Field and temperature microwave measurements have been carried out on MgB2
thin film grown on Al2O3 substrate. The analysis reveals the mean field
coherence length xi_{MF} in the mixed state and a temperature independent
anisotropy ratio gamma_{MF} = xi_{MF}^{ab} / xi_{MF}^c approximately 2. At the
superconducting transition, the scaling of the fluctuation conductivity yields
the Ginzburg-Landau coherence length with a different anisotropy ratio
gamma_{GL} = 2.8, also temperature independent.Comment: submitted to PR

A. Dulčić

A.A. Golubov

A.V. Sologubenko

B.B. Jin

C. Buzea

C. Ferdeghini

D. Paar

D.-N. Peligrad

Eun-Mi Choi

H.-J. Kim

Hyun-Jung Kim

I. Ukrainczyk

J. Nagamatsu

J. Owliaei

K. Takahashi

K.H.P. Kim

L. Lyard

M. Angst

M. Golosowsky

M. Požek

M. Zehetmayer

M.-S. Kim

S. Ullah

Sung-Ik Lee

U. Welp

W. N. Kang

W.N. Kang

English

arXiv

Field and temperature microwave measurements have been carried out on MgB2 thin film grown on Al2O3 substrate. The analysis reveals the mean field coherence length in the mixed state and a temperature independent anisotropy ratio 2. At the superconducting transition, the scaling of the fluctuation conductivity yields the Ginzburg-Landau coherence length with a different anisotropy ratio 2.8, also temperature independent

Dulčić, Antonije

Požek, Miroslav

Paar, Dalibor

Choi, Eun-Mi

Kim, Hyun-Jung

Kang, W. N.

