We report on specific heat, high magnetic field transport and
$ac-$susceptibility measurements on magnesium diboride single crystals. The
upper critical field $H_{c2}$ for magnetic fields perpendicular and parallel to
the Mg and B planes is presented for the first time in the entire temperature
range. A very different temperature dependence has been observed in the two
directions which yields to a temperature dependent anisotropy with $\Gamma
\sim$ 5 at low temperatures and about 2 near $T_c$. A peak effect is observed
in susceptibility measurements for $H \sim $2 T parallel to the $c-$axis and
the critical current density presnts a sharp maximum for $H$ parallel to the
ab-plane.Comment: 6 pages, 5 figure

A. G. M. Jansen

A.B. Pipard

A.K. Pradhan

A.V. Sologubenko

A.Y. Liu

B. Kang

C. Marcenat

C. U. Jung

C.F. Hempstead

D. Lipp

F. Bouquet

G. Karapetrov

G. Pasquini

H.-S. Lee

H.H. Wen

H.J. Choi

J. Marcus

J. Nagamatsu

J.A. Woollam

K. H. P. Kim

K.H.P. Kim

L. Lyard

L. Paulius

M. Angst

M. Pissas

M. Tachiki

M. Zehetmayer

P. Samuely

P. Szabo

P. Szabó

P.F. Sullivan

S. Blanchard

S. Choi

S. Sen

S.-I. Lee

T. Klein

T. Park

U. Welp

W. K. Kwok

Yu. Eltsev

English

arXiv

International audienceWe report on specific-heat, high-magnetic-field transport, and ac-susceptibility measurements on MgB2 single crystals. The upper critical field for magnetic fields perpendicular and parallel to the basal planes is presented in the entire temperature range. A very different temperature dependence has been observed in the two directions, which yields a temperature-dependent anisotropy with G;5 at low temperatures and ;2 near Tc . A peak effect is observed for m0H;2 T parallel to the c axis, and the critical current density presents a sharp maximum for H parallel to the ab plane

Lyard, L.

Samuely, P.

Szabo, P.

Klein, Thierry

Marcenat, C.

Paulius, L.

Kim, K.H.P.

Jung, C.U.

Lee, H.-S.

Kang, B.

Choi, S.

Lee, S.-I.

Marcus, J.

Blanchard, S.

Jansen, A.G.M.

Welp, U.

Karapetrov, G.

Kwok, W.K.

