. This difference could be due to the ex-istence of a pseudogap but, in contrast to cuprates, thispseudogap would occur only in a nonzero magnetic field.177201-2 177201-2VOLUME 88, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 29 APRIL 20020.80.9124 26 28 30 32R/RNT (K)T∆TCpTvgH = 3T00.40.81.220 22 24 26 28 30 32∆ Cp(T)/∆ Cp,maxT (K)TVGTCp T∆H = 3TFIG. 3. Resistive transition at H  3 T. The onset of thespecific heat anomaly (see Fig. 1) corresponds to the tempera-ture below which the resistivity rapidly decreases. R ! RN forT  TD (temperature for which the superconducting gap closes,and RN is the normal state resistivity). Inset, renormalized spe-cific heat vs temperature. As shown, Tvg is close to the midpointof the specific heat anomaly.To complete this study of the thermodynamic proper-ties, we performed reversible magnetization measurements(Mrev) using a SQUID magnetometer. In the intermedi-ate magnetic field range, Hc1 ø H ø Hc2, the reversiblemagnetization of extreme type-II superconductors in theLondon model [14] is given by Mrev  2 aF032pl2 lnbHc2TH ,where a  1, F0 is the flux quantum, lT is the mag-netic penetration depth, Hc2T  is the upper critical field,and b  0.37 [15]. Thus, ≠Mrev≠ lnH is expected to beproportional to 1l2T  1 2 TTc close to Tc. Mrevpresents a clear logarithmic dependence (see [16]), and thecorresponding ≠Mrev≠ lnH are shown in Fig. 4. How-ever, as shown, strong deviations from the expected linearbehavior are visible and ≠Mrev≠ lnH can be describedmuch better by a 1 2 TTc1.5 law (solid line, the dottedline is a WHH dependence for 1l2). A similar devia-tion is usually observed in high Tc cuprates [17] and hasbeen attributed to the presence of strong fluctuations. Itwas originally suggested by Nelson et al. [18] that elasticdistortions of the vortex lattice (in the presence of strongthermal fluctuations) may lead to a significant contributionto the entropy of the system. However, the correspond-ing contribution to ≠Mrev≠ lnH is expected to be of theorder of kBTF0j [19] (where kB is the Boltzmann con-stant), which is about 1 order of magnitude smaller thanthe observed deviation in K, BaBiO3 [20].Our specific heat and magnetization measurements givenew insight into the magnetotransport data. Those dataare well described by the vortex-glass scaling formalism[10], suggesting that the vortex solid melts into a liquidat high temperature through a second order phase tran-00.20.40.60.80.5 0.6 0.7 0.8 0.9 1∂Mrev/∂ln(H)T/TcWHH Fit(1 - T/Tc)1.5FIG. 4. Temperature dependence of ≠Mrev≠ lnH in aK, BaBiO3 single crystal. The dotted line is a WHH fit forthe temperature dependence of 1l2 (see text for details). Thesolid line is a 1 2 TTc1.5 fit to the data.sition. The physical image emerging from those mea-surements was then that of a liquid phase existing forHvg , H , HD  Hc2 (the vortex-glass transition fieldHvg is defined as the field for which R ! 0). However,as shown in Fig. 2, Hvg and HCp present a very similartemperature dependence emphasizing the close relation-ship between those two lines. As shown in the inset ofFig. 3, the R  0 criterion is close to the midpoint of theCp transition. This then suggests two possibilities: either(i) the positive curvature in Hvg is not due to the meltingof the vortex solid but is an intrinsic property of the Hc2line ( HCp ) or (ii) the specific heat anomaly is not re-lated to Hc2 ( HD) but instead marks a transition in thevortex state. Many theoretical models have been devel-oped in order to explain a “possible” upward curvature ofthe upper critical field in cuprates (including a spin-chargeseparation [21] or very strong coupling [22]) but none ofthose models can be applied to the K, BaBiO3 system. Apositive curvature has also been predicted by Ovchinnikovand Kresin [23] in the presence of inhomogeneities and/ormagnetic impurities. However, in this case this curvatureis expected to appear only at low temperature (i.e., whenthe superconducting coherence length becomes smaller oron the order of the size of the impurity) and Hc2 is stillexpected to vary linearly with T close to Tc. Finally, thecondensation of charged bosons in the magnetic field isalso expected to lead to a positive curvature [24]. But onehas then to take into account the fact that we do not ob-serve any feature in the tunneling spectra above TCp in zeromagnetic field. On the other hand, a second scenario is thatHc2  HD and that the specific heat anomaly marks a tran-sition within the vortex state. For instance, specific heatanomalies, both peaks and/or steps, have been observedfor transitions in the