j.r. kirtley et al- magnetic imaging of interlayer josephson vortices

8/3/2019 J.R. Kirtley et al- Magnetic imaging of interlayer Josephson vortices

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Magnetic imaging of interlayer Josephson vortices

J.R. Kirtleyl, K.A. MoleF, J.A. SchlueteP, J.M. Williams3, D.G. Hinks3, T.W. Li3, G. Villard,and A. Maignan41IBM Research Division, Yorktown Heights, NY 10598, USA2Dept. of Applied Physics, Stanford University, Stanford, CA 94305, USA3Materials Science Division, Argonne National Laboratory, Argome, IL 60439, USA4CRISMAT-ISMRA, 14050 Caen Cedex, France s. .. mm

o soAbstract: We have magnetically imaged interlayer Josephson vortices emergin%!!?g%lanes of single crystals of the organic superconductor ~-(BEDT-TTF)z CU(N5ingle layer cuprate high-T~ superconductors TkBazCuOcti (TI-2201) and (Hg,Cu Bz@u~(Hg-1201), using a scanning Superconducting Quantum Interference Device (@I@microscope. These images provide a direct measurement of the interIayer penetration dept~which is approximately 63pm for ~-(BEDT-TTF)z CU(NCS)Z, 18~m for T1-2201 and 8pm for

Hg-1201. The lengths for the cuprates are about a factor of 10 larger than originally pre&cted bythe interlayer tunneling model for the mechanism of superconductivity in layered compounds,irdcating that thk mechanism alone cannot account for the high critical temperatures in thesematerials. .Key words: interlayer, vortex, SQUID, magnetic, microscopy

Many unconventional superconductors, notably cuprates and some organics, have a stronglyanisotropic layered structure. The layered superconductors are commonly modekd using theLawrence-Doniach model[l], as a stack of conventional superconducting layers withJosephson coupliig beh.veen the layers. The strength of the interlayer coupling is an importantpartieter in any phenomenological description of these materials, but it can be difllcult tomeasure. We discuss in this paper a duect way to measure this interlayer couplin~ by imagingvortices trapped parallel to, and screened by, the superconducting layers. The magneti? shapeof these vortices is directly related to the strength of the interlayer coupling, through the interlayerpenetration depth lL=(c0J8z%J0 )ln [2], where JOis tie interlayer critical current density, c isthe speed of Iigh$ @O =hd2e is the superconducting flux quanu h is Plancks constan; e isthe charge on the electro~ and s is the interlayer spacing. Clem and Coffey derived expressionsfor the structure of vortices parallel to the layers (Fig. la), called interlayer Josephson vortices,in the context of the Lawrence-Doniach mode1[2]. Except at the smalkst length scales, thesevortices are identical to vortices in an anisotropic London model. Kogan and Clem [3] calculatedthe magnetic fields from an anisotropic vortex extending above a superconducting surface. Bycomparing these expression with our measurements, we get quantitative values for the interlayerpenetration depths. ~

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DISCLAIMERThis report was prepared as an account of work sponsoredby an agency of the United States Government. Neither theUnited States Government nor any agency thereof, nor anyof their employees, make any warranty, express or implied,or assumes any legal liability or responsibility for theaccuracy, completeness, or usefulness of any information,apparatus, product, or process disclosed, or represents thatits use would not infringe privately owned rights. Referenceherein to any specific commercial product, process, orservice by trade name, trademark, manufacturer, orotherwise does not necessarily constitute or imply itsendorsement, recommendation, or favoring by the UnitedStates Government or any agency thereof. The views andopinions of authors expressed herein do not necessarilystate or reflect those of the United States Government orany agency thereof.