Hal - Université Grenoble Alpes

Anisotropy of the upper critical field and critical currentin single crystal MgB2L. Lyard, P. Samuely, P. Szabo, Thierry Klein, C. Marcenat, L. Paulius,K.H.P. Kim, C.U. Jung, H.-S. Lee, B. Kang, et al.To cite this version:L. Lyard, P. Samuely, P. Szabo, Thierry Klein, C. Marcenat, et al.. Anisotropy of the upper crit-ical field and critical current in single crystal MgB2. Physical Review B : Condensed matterand materials physics, American Physical Society, 2002, 66, pp.180502(R). <10.1103/Phys-RevB.66.180502>. <hal-00957733>HAL Id: hal-00957733https://hal.archives-ouvertes.fr/hal-00957733Submitted on 12 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.Anisotropy of the upper critical field and critical current in single crystal MgB2L. Lyard,1,2 P. Samuely,3,4 P. Szabo,4 T. Klein,1,3 C. Marcenat,2 L. Paulius,2 K. H. P. Kim,5 C. U. Jung,5 H.-S. Lee,5B. Kang,5 S. Choi,5 S.-I. Lee,5 J. Marcus,1 S. Blanchard,1 A. G. M. Jansen,6 U. Welp,7 G. Karapetrov,7 and W. K. Kwok71Laboratoire d’Etudes des Proprie´te´s Electroniques des Solides, CNRS, Boıˆte Postale 166, F-38042 Grenoble Cedex 9, France2Commissariat a` l’Energie Atomique-Grenoble, DRFMC-SPSMS, 17 Rue des Martyrs, F-38054 Grenoble Cedex 9, France3University Joseph Fourier, Boıˆte Postale 53, F-38041 Grenoble Cedex 9, France4Institute of Experimental Physics, Slovak Academy of Sciences, SK-04353 Kosˇice, Slovakia5NVCRICS and Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea6Grenoble High Magnetic Field Laboratory, MPI-CNRS, Boıˆte Postale 166, F-38042 Grenoble Cedex 9, France7Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439~Received 13 June 2002; published 27 November 2002!We report on specific-heat, high-magnetic-field transport, and ac-susceptibility measurements on MgB2single crystals. The upper critical field for magnetic fields perpendicular and parallel to the basal planes ispresented in the entire temperature range. A very different temperature dependence has been observed in thetwo directions, which yields a temperature-dependent anisotropy with G;5 at low temperatures and ;2 nearTc . A peak effect is observed for m0H;2 T parallel to the c axis, and the critical current density presents asharp maximum for H parallel to the ab plane.DOI: 10.1103/PhysRevB.66.180502 PACS number~s!: 74.25.Bt, 74.25.Dw, 74.60.EcSince the discovery of superconductivity in magnesiumdiboride at 39 K in 2001 ~Ref. 1! an enormous amount ofwork has been done, which helped to elucidate many of itsphysical properties. Among others, the two-bandsuperconductivity2 has been confirmed by different tech-niques such as specific heat3 or Andreev reflection.4 Thispicture suggests a significant anisotropy of the superconduct-ing state but data reported on the anisotropy of the uppercritical field Hc2 scatter from 1.1 to 13, depending on theform of material ~polycrystals, thin films, single crystals! andmethod of evaluation. The problem thus remains to be clari-fied on high-quality single crystals.We have determined Hc2 in MgB2 single crystal for Hparallel and perpendicular to the ab planes by magnetotrans-port ~down to 5 K and up to 28 T!, ac-susceptibility ~up to 5T!, and specific heat ~up to 7 T! measurements. Hc2'ab re-veals a classical linear temperature dependence near Tc @withm0Hc2'ab(0).3.5 T], while Hc2uuab shows a positive curva-ture at temperatures above 20 K and saturates atm0Hc2uuab(0).17 T. As a consequence G5Hc2uuab /Hc2'abis temperature dependent with G(0 K)'5 and G(near Tc)'2. On the other hand, the critical current deduced fromac-susceptibility measurements presents a sharp maximumfor Huuab .Experiments have been performed on high-quality MgB2single crystals5 showing clear hexagonal facets with flat andshiny surfaces ~of typical dimensions 50350310 mm3).Four-probe magnetoresistance measurements have been per-formed for different temperatures and angles (u) between Hand the ab planes. Gold electrodes have been evaporated asstripes overlapping the top plane of the sample with a contactresistance of ;1V , and H was always orthogonal to themeasuring current. The ac susceptibility has been deducedfrom the local transmittivity measured with a miniature Hallprobe. The ac excitation field (hac;3 G, v;23 Hz) wasperpendicular to the ab plane and to the Hall-probe plane,and superimposed over a dc field with an angle 0,u,90°. The specific heat was measured by an ac technique.6Heat was supplied to the sample at a frequency v of theorder of 70 Hz by a light-emitting diode via an optical fiber.The induced temperature oscillations were measured by a12-mm-diameter chromel-constantan thermocouple cali-brated in situ.Figure 1 displays the temperature dependence of the field-dependent part of the specific heat up to 7 T for Huuab andup to 2 T for H'ab . In zero field, the specific-heat discon-tinuity at Tc represents about 3% of the total signal. Thisvalue is five to six times smaller than that obtained in thebest polycrystalline samples,3 which can be attributed to thelarge contribution of the addenda, given the extremely smallFIG. 