vortex state in YBCO [25,26]. How-ever, even though the amplitude of DCp per unit volume177201-3 177201-3VOLUME 88, NUMBER 17 P H Y S I C A L R E V I E W L E T T E R S 29 APRIL 2002measured here is similar to the one associated with vortexmelting in YBCO, its shape is quite different and looksmuch like a classical superconducting transition.The K, BaBiO3 system thus presents very unusual be-havior. Indeed, any characteristic field deduced either fromspecific heat or from transport measurements presents astrong positive curvature; a structure in the density of statesis visible well above the specific heat anomaly and strongdeviations from the standard Ginzburg-Landau theory areobserved in the reversible magnetization. This behavioris reminiscent of high Tc oxides, where strong fluctuationsoccur. In K, BaBiO3, thermal fluctuations are expected toplay only a minor role, but the superconducting transitionoccurs in the vicinity of a metal-insulator transition. Thevery small carrier density might thus lead to the presenceof large quantum fluctuations [27,28]. Further studies areneeded to fully understand the superconducting transitionin this remarkable system.We thank L. Paulius for interesting discussions and N. E.Phillips and R. A. Fischer for sending us their specific heatdata on K, BaBiO3.[1] G. Blatter, M. V. Feigel’man, V. B. Geshkenbein, A. I.Larkin, and V. M. Vinokur, Rev. Mod. Phys. 66, 1125(1994).[2] See, for instance, I. W. Sumarlin et al., Phys. Rev. Lett.68, 2228 (1992); A. P. Mackenzie et al., Phys. Rev. Lett.71, 1238 (1993); M. S. Osofski et al., Phys. Rev. Lett. 71,2315 (1993).[3] M. Roulin, A. Junod, and E. Walker, Physica (Amsterdam)296C, 137 (1998).[4] A. Carrington, A. P. Mackenzie, and A. Tyler, Phys. Rev. B54, R3788 (1996).[5] A. Junod, A. Erb, and C. Renner, Physica (Amsterdam)317C–318C, 333 (1999).[6] C. Marcenat et al., in Coherence in High TemperatureSuperconductors (World Scientific, Singapore, 1996);A. Carrington et al., Phys. Rev. B 55, R8674 (1997).[7] P. F. Sullivan and G. Seidel, Phys. Rev. 173, 679 (1968).[8] B. F. Woodfield, D. A. Wright, R. A. Fisher, N. E. Philips,and H. Y. Tang, Phys. Rev. Lett. 83, 4622 (1999).[9] J. E. Graebner, L. F. Schneemeyer, and J. K. Thomas, Phys.Rev. B 39, 9682 (1989).[10] T. Klein, A. Conde-Gallardo, J. Marcus, P. Szabo,P. Samuely, A. G. M. Jansen, and C. Escribe-Filippini,Phys. Rev. B 58, 12 411 (1998).[11] V. F. Gantmakher et al., Phys. Rev. B 54, 6133 (1996);D. Hall et al., Philos. Mag. B 80, 61 (2000).[12] P. Samuely, P. Szabo, T. Klein, A. G. M. Jansen, J. Marcus,C. Escribe-Filippini, and P. Wyder, Europhys. Lett. 41, 207(1998).[13] C. Marcenat et al. (to be published).[14] P. De Gennes, in Superconductivity of Metals and Alloys(Addison-Wesley, New York, 1989); M. Tinkham, in In-troduction to Superconductivity (McGraw-Hill, New York,1996); A. A. Abrikosov, in Fundamentals of the Theory ofMetals (North-Holland, New York, 1988).[15] This model was later improved by Z. Hao and J. R. Clem[Phys. Rev. Lett. 67, 2371 (1991)], taking into account thecontribution of the vortex core to the free energy density.Despite this nonlogarithmic contribution to the magneti-zation, it has been shown that Mrev remains approxima-tively linear with lnH on a large magnetic field range witha  0.77 and b  1.44.[16] I. Joumard, T. Klein, A. Conde-Gallardo, J. Marcus, andA. Sulpice, Physica (Amsterdam) 341C–348C, 1067(2000).[17] See, for instance, P. H. Kes et al., Phys. Rev. Lett. 67,2383 (1991); U. Welp et al., Phys. Rev. Lett. 67, 3180(1991).[18] D. R. Nelson and H. S. Seung, Phys. Rev. B 39, 9153(1989).[19] L. N. Bulaevskii et al., Phys. Rev. Lett. 68, 3773 (1992). Inhighly anisotropic samples the coherence length j shouldbe replaced by the interlayer spacing s.[20] The main difference between K, BaBiO3 and cuprates isthat ≠Mrev≠ lnH remains positive on the entire tempera-ture range in K, BaBiO3.[21] R. G. Dias and J. M. Wheatley, Phys. Rev. B 50, R13 887(1994).[22] F. Marsiglio and J. P. Carbotte, Phys. Rev. B 36, 3633(1987).[23] Y. N. Ovchinnikov and V. Z. Kresin, Phys. Rev. B 54, 1251(1996).[24] A. S. Alexandrov, Phys. Rev. B 48, 10 571 (1993).[25] A. Schilling et al., Nature (London) 382, 791 (1996);M. Roulin, Science 273, 1210 (1996).[26] F. Bouquet, C. Marcenat, E. Steep, R. Calemczuk, W. K.Kwok, U. Welp, G. W. Crabtree, R. A. Fisher, N. E.Phillips, and A. Schiling, Nature (London) 411, 448(2001).[27] G. Blatter and B. I. Ivlev, Phys. Rev. B 50, 10 272(1994).[28] V. J. Emery and S. A. Kivelson, Nature (London) 374, 434(1995); ibid., Phys. Rev. Lett. 74, 3253 (1995).177201-4 177201-4