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Fig 1. (a) Sketchof the current flow, equivalentto contours of constantmagnetic field, for an isolatedinterlayer Josephson vortex with its axis parallel to the planes. The gray regions indicatesuperconductinglayerswith Josephson coupling between the layers. The interlayer spacings, in-planepenetration depth 2 [1 and interlayer penetration depth ~~ are shown. b) For length scales largecomparedtoS, the vortex structure becomesindistinguishable from a vortex in a continuousanisotropicLondonmodel. c) Sketch of the measuremmt geometry showing the pickup loop nearly parallel to the,edge of a single crystal (not drawn to scale)with a 3-d rendering of scanning SQUIDmicroscopedataof aninterlayer vortex in T1-2201 superimposed. d) Schematic of the SQUID sensor. The signal isproportionalto changes in the amount ofmagneticflux through the pickuploop. . ..Our measurements were made with a scanning SQUID microscope [4], in which a sample isscanned relative to a superconducting pickup Ioop oriented approximately parallel to the samplestiace (Fig. lc). At any given positioz the magnetic flux through the pickup loop, 0,, is theintegral of the z-component of the magnetic field over the area of the pickup loop. The data arerepresented as intensi~ maps of@ vs. tie position of the pic~p 100P in the XJ pl~e. Thepickup loop is fabricated with well-shielded leads to an integrated niobium SQUID (Fig. id).The crystal growth of our ~-(BEDT-TTF)zCU(NCS)Z [5], T1zBazCuOA@ [6], and(Hg,Cu)BazCuO,M[7] single ctystals has been d~cribed elsewhere. The organic superconductingcrystals were mounted with vacuum grease with the highly conducting planes perpendicular to the

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Fig.2 Scanning SQUID microscope images of interlayer Josephson vortices emerging parallel to theplanes from single crystals of (a) (Hg,Cu)BazCuOJ+~,(b)TIZBaZtios+;, and(c)w(BEDT-TTF)zCU(NCS)ZScaled schematic drawings of the SQUIDpickup loops used for eachimage are superimposedon the images: an octagonal loop4pm in diameterwas used for (a), and squarepickup loops 8.2pm on a side were used for (b) and (c). Lnages of vorticesemerging perpendicular tothe planes of a single crystal of YBazCuOT+6sing the same types of pickup loops are superimposed atthe top of the images (a) and (b). The images are aligned so that the highly conducting planes arevertieal. The vortex images are resolution limited horizontally (perpendicularto the planes), but have awell defined spatial extent vertically (parallel to the planes). The lm@ of the vortices parallel to theplanesis setby the interlayerpenetrationdepth.scan plane. The Hg-1201 and T1-2201 crystals were embedded in epoxy in the same orientationand polished to expose a plane pe~endicukw to the c-axis direction. ..Both sample and SQUID were immersed in liquid helium at 4.2K in a magnetically shieIdedcryostat, A small magnet was used to adjust the component of the magnetic field perpendicular tothe scan plane so that only a few well separated vortices were trapped in the crystal face. In theorganic superconductors, there is an inhomogeneous magnetic background in addition to welldefinedvortices. This takes the form of rippling of the fields parallel to the layered planes. Wespeculate that these rippling f=tures result from-penetration of the external field on a length scalewhich is longer than the intrinsic interlayer penetration deptk and that these regions with weakcoupling result from mechanical or chemical defects. In additiou the trapped positions of vorticestend to be inhomogeneous, as opposed to scattered uniformly throughout the crystal face, as isseen for vortices trapped with their axes perpendicular to the planes. This non-uniform trapping