1. Temperature dependence of the specific heat at differentmagnetic fields for Huuab ~closed circles! and H'ab ~open squares!.Inset: specific-heat transition at m0H'ab51 T and m0H uuab5Gm0H'ab.3.5 T.RAPID COMMUNICATIONSPHYSICAL REVIEW B 66, 180502~R! ~2002!0163-1829/2002/66~18!/180502~4!/$20.00 ©2002 The American Physical Society66 180502-1size of our single crystals (;100 ng). The data are thereforegiven in arbitrary units and the temperature range is limitedto T.12 K. No significant increase of the transition width,DT;2 K, is observed for m0Huuc,2 T and m0Huuab,5 T. Despite a clear broadening at higher fields, thespecific-heat anomaly remains well defined in our exploredtemperature range. This implies that the broadening observedin polycrystalline samples3,7 is due to randomly oriented an-isotropic grains rather than thermodynamic fluctuations.7 Thecurves are remarkably identical for both directions once thefield is renormalized by the temperature-dependent anisot-ropy coefficient ~see inset of Fig. 1!. It is also worth noticingthat the amplitude of the specific-heat jump decreases veryrapidly with H, implying a rapid increase of the Sommerfeldcoefficient g and therefore of the density of states. An en-tropy conservation construction shows that g;0.9gN ~wheregN is related to the normal-state density of states! for H;0.5 Hc2, in good agreement with recent low-temperaturemeasurements by Bouquet et al.8The Tc(H) values deduced from the classical entropyconservation construction, as well as those deduced fromsusceptibility ~onset of the diamagnetic response! and trans-port measurements have been reported in Fig. 2. In the lattercase, Tc(H) has been defined at the onset of finite resistivity~see Fig. 3!. All three methods reveal the same results in thecommon field range, and the entire H-T phase diagram couldbe determined from magnetotransport data for both field di-rections. Note that the resistivity reaches the normal-statevalue at a field HRN.Hc2, as previolusly shown by Welpet al.9 for H'ab ~see discussion below!. As expected for atype-II superconductor, Hc2'ab varies linearly close to Tcand saturates at low temperature (m0Hc2'ab.3.5 T). On theother hand, Hc2uuab reveals a positive curvature close to Tc ,which changes to negative below 20 K and saturates at amuch higher value ;17 T. A direct consequence of thesetwo different shapes is that G is temperature dependent, de-creasing from ;5 at low T down to ;2 near Tc ~see inset ofFig. 2!. Despite this T-dependent anisotropy, the Hc2(u) de-duced from the magnetotransport measurements ~see Fig. 3!can be well fitted by the ellipsoidal Lawrence-Doniach formfor anisotropic three-dimensional superconductors:10@Hc2(u)sin u/Hc2'ab#21@Hc2(u)cos u/Hc2uuab#251 with G54.8at T55.4 K ~Fig. 4! and G53.4 at T526 K ~not shown!.It has been suggested that the positive curvature observedfor Huuab is a consequence of the two-gap structure.11 How-ever, it is worth mentioning that a very similar behavior hasalso been observed in single-gap superconductors such asNbSe2 ~Ref. 12! or borocarbides.13 This behavior was be-lieved to be a characteristic of layered compounds,12 but it iseven more ‘‘general’’ as it has also been observed in theisotropic (K,Ba)BiO3 system.14 The origin of this effect thusstill has to be clarified.Our specific-heat measurements clearly show that Hc2 islocated at the onset of finite resistivity and the resistance RFIG. 2. Temperature dependence of the upper critical field ob-tained by transport ~circles!, ac-susceptibility ~squares!, andspecific-heat ~triangles! measurements. Inset: temperature depen-dence of the anisotropy.FIG. 3. Magnetic-field dependence of the resistance at T55.4 K for various angles between H and the ab plane. Hc2 andHc3 are marked by arrows for the two principal field orientations.The influence of the current density is presented for these two ori-entations ~dashed lines from right to left, j517,50,170 A/cm2,solid lines j5500 A/cm2).FIG. 4. Angular dependence of the upper critical field ~opencircles! at 5.4 K. The solid line is a fit to the data by the Lawrence-Doniach formula. Triangles are critical fields taken at the end of theresistive transition HRN. Inset: angular dependence of the criticalcurrent at m0H52 T and T518 K (J0;53103 A/cm23).RAPID COMMUNICATIONSL. LYARD et al. PHYSICAL REVIEW B 66, 180502~R! ~2002!180502-2only reaches its normal-state value (RN) for a higher fieldHRN. For HRN.H.Hc2, the highly