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Anomalous Magnetic Field Dependence of the Thermodynamic Transition Line in the Isotropic Superconductor
                    
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4 pages, 4 figures, 28 referencesInternational audienceThermodynamic (specific heat, reversible magnetization, tunneling spectroscopy) and transport measurements have been performed on high quality (K,Ba)BiO$_3$ single crystals. The temperature dependence of the magnetic field $H_{Cp}$ corresponding to the onset of the specific heat anomaly presents a clear positive curvature. $H_{Cp}$ is significantly smaller than the field $H_\Delta$ for which the superconducting gap vanishes but is closely related to the irreversibility line deduced from transport data. Moreover, the temperature dependence of the reversible magnetization present a strong deviation from the Ginzburg--Landau theory emphasazing the peculiar nature of the superconducting transition in this material

Sulpice, André

Jansen, A. G. M.

Anomalous magnetic field dependence of the thermodynamic transition line in the isotropic superconductor (K,Ba)Bi03

Thermodynamic (specific heat, reversible magnetization,
 tunneling spectroscopy) and transport measurements have been
 performed on high quality (K, Ba)BiO3 single crystals. The
 temperature dependence of the magnetic field H-Cp corresponding
 to the onset of the specific heat anomaly presents a clear
 positive curvature. H-Cp is significantly smaller than the
 field H-Delta for which the superconducting gap vanishes but is
 closely related to the irreversibility line deduced from
 transport data. Moreover, the temperature dependence of the
 reversible magnetization presents a strong deviation from the
 Ginzburg-Landau theory emphasizing the peculiar nature of the
 superconducting transition in this material

Klein, T.

Szabó, P.

Max Planck Society eDoc Server

Anomalous magnetic field dependence of the thermodynamic transition line in the isotropic superconductor (K,Ba)BiO3

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Anomalous magnetic field dependence of the thermodynamic transition line
  in the isotropic superconductor (K,Ba)Bi03

Anomalous magnetic field dependence of the thermodynamic transition line in the isotropic superconductor (K,Ba)Bi03

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