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Fig. 3 a) Cross-sectionaldata through the imagesof Fig. 2, along vertical lines throwzhthe centers ofth;vort~ces and parallel to the highly conductingplanes. The open circles are the data, and the lines arefits to this data using the theory of Ref. [3], with the height z of the pickup lcmpabove the samplesurface, and the interlayer penetration depth A or k as the two fitting parameters. The organicsuperconductor and T1-2201 data were taken with a square pickup loop 8.2pm on a side, and theHg-1201 data was taken with an octagonalloop 4flm on a side. b) For comparison, a c-axis Abrikosovvortex inYBCO, also takenwith a 4gm octagonalIoop.Note the change in the horizontal axis scale.is a source for conce~ as one could imagine that vortices trap in regions with exceptionallyweak, interpIane coupling, so that our measurements might overestimate the intrinsic penetrationdepths. However, measurements of the Josephson plasma resonance, which average eve; largeregions of the sample, are in good agreement with our measurements for T1-2201[15]. .A survey of our images of interlayer vortices in several superconductors is shown in Fig. 2.Cross-sections through these images, in the vertical d~ection parallel to the conducting planes,are shown as the open circles in Fig. 3. The limes in Fig. 3 are fits to these cross-sections asfollows: The z component of the magnetic field of an interlayer voflex (modelled as anartisotropic Ginzburg-Landau vortex) above the superconducting surface (including spreading ofthe vortex as it approaches the surface), is given by:

where

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q@j = - @,(l +m]k;)/n3a3[/nlk;a3(k+ al)+ka3+k; ]al = ((1 -1-m#)/ml)l/2 , a3 =((1 +lnlk; +7113k;)/7123)2 , k=(k; +k;)lc , ml =2;/12 ,nZ3= J.~/l.z, 1 = (1~~~) 13,where 1 II is the (short) in-plane penetration dept~ and ).~ is the(long) interplane penetration depth. The fields are summed over the geometry of the pickup loop.The solid circles in Fig. 3 are the experimental data, the lines are the fits to the equations above.With the London penetration depth 211fixed at O.17~m forHg-1201 and T1-2201, and 0.52Amfor the organic superconductor, the two fitting pammeters are the height z of the pickup loopabove the surface, and lA. Fits of a number of such vortices for each crystal resulted in values of. ...- ?. = 8~l\[m for(Hg,Cu)Ba~CuO~ti [9] , 2 = 18S~m for T]zBazC@c# [6,3], and 21 = 63A15~m for w(BEDT-TTF)zCu(NCS) [8].These values of IL are of special interest as a test for a candidate mechanism forsuperconductivi~ in these materials. It has been proposed that non-Fermi liquid behavior in thenormal state may d.rNe the superconducting transition because of a change in the interlayercoupliig between the two states[lO, 11,12,13]. This class of mechanisms is known as theInterlayer Tunneling (ILT) model. In the simplest version of the ILT model, the superconductingcondensation energy, E., is supplied entirely by a change in the kinetic energy pe~endicular tothe planes. The model therefore requir~C~a~lrit$mship between the interlayer penetration depthand the condensation energy ~ILT =.(~~) - , where l?== &As/87r is the condensationenergy per formula unit, JYCis the thermodynamic critical fiel~ A is the area per formula unig mis the mass of the electrou and a. is theBohrnwmetodY2-14]. The ork~al =ti.mat~of thecondensation energy from specific heat measurements lead to ALCT Ipm for T1-2201 and- lopm for ~-(BEDT-TTF)2CU(NCS) .ThiS would irnpIy that the amount ofg-1201, and 21LT energy available to the superconducting transition from the interlayer coupling is about 2 ordersof magnitude smaller than the condensation energy. Recently Chalmwariy and co-workers havesuggested that the condensation energies can be much lower than originally estimated due tofluctuation effects[16]. When these effects are taken into accOUn~their valut% for &L~ arewithii a factor of ~o of our measurements for Ic for T1-2201. However, thk still implies thatthe ILT mechanism alone cannot account for the large critical tempemtures in these materials..An aItemate view of interlayer Josephson coupliig results if we start with the no~l-stateconductivity, and assume either specular or diffuse interlayer pair trmsport. For difise pairtransport (parallel momentum not conserved [17, 18,19], the Josephson current densily betweentwo identical superconducting sheets at T=O is given by J. = zAO/2eR~ [20], where AO is thezero temperature energy gap, and RL is the nornud state resistance per plane perpendicular ~otheplanes. If we take measured values for RL just above T., and the BCS value AO= 1.76kBTc,we find values of 1A- 20pn for @3EDT-TTF)zCu(NCS), IL - 6pI for T1-2201, andJ,L - 8~m for Hg-1201. The application of this model requires at least two assumptions: that RLis temperature independent below TC,and that the gap is s-wave. One would expect the couplingfor a d-wave gap (as is believed to be true for the cuprates) to be smaller than estimated here: infacq the inte~l~ne coupling isdiffisive interplanc coupling.