Lee, Sung-Ik

University of Zagreb Repository

RAPID COMMUNICATIONSPHYSICAL REVIEW B 67, 020507~R! ~2003!Coherence lengths and anisotropy in MgB2 superconductorA. Dulcˇic´, M. Pozˇek, and D. PaarDepartment of Physics, Faculty of Science, University of Zagreb, P.O. Box 331, HR-10002 Zagreb, CroatiaEun-Mi Choi, Hyun-Jung Kim, W. N. Kang, and Sung-Ik LeeNational Creative Research Initiative Center for Superconductivity and Department of Physics, Pohang University of Scienceand Technology, Pohang 790-784, Republic of Korea~Received 26 July 2002; published 17 January 2003!Field- and temperature-dependent microwave measurements have been carried out on MgB2 thin film grownon Al2O3 substrate. The analysis reveals the mean-field coherence length jMF in the mixed state and atemperature-independent anisotropy ratio gMF5jMFab /jMFc ’2. At the superconducting transition, the scaling ofthe fluctuation conductivity yields the Ginzburg-Landau coherence length with a different anisotropy ratiogGL52.8, also temperature independent.DOI: 10.1103/PhysRevB.67.020507 PACS number~s!: 74.25.Op, 74.25.Nf, 74.40.1k, 74.78.DbThe recent discovery of superconductivity at 39 K in thesimple binary compound MgB2 ~Ref. 1! has sparked a con-siderable effort in the scientific community to determine thefundamental parameters and the nature of superconductivityin this compound. Quite surprisingly, the usually simple de-termination of the upper critical field Bc2 has emerged as acontroversial issue. The early attempts to determine Bc2c (Bic axis!, and Bc2ab (Bi ab plane!, have shown a large span ofvalues and anisotropy ratio g5Bc2ab/Bc2c varying in the range1.2–9.2 One could have ascribed these discrepancies to aninsufficient control of the sample preparation conditions atthe early stage. However, the controversy has not been fullysettled even with the improved sample quality in the recentlyprepared thin films and single crystals of MgB2.3–12 One ofthe puzzling observations was that different experimentaltechniques often yielded strongly diverse Bc2 values in oneand the same sample. Thus, Welp et al.9 have shown thatresistive onset of superconductivity in a given field, whichwas traditionally taken as the upper critical field, was in dis-accord with the Bc2c values obtained in the same sample byspecific heat and magnetization measurements. Similar dis-crepancy has been observed in the results of the resistiveonset and the thermal conductivity.12 On the other hand, theonset of the diamagnetic response was found to corroboratewith the zero resistance ~or the onset of finite resistivity!.11The common approach in these methods is to make achoice of a percentage in cutting the transition curves. Thecorresponding points are then taken for Bc2(T). Alterna-tively, one looks for the geometrical intersection of the tan-gents above and below the transition. None of these choices,however, is guided by a physical law describing the transi-tion.In this Rapid Communication, we show that the problemof the upper critical field, and the related coherence length, ismore subtle than implicitly assumed before. Our analysis isbased on the physical process that defines the shape of theexperimental curve, and yields unequivocally the value ofBc2. We find the mean-field ~MF! coherence length jMF asthe radius of the vortex core in the mixed state and, sepa-rately, the Ginzburg-Landau ~GL! coherence length jGL at0163-1829/2003/67~2!/020507~4!/$20.00 67 0205the transition. The two coherence lengths are quite differentin MgB2. The anisotropy ratios are also different (gGL.gMF), but both turn out to be temperature independent.The thin film of MgB2 was grown on (11¯02) Al2O3 sub-strate using a two-step method.13,14 Precursor thin film of Bwas deposited by pulsed laser deposition at room tempera-ture. The B thin film was sealed together with high purity Mginto Nb tube with Ar atmosphere. The heat treatment wascarried out at 900 °C for 10–30 min. The film thickness was400 nm. X-ray diffraction indicated that the MgB2 film hasa highly c-axis oriented crystal structure normal to thesubstrate surface with no impurity phase observed. Thesefilms have been studied previously by dc resistivity,magnetization,13,14 penetration depth,15 and zero-field micro-wave measurements.16 These studies have supported the gen-erally observed features of MgB2 superconductor, anisot-ropy, and two-gap nature.Microwave measurements were carried out in an ellipticalcavity resonating in eTE111 mode at 9.3 GHz. The thin filmwas mounted on a sapphire sample holder and placed in thecenter of the cavity where the microwave electric field Evwas maximum. The sample was oriented with ab plane par-allel to Ev . The measured quantities were the Q factor of thecavity loaded with the sample and the shift of the resonantfrequency f. From the complex-frequency shift Dv˜ /v5D f / f 1iD(1/2Q), one can obtain by inversion the com-plex conductivity s˜ 5s12is2 of the film using the cavityperturbation expression.17Figure 1 shows the experimental results in zero magneticfield. From the imaginary part of the conductivity s251/m0vlL2, one can infer the zero-temperature London pen-etration depth lL(0)579 nm in our film. With this value,and the shape of s2, this film is found to be between theclean and the dirty limit, closer to the latter.18Here we focus on the effects of the applied magnetic fieldin the superconducting state. Figure 2 shows the field depen-dences (Bic) of the complex-frequency shift at various tem-peratures. By inversion of these data points, one can obtainthe field-dependent complex conductivity at each given tem-perature. Theoretically, the response of the superconductor in©2003 The American Physical Society07-1RAPID COMMUNICATIONSDULCˇ IC´ , POZˇ EK, PAAR, CHOI, KIM, KANG, AND LEE PHYSICAL REVIEW B 67, 020507~R! ~2003!the mixed state to an oscillating electric field Ev is given byan effective complex conductivity191s˜ eff512B/Bc212i~v0 /v!S 12 BBc2D ~s12is2!1 BBc2 sn11snB/Bc212i~v0 /v!.~1!The first term is due to the microwave current outside thevortex cores, and the second due to the normal current in thecores of the oscillating vortices. The meaning of the fractionB/Bc2 in Eq. ~1! is the volume fraction of the sample takenFIG. 1. Plots of imaginary and real parts of the complex-frequency shift in MgB2 thin film in zero magnetic field. Insetshows the corresponding conductivities.FIG. 2. Magnetic-field dependences of the complex-frequencyshift in MgB2 thin film for Bic . The arrows indicate increasingtemperatures.02050by the normal vortex cores. This parameter determines the dcresistivity in the flux flow regime,20 and has been used alsoin the microwave studies on classical superconductors.21 Thedepinning frequency v0 may change with field and tempera-ture from the strongly pinned case (v0@v) to the flux flowlimit (v0!v). In Eq. ~1!, the zero-field conductivity is s12is2, and sn is the normal-state conductivity. Similarmagnetic-field-dependent microwave studies have been car-ried out extensively on high-Tc superconductors.22–24Using the experimental field-dependent complex conduc-tivity and Eq. ~1!, we have determined the values of B/Bc2and v0 /v . Figure 3 shows some of the results. One observesthat each of the curves has initially a constant slope ~dashedlines in Fig. 3!. It defines very precisely the value of Bc2 at agiven temperature. Note that in this region the actual field Bis much smaller than Bc2, so that the superconducting film iswell in the mixed state. Hence, we determine, in fact, themean-field coherence length jMF as the radius of the normalvortex core (Bc2MF5F0 /2pjMF2 , where F0 is the flux quan-tum!. The fundamental property of a vortex much below thetransition to the normal state is that it contains many Landaulevels as bound superconducting states.20 When the field isincreased so that the transition to the normal state is ap-proached, the upper Landau levels are gradually lifted andfinally only the lowest Landau level remains. The field atwhich this level nucleates is conventionally known as theupper critical field Bc2. When the transition is very sharp,Bc2 can be determined straightforwardly from the singleturning point. However, in the cases of rounded transitions,one has to consider the fluctuation conductivity and the scal-ing laws, which govern the physics of the transition. At highFIG. 3. Variations of the volume fraction of the normal elec-trons. The dashed lines mark the low-field linear segments of thecurves wherefrom Bc2MF can be determined. The arrows indicate theBc2LLL values obtained from the 3D LLL scaling of the fluctuationconductivity in Fig. 4.7-2RAPID COMMUNICATIONSCOHERENCE LENGTHS AND ANISOTROPY IN MgB2 . . . PHYSICAL REVIEW B 67, 020507~R! ~2003!magnetic fields, one can use the scaling law based on thelowest Landau level ~LLL! scheme.25 It has been used suc-cessfully in high-Tc superconductors to determine the Bc2line.26In Fig. 4 we show the scaling of the fluctuation conduc-tivity s12sn according to the three-dimensional ~3D! LLLscheme.25,27 A very good scaling is achieved only with alinear choice of Tc(B) line ~equivalently Bc2 line! for thetemperature interval indicated in Fig. 4. The correspondingvalues are marked by arrows in Fig. 3. It is obvious that thevalues of Bc2 obtained from the 3D LLL scaling are close tothe points where the normal state seems to be reached, butnot precisely there. This feature is due to the superconduct-ing fluctuations, which appear also above the mean-fieldtransition. By taking the deviation from the normal-state be-havior as the onset of superconductivity, one selects, in fact,the point where the superconducting fluctuations start to ex-hibit a contribution noticeable above the noise level in theexperimental curve.The results of the present analysis are synthesized in Fig.5. The full symbols represent the mean-field results Bc2MFwith vortices formed by a great number of Landau levels andhaving radius jMF . The anisotropy ratio gMF5jMFab /jMFc’2 is practically temperature independent. The full lines inFig. 5 are obtained from the 3D LLL scaling. These linesdelineate the nucleation of vortices with the lowest LandauFIG. 4. 