In-Plane Anisotropy of Flux-Flow Resistivityin Layered Organic Superconductor ­-(BETS)2GaCl4

Syuma Yasuzuka1+, Shinya Uji2, Taichi Terashima2, Satoshi Tsuchiya2†

, Kaori Sugii2,Biao Zhou3, Akiko Kobayashi3, and Hayao Kobayashi3

1Research Center for Condensed Matter Physics, Hiroshima Institute of Technology, Hiroshima 731-5193, Japan2National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0003, Japan

3Department of Chemistry, College for Humanities and Sciences, Nihon University, Setagaya, Tokyo 156-8550, Japan

(Received October 15, 2013; accepted November 14, 2013; published online December 9, 2013)

We recently observed in-plane fourfold-symmetric anisotropy in the flux-flow resistivity (FFR) of d-wave organicsuperconductor ¬-(ET)2Cu(NCS)2. Origin of the fourfold-symmetric anisotropy was discussed in terms of the interplaybetween the Josephson-vortex dynamics and the superconducting gap structure. Here, we report the in-plane anisotropyof the FFR of layered organic superconductor ­-(BETS)2GaCl4. The in-plane angular dependence is mainly described bytwofold symmetry. The dip structure appears when the magnetic field is applied parallel to the c-axis. These results aredifferent from the case of ¬-(ET)2Cu(NCS)2, even though the Fermi-surface topology of ­-(BETS)2GaCl4 is muchsimilar to that of ¬-(ET)2Cu(NCS)2. The different anisotropic behavior is discussed in terms of interlayer couplingstrength.

The unconventional mechanism of superconductivity inhighly correlated materials, such as high-Tc cuprates,1) heavyfermion compounds,2) iron-pnictide superconductors,3) andorganic molecular crystals,4) have attracted considerableattention. Because the gap structure is intimately related topairing interaction,5) it is necessary to clarify the super-conducting (SC) gap structure.

To this end, various experimental methods have beendeveloped. The power-law temperature dependence ofphysical quantities such as specific heat and nuclear magneticrelaxation rate provide information on the existence of lineor point nodes in the SC gap structure. By measuring theangular-oscillation of the specific heat with respect to theapplied magnetic field orientation, one can detect the detailsof the SC gap structure, especially the locations of its nodes.6)

Angular-resolved thermal conductivity is also such anexperimental technique.7) The oscillatory behaviors in thespecific heat and the thermal conductivity are understood onthe basis of the “Doppler shift” in the energy spectrum of thequasiparticles (QPs) due to the superfluid flow around thevortices.8–11)

Besides specific heat and thermal conductivity, gap nodesmay also affect the flux-flow transport.12,13) Basically, flux-flow resistivity is a measure of QP dissipation in vortexdynamics.14,15) Recently, we observed in-plane fourfold-symmetric anisotropy in the flux-flow resistivity (FFR) ofthe d-wave organic superconductor ¬-(ET)2Cu(NCS)2,16)

where ET stands for bis(ethylenedithio)tetrathiafulvalene.The origin of the fourfold-symmetric anisotropy was dis-cussed in terms of the interplay between the Josephson-vortexdynamics and the SC gap structure. Searches for othersuperconductors with d-wave pairing symmetry is now neededin order to make further understanding of the relationshipbetween the vortex dynamics and the SC gap structure.

The organic molecular crystal ­-(BETS)2GaCl4 is a quasitwo-dimensional (2D) superconductor with a transitiontemperature Tc of ³8K, where BETS stands for bis(ethylene-dithio)tetraselenafulvalene.17) The crystal structure has tri-clinic symmetry.18) The planar BETS molecules are stackedalong the a- and c-axes, and consequently form 2Dconduction layers. The GaCl4¹ ion (insulating) layer is

intercalated between the BETS layers, which makes theb-axis the direction of least conduction. Band-structurecalculation predicts that ­-(BETS)2GaCl4 has one closed(2D) and two open Fermi surfaces which is topologicallysimilar to ¬-(ET)2Cu(NCS)2.19) Measurements of theShubnikov-de Haas (SdH) and angular-dependent magneto-resistance oscillations (AMROs) qualitatively agree withthe band calculation.20) Reflecting the layered structure, itsGinzburg–Landau coherence length perpendicular to thelayers, �?ð0Þ (³12Å), is less than the interlayer spacing d(¼ 18:6Å).21) A recent scanning tunneling microscopy(STM) study suggested dxy gap symmetry with the linenodes along the a�- and c�-axes.22) In this Letter, we reportthe experimental results of the in-plane anisotropy of the FFRfor ­-(BETS)2GaCl4.