non-Ohmic current de-pendence of the transition has been attributed to surface con-ductivity by some of us.9 As shown in Fig. 3, for low currentdensities ( j517, 50, and 170 A/cm2) the transitions aresmooth for both field orientations and, for H'ab , the onsetof finite resistivity even shifts towards higher fields as thecurrent density is decreased. This onset becomes sharp andcurrent independent above 500 A/cm2 for H'ab and170 A/cm2 for Huuab . The ratio between the fields HR505Hc2 ~for j5500 A/cm2) and HRN ~measured at the lowestcurrent! is about 1.8 for H'ab and 1.4 for Huuab . This ratioremains constant for all temperatures apart from those veryclose to Tc , where it is affected by the width of the transitionDTc .For Huuab , our data are strikingly similar to those ob-tained by Hempstead and Kim15 in their pioneering work onsurface surperconductivity in Nb0.5Ta0.5 and Pb0.83In0.17sheets. The resistive transition can be analyzed as follows: upto some characteristic j value, the onset of finite resistance issensitive to j due to the existence of a surface sheath whichcan bear a current keeping the zero resistance above Hc2.For higher j values, this sheath is destroyed and the resis-tance increases sharply at H5Hc2 to a fraction of RN whichincreases with j. For the lowest j values, HRN5Hc3'1.7Hc2, but the experimental Hc3 /Hc2 ratio in Ref. 15 wasscattered between 1.6 and 1.96 and even droped down to1.14 for copper coated Pb-In sheets. Surface superconductiv-ity effects should be negligible for H'ab , but in our experi-mental setup, the current and voltage electrodes overlappingthe sample go over the vertical side planes, which thus in-evitably contribute to surface superconductivity as well.16With triangles, we have plotted in Fig. 4 the angular depen-dence of HRN at T55.4 K. If surface conductivity is impor-tant for H'ab and Huuab , this effect is diminished for otherfield orientations and HRN /Hc2 drops down to '1.1. Thisincrease of surface conductivity close to the ab planes canthus account for the cusplike behavior of HRN at small angleswhich has been first attributed to Hc2 by other authors.17,18The anisotropy of Hc2 in MgB2 crystals has been mea-sured recently by several authors in a limited temperaturerange by either magnetometric19,20 or thermal-conductivity21measurements. Those measurements yield results very simi-lar to ours, but it was of fundamental importance to showthat the ‘‘critical fields’’ obtained from all those measure-ments coincide with the thermodynamic transition field de-duced from specific-heat measurements. Indeed, in manynovel superconductors, fluctuations broaden the transitionsfrom the superconducting to the normal state. One of themost striking phenomenon that has been observed in thesesystems is the existence of a melting line Tm(H). The pres-ence of this vortex liquid phase above Tm complicates thedetermination of the upper critical field Hc2. For instance,the onset of a finite R in these systems indicates the meltingtransition, and Hc2 is shifted to a much higher resistance~close to RN ; see, for instance, Ref. 22!. However, fluctua-tions are not expected to play any significant role in MgB2 asconfirmed by specific-heat measurements. A incorrect crite-rion for the Hc2 determination partly explains the discrep-ancy in the Hc2 values deduced from transportmeasurements.23,17Another interesting phenomenon is the observation of apeak effect in the critical current (J), which shows up in ourtransport data in the same way as in Ref. 9. Similarly, thisincrease in J appears as a dip in our ac-susceptibility mea-surements, which could be observed for H'ab in a narrowmagnetic-field range ;2 –3 T ~see inset of Fig. 5!. As re-cently reported by Pissas et al.,24 this dip is replaced by asharp drop for lower magnetic fields and has been attributedto a possible melting of the vortex solid,24 in contradictionwith our specific-heat data, which show that the onset ofdiamagnetism actualy coincides with the Hc2 line. As shownin Fig. 5, the J value at the peak position—deduced from thesusceptibility, following the procedure introduced by Pas-quini et al.25—rapidly decreases for increasing temperature~i.e., for decreasing magnetic field!. Similarly, as shown inthe inset of Fig. 5, the peak effect also ‘‘disappears’’ in thesusceptibility measurements when the magnetic field isturned away from the c axis. However, this peak is still vis-ible in our transport measurements for Huuab , suggestingthat it could exist for all H and u values. In MgB2 this effectmost probably reflects the fact that the shear energy of theflux lattice drops towards zero more rapidly than the pinningenergy in the vicinity of the normal state, allowing the vortexmatter to accomodate the disorder close to the