expected to be zero for a isotropic d-wave superconductor withTherefore one cannot expect such a picture to give good


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quantitative agreement with experiment, but it does agree to within a factor of roughly 3 for all ofour measurements, and in fact works welI for a number of the cuprate superconductors[2 1].In conclusion magnetic imaging of interlayer vortices with the scanning SQUID microscope is apowerfid tool for directly measuring the interlayer penetration depth. Measurements on anorganic superconductor and WOsingle-plane cuprate superconductors indicate that the interlayertunneling mechanism alone camot account for the high critical temperatures observed in thesematerials,We would like to thank M.B. Ketchen for the desig% and M. Bhushan for the fabricatio~ of theSQUIDS used in our microscope. We wouid also like to acknowledge usel?d conversations with- P.W. Anderso% S. Chakravarty, A.J. Legge% D.J. Scalapino, C. Panagopoulos, D. van derMare], V.G. Koga% and J. Clem. K.A. Moler would like to acknowledge the support of an R.H.Dicke post-doctoral fellowship, and NSF fimdimg through the MRSEC award to PrincetonUniversity (DMR 97-00362).

[1] Lawrence WE, and Doniach S (1971) In E. Kanda (cd) Proceedings of the 12th InternationalConferenceonLowTemperaturePhysics.Acadenic Press.Kyoto.pp 361-62[2] ClemJR and C&feyMW (1990)Phys. Rev. B 42:6209-16; ClemJR CoffeyMW, and HaroZ (1991)Phys. Rev. B 44:2732-3%GurevichA, BenkraoudaM, and Clem JR (1996)Phys.Rev.B 543196-206[3] KirtleyJR KoganV, Clem JIL and MolerKA, Phys. Rev.B in press[4]KirtleyJR et al. (1995)Appl. Phys. Lett. 66:113840[5] CarlsonKD et al. (1988) Inorg. Chem. 27:965-67[6] Moler KA, Kirtley@ HinksDG, LiTW, and XuM (1998)Science279:1193-96[7]D. Pelloquin et al. (1997) Physics C 273:205-212[8]KirtIeyJ& MolerKA, Schlueter JA, andWNiams JM, submittedto J. Phys. Condens.Matt.[9] Kinky m MolerKA,Villard G, andMaignan A (1998)Phys.Rev.Lett. 81:2140-2143[10]WheatleyJ, HsuT, AndersonPW (1988)Nature 333:121-21[11] Anderson PW (1991) Physics C 185:11-16; (1991) Phys. Rev. Lett. 6%660-63; (1992) Science256:1526-31[12]ChakravartyS, SudboA, AndersonPW, and Strong S (1993)Science261:33740[13] hderson PW(1995)Science268:1154-55[14]LeggettAJ (1996)Science274:587-89 .[15]TsvetkovAA (1998)Nature 395:360-62 .[16] ChakravartyS,KeeH.Y. and Abrahams E., preprint[17] GrafMJ, RainerD, Sauls JA (1993) Phys. Rev. B 47:2089-98[18] RojoAG and LevinK (1993)Phys. Rev.B 48:6861-64[19]HirschfeldPJ,Quinlan SM, ScalapinoDJ (1997) Phys.Rev. B 55:2742-47[20] AmbegaokarV and Baratoff A (1963) Phys. Rev. Lett 10:456-59; 11:401(E)[21] Basov DN et al. (1994) Phys. Rev. B 50:3511-14

j.r. kirtley et al- magnetic imaging of interlayer josephson vortices

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