Needlelike single crystals of ­-(BETS)2GaCl4 weresynthesized electrochemically.18) The interlayer resistancewas measured by a conventional four-probe ac techniquewith electric current along the b�-axis which is normal to theconducting (a–c) plane. In the present measurements, it isvery important to rotate H within the conducting plane withvery high accuracy because a slight field misalignment causestwofold anisotropy of the resistance due to the large Hc2

anisotropy.21) In this experiment, the samples were mountedon a two-axis rotator in a 4He cryostat with a 17-T SCmagnet. In this rotator, it is possible to continuously changethe ª angle with a resolution of �� ¼ 0:1°, where ª is theangle between the magnetic field and the least conductingb�-axis, and discretely changed the plane of rotation,described by the azimuthal angle º with a step of �� ¼ 10°which is defined as the inclination from the c-axis within theconducting plane. The magnetic field orientation relative to ª

and º is shown in the inset of Fig. 1. Temperatures down to1.5K were readily accessible.

First, we measured the interlayer resistance as a function ofthe angle ª at various º values to find the position of theH k ac plane. As an example of this procedure, the interlayerresistance as a function of the field angle ª is shown in Fig. 1,where the field is rotated at � ¼ 20°. At the highest currentof 250 µA and the magnetic field applied parallel to theconducting plane, the �ð�Þ curve shows a sharp peak, which

Journal of the Physical Society of Japan 83, 013705 (2014)

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is related to the vortex dynamics at � ¼ 90°. Note thatthe peak at � ¼ 90° strongly depends on the current. Withincreasing current, the peak height increases gradually.Similar peaks have previously been observed for the mixedstate of ¬-(ET)2Cu(NCS)2.16)

Figure 2 shows the interlayer resistance as a function ofthe normal component of magnetic field, H cos �, at � ¼ 20°at various magnetic fields. At H ¼ 7T, a quasisinusoidaldependence is observed and the SC state is not destroyed ataround the parallel position. As the field further increases, theSC transition becomes narrow and the peak becomes clearer.The peak is visible up to 12T, beyond which it is graduallysuppressed. The peak width 2�H is almost independent ofthe normal component of the magnetic field, where 2�H isdefined as the region between the minima on both sides of thepeak. From Fig. 2, �H is found to be µ0.35 T. Similar peakbehavior is reported in various Josephson-coupled layeredcompounds.16,23,24)

One may expect the sharp peak to be associated with thedynamics of the Josephson vortices induced by the lock-intransition.24,25) This is because, in the lock-in state, theJosephson vortices are weakly pinned in the insulating layersand can be easily depinned by the Lorentz force provided theinterlayer current is sufficiently large, leading to large energy-dissipation for fields nearly parallel to the layers.24) In thelock-in state, the perpendicular component of the magneticfield H cos � should be smaller than the lower critical fieldnormal to the layers. Although the lower critical field of­-(BETS)2GaCl4 has not been determined experimentally,it should be comparable to ³90G in ¬-(ET)2Cu(NCS)2(Tc � 10K).26) Because a �H value of ³0.35 T is too large,it is unlikely that the sharp peak is due to the motion of theJosephson vortex induced by the lock-in transition. Instead,the motion of the combined vortex made by pancake andJosephson vortices is more likely the origin of the sharppeak, as previously discussed for the mixed state of ¬-(ET)2Cu(NCS)2.16)

Figure 3 shows the ª-dependence of the interlayerresistance at 4.2K, a magnetic field of 8.5 T, and at variousº values with a step of �� ¼ 10°. We clearly observe thepeak structure at � ¼ 90° at all º values, which reveals thevortex dynamics for all in-plane field directions. The peakstructure gradually changes with º. For a detailed image ofthe anisotropic in-plane field effect, we plot the º dependenceof the interlayer resistance at � ¼ 90° for various currentsin Fig. 4. In the entire current range, the in-plane angulardependence is mainly described by the twofold symmetryand the dip structure appears when the magnetic field isapplied parallel to the c-axis. This result is different from thecase of ¬-(ET)2Cu(NCS)2, even though the Fermi-surfacetopology of ­-(BETS)2GaCl4 is very similar to that of ¬-(ET)2Cu(NCS)2.