transitionmore efficiently.26Our J values for H'ab are much smaller than those pre-viously obtained in polycrystals.27 However, as shown in theinset of Fig. 5, if the susceptibility only weakly depends on udown to ;10°, it decreases rapidly close to the ab plane,FIG. 5. Magnetic-field dependence of the critical current forH'ab at T58.5, 13, 17, 21.5, and 26 K ~from top to bottom!,showing a peak effect at low temperatures (J0'53103 A/cm3).Inset: temperature dependence of the ac suscetibility at m0H52 Tfor different angles between H and the ab plane.RAPID COMMUNICATIONSANISOTROPY OF THE UPPER CRITICAL FIELD AND . . . PHYSICAL REVIEW B 66, 180502~R! ~2002!180502-3showing that the pinning of the vortices is much more effi-cient for Huuab . The corresponding J values at 18 K aredisplayed in the inset of Fig. 4, showing that J increases by afactor of about 4 for Huuab . A similar behavior has beenobserved in the critical current deduced from transport mea-surements in c axis oriented thin films28 and Eltsev et al.recently reported on a rapid drop of the dissipation when themagnetic field is applied parallel to the ab planes in singlecrystals.17 A similar cusp in the critical current has been ob-served in high-Tc cuprates in which vortices are stronglypinning by the weakly superconducting layers between theCuO2 planes when the field is applied parallel to those planes~so-called intrinsic pinning29!. However, the origin of thestrong pinning of the ab planes in diborides still has to beclarified, given the rather small anisotropy of this material.In summary, the upper critical field has been deducedfrom specific-heat, high-magnetic-field transport, and ac-susceptibility measurements for H parallel and perpendicularto the ab planes. Hc2'ab reveals a conventional tempera-ture dependence with m0Hc2'ab(0).3.5 T, but the parallelcritical field has a positive curvature above 20 K and satu-rates at m0Hc2uuab(0).17 T. Consequently, the anisotropyfactor G is temperature dependent, decreasing from ;5 atlow temperature to ;2 close to Tc . The critical current de-duced from the susceptibility measurements presents a peakeffect for m0H'ab;2 –3 T and rapidly increases forHuuab .1 J. Nagamatsu et al., Nature ~London! 410, 63 ~2001!.2 A.Y. Liu et al., Phys. Rev. Lett. 87, 087005 ~2001!; H.J. Choiet al., Phys. Rev. B 66, 020513~R! ~2002!; Nature ~London!418, 758 ~2002!.3 F. Bouquet et al., Phys. Rev. Lett. 87, 047001 ~2001!.4 P. Szabo´ et al., Phys. Rev. Lett. 87, 137005 ~2001!.5 K.H.P. Kim et al., Phys. Rev. B 65, 100510~R! ~2002!.6 P.F. Sullivan and G. Seidel, Phys. Rev. 173, 679 ~1968!.7 T. Park et al., Phys. Rev. B 66, 134515 ~2002!.8 F. Bouquet et al., cond-mat/0207141 ~unpublished!.9 U. Welp et al., cond-mat/0203337 ~unpublished!.10 W. E. Lawrence and S. Doniach, in Proceedings of the 12th In-ternational Conference Low Temperature Physics, edited by E.Kanda ~Keigaku, Tokyo, 1981!.11 S.V. Shulga et al., cond-mat/0103154 ~unpublished!.12 J.A. Woollam, R. Somoano, and P. O’Connor, Phys. Rev. Lett. 32,712 ~1974!.13 D. Lipp et al., Europhys. Lett. 58, 435 ~2002!, and referencestherein.14 S. Blanchard et al., Phys. Rev. Lett. 88, 177201 ~2002!.15 C.F. Hempstead and Y.B. Kim, Phys. Rev. Lett. 12, 145 ~1964!.16 Reference 9 has discussed possible arguments for weaker surfacesuperconductivity effects in the Huuab configuration based onsurface electronic states in MgB2.17 Yu. Eltsev et al., Phys. Rev. B 65, 140501~R! ~2002!.18 C. Ferdeghini et al., cond-mat/0203246 ~unpublished!.19 M. Angst et al., Phys. Rev. Lett. 88, 167004 ~2002!.20 M. Zehetmayer et al., Phys. Rev. B 66, 052505 ~2002!.21 A.V. Sologubenko et al., Phys. Rev. B 65, 180505~R! ~2002!.22 P. Samuely et al., Europhys. Lett. 41, 207 ~1998!.23 A.K. Pradhan et al., Phys. Rev. B 64, 212509 ~2001!.24 M. Pissas et al., Phys. Rev. Lett. 89, 097002 ~2002!.25 G. Pasquini et al., Phys. Rev. B 59, 9627 ~1999!.26 A.B. Pipard, Philos. Mag. 19, 217 ~1967!.27 H.H. Wen et al., Supercond. Sci. Technol. 15, 315 ~2002!.28 S. Sen et al., Phys. Rev. B 65, 214521 ~2002!.29 M. Tachiki and S. Takahaski, Solid State Commun. 72, 1083~1989!.RAPID COMMUNICATIONSL. LYARD et al. PHYSICAL REVIEW B 66, 180502~R! ~2002!180502-4

Anisotropy of the upper critical field and critical current in single crystal MgB2

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Anisotropy of the upper critical field and critical current in single crystal
                    
                      
                        
                          
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Anisotropy of the Upper Critical Field and Critical Current in Single
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Anisotropy of the Upper Critical Field and Critical Current in Single Crystal MgB $_2$