3D LLL scaling of the fluctuation conductivity s12sn .02050level only. The field required for this nucleation is related tothe Ginzburg-Landau coherence length Bc2LLL5f0 /2pjGL2.The anisotropy ratio is gGL5jGLab /jGLc 52.8, and also tem-perature independent in the interval where the 3D LLL scal-ing could be applied.We show by the dashed lines in Fig. 5 the results obtainedby cutting the experimental curves of 1/2Q in Fig. 2 at 95%of the normal-state value. The line obtained in this way forBc2ab(T) exhibits a positive curvature and, consequently,yields a temperature-dependent anisotropy ratio. Similar re-sults have been obtained in other recent reports,8–12 wherevarious cutting criteria have been used rather than the scalinglaw. It is not possible to find a single cutting level that wouldmimic the 3D LLL scaling procedure. It appears that thecutting level should be changed from one experimental curveto another at a different temperature in a way that is, a priori,not known. Obviously, the effects of the superconductingfluctuations cannot be simply accounted for by a cutting pro-cedure.One may remark that the extrapolated Bc2LLL lines in Fig. 5point to Tc533.8 K, while the dashed lines based on the95% cutting criterion reach 35.5 K. With a higher percentagefor the cutting level, one could reach even higher tempera-tures. These values are in the fluctuation region above thetrue Tc defined as the temperature where jGL diverges.In conclusion, we have shown that in MgB2, one candistinguish the mean-field coherence length in the mixedstate, and the Ginzburg-Landau coherence length at the tran-sition. The latter is found by considering the superconductingfluctuations and the proper scaling law of the measuredphysical quantity. We find the anisotropy ratios gMF’2 andgGL52.8, both with no temperature dependences.FIG. 5. The upper critical fields determined by various methods,Bc2MF ~symbols!, Bc2GL ~full lines!, and the values resulting from cut-ting the experimental curves ~dashed lines!.1 J. Nagamatsu, N. Nakagava, T. Muranaka, Y. Zenitani, and J.Akimitsu, Nature ~London! 410, 63 ~2001!.2 C. Buzea and T. Yamashita, Supercond. Sci. Technol. 14, R115~2001!.3 K.H.P. Kim, J.-H. Choi, C.U. Jung, P. Chowdhury, H.-S. Lee,M.-S. Park, H.-J. Kim, J.Y. Kim, Z.L. Du, E.-M. Choi, M.-S.Kim, W.N. Kang, S.-I. Lee, G.Y. Sung, and J.Y. Lee, Phys. Rev.B 65, 100510 ~2002!.7-3RAPID COMMUNICATIONSDULCˇ IC´ , POZˇ EK, PAAR, CHOI, KIM, KANG, AND LEE PHYSICAL REVIEW B 67, 020507~R! ~2003!4 C. Ferdeghini, V. Ferrando, G. Grassano, W. Ramadan, E. Bell-ingeri, V. Braccini, D. Marre, M. Putti, P. Manfrinetti, A. Palen-zona, F. Borgatti, R. Felici, and C. Aruta, Physica C 378-381, 56~2002!.5 C. Ferdeghini, V. Braccini, M.R. Cimberle, D. Marre, P. Manfri-netti, V. Ferrando, M. Putti, and A. Palenzona, Eur. Phys. J. B.30, 147 ~2002!.6 M. Angst, R. Puzniak, A. Wisniewski, J. Jun, S.M. Kazakov, J.Karpinski, J. Roos, and H. Keller, Phys. Rev. Lett. 88, 167004~2002!.7 K. Takahashi, T. Atsumi, N. Yamamoto, M. Xu, H. Kitazawa, andT. Ishida, Phys. Rev. B 66, 012501 ~2002!.8 M. Angst, R. Puzniak, A. Wisniewski, J. Roos, H. Keller, and J.Karpinski, cond-mat/0206407 ~unpublished!.9 U. Welp, G. Karapetrov, W.K. Kwok, G.W. Crabtree, Ch. Marce-nat, L. Paulius, T. Klein, J. Marcus, K.H.P. Kim, C.U. Jung,H.-S. Lee, B. Kang, and S.-I. Lee, cond-mat/0203337 ~unpub-lished!.10 M. Zehetmayer, M. Eisterer, J. Jun, S.M. Kazakov, J. Karpinski,A. Wisniewski, and H.W. Weber, Phys. Rev. B 66, 052505~2002!.11 L. Lyard, P. Samuely, P. Szabo, T. Klein, C. Marcenat, L. Paulius,K.H.P. Kim, C.U. Jung, H.-S. Lee, B. Kang, S. Choi, S.-I. Lee,J. Marcus, S. Blanchard, A.G.M. Jansen, U. Welp, G. Kara-petrov, and W.K. Kwok, Phys. Rev. B 66, 180502~R! ~2002!.12 A.V. Sologubenko, J. Jun, S.M. Kazakov, J. Karpinski, and H.R.Ott, Phys. Rev. B 65, 180505~R! ~2002!.0205013 W.N. Kang, H.J. Kim, E.M. Choi, C.U. Jung, and S.-I. Lee, Sci-ence 292, 1521 ~2001!.14 H.-J. Kim, W.N. Kang, E.-M. Choi, M.-S. Kim, K.H.P. Kim, andS.-I. Lee, Phys. Rev. Lett. 87, 087002 ~2001!.15 M.-S. Kim, J.A. Skinta, T.R. Lemberger, W.N. Kang, H.-J. Kim,E.-M. Choi, and S.-I. Lee, Phys. Rev. B 66, 064511 ~2002!.16 B.B. Jin, N. Klein, W.N. Kang, H.-J. Kim, E.-M. Choi, S.-I. Lee,T. Dahm, and K. Maki, Phys. Rev. B 66, 104521 ~2002!.17 D.-N. Peligrad, B. Nebendahl, M. Mehring, A. Dulcˇic´, M. Pozˇek,and D. Paar, Phys. Rev. B 64, 224504 ~2001!.18 A.A. Golubov, A. Brinkman, O.V. Dolgov, J. Kortus, and O.Jepsen, Phys. Rev. B 66, 054524 ~2002!.19 A. Dulcˇic´ and M. Pozˇek, Physica C 218, 449 ~1993!.20 M. Tinkham, Introduction to Superconductivity ~McGraw-Hill,New York, 1975!.21 Y. B. Kim and M. J. Stephen, in Superconductivity, edited by R.D. Parks ~Dekker, New York, 1969!, Vol. 2.22 J. Owliaei, S. Sridhar, and J. Talvacchio, Phys. Rev. Lett. 69,3366 ~1992!.23 I. Ukrainczyk and A. Dulcˇic´, Europhys. Lett. 28, 199 ~1994!.24 M. Golosowsky, M. Tsindlekht, and D. Davidov, Supercond. Sci.Technol. 9, 1 ~1996!.25 S. Ullah and A.T. Dorsey, Phys. Rev. B 44, 262 ~1991!.26 U. Welp, S. Fleshler, W.K. Kwok, R.A. Klemm, V.M. Vinokur, J.Downey, B. Veal, and G.W. Crabtree, Phys. Rev. Lett. 67, 3180~1991!.27 I. Ukrainczyk and A. Dulcˇic´, Phys. Rev. B 51, 6788 ~1995!.7-4

Coherence lengths and anisotropy in MgB_2 superconductor

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Coherence lengths and anisotropy in
                    
                      
                        
                          
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Coherence lengths and anisotropy in MgB2 superconductor

Coherence lengths and anisotropy in MgB2 superconductor

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