Let us discuss the origin of the different behavior between¬-(ET)2Cu(NCS)2 and ­-(BETS)2GaCl4. Mielke et al.20)

investigated the Fermi-surface topology of ­-(BETS)2GaCl4using SdH and AMROs. The data show that the Fermi-surface topology of ­-(BETS)2GaCl4 is very similar to that of¬-(ET)2Cu(NCS)2, except for one important respect; theinterplane transfer integral of ­-(BETS)2GaCl4 is a factor ³5larger than that in ¬-(ET)2Cu(NCS)2. According to magneto-resistance studies,21,27) the anisotropic parameter � ¼Hc2k=Hc2? is estimated to be 9.7 for ­-(BETS)2GaCl4 and19 for ¬-(ET)2Cu(NCS)2. The stronger interlayer coupling in­-(BETS)2GaCl4 may be responsible for the origin of thetwofold symmetry in the FFR.

Since ­-(BETS)2GaCl4 is much more three-dimensionalthan ¬-(ET)2Cu(NCS)2, an orbital pair breaking effect in­-(BETS)2GaCl4 plays a more important role than in¬-(ET)2Cu(NCS)2. In fact, as shown in Fig. 2, all the datafor j�Hj > 0:35T do not collapse onto a single curve,

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J. Phys. Soc. Jpn. 83, 013705 (2014) Letters S. Yasuzuka et al.

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suggesting that the parallel field component also contributesto the destruction of the SC state. Namely, the orbital pairbreaking effect works to some extent even for the in-planefield. In this case, the effect of the normal-state magneto-resistance cannot be avoided in the in-plane anisotropy of theFFR. Figure 5 shows the normal-state magnetoresistancein the magnetic field of 14.8 T rotating within the 2Dconducting plane. The normal-state magnetoresistance showsthe twofold symmetry with maximum at around � ¼ �20°.The result is similar to that of Tanatar et al., where the in-plane resistance with electric current along the c-axis wasmeasured.28) The twofold symmetric behavior can beexplained in terms of Fermi-surface anisotropy if thenormal-state magnetoresistance mainly arises from the 2Dellipsoidal pocket elongated along the c-axis.18) In the small£ system, large twofold component due to the normal-statemagnetoresistance may mask the fourfold ones.

Another possibility is the relation with the intrinsic pinningof the vortices. Because of the larger £ value, the couplingbetween the 2D conducting planes is weaker in ¬-(ET)2Cu(NCS)2. The fact shows that the vortices are pinnedmore weakly (driven more easily) in the insulating layers.Therefore, the intrinsic nature of the in-plane anisotropy,the fourfold symmetric behavior will be evident in ¬-(ET)2-Cu(NCS)2. To confirm the validity of these scenarios, studiesin the highly 2D superconductor �00-(ET)2SF5CH2CF2SO3

are now in progress, in which the incoherent nature of theinterlayer transport is evident.29)

Finally, the origin of the dip structure at � ¼ 0° in thetwofold symmetry is briefly discussed. A similar dip structurewas observed in ¬-(ET)2Cu(NCS)2.16) The origin of the dipin ­-(BETS)2GaCl4 may be the same as that in ¬-(ET)2Cu(NCS)2. The sharp dip appears for H parallel to thec-axis, which almost coincides with the node directionsdetermined by the STM experiment,22) but not for theantinodal directions in ¬-(ET)2Cu(NCS)2.30) In interpretingthe STM experiments, one needs to bear in mind that theSTM spectrum parallel to the 2D plane can be stronglyaffected by the atomic state at the edge. For ­-(BETS)2GaCl4,experiments sensitive to the nodal direction, such as the fieldangle dependences of thermal conductivity and specific heatmeasurements,9–11,31,32) are needed.

In summary, we investigated the in-plane anisotropy of theFFR in the layered organic superconductor ­-(BETS)2GaCl4.Despite the similarities of the Fermi surface and the SC gapstructure between ¬-(ET)2Cu(NCS)2 and ­-(BETS)2GaCl4,the fourfold symmetry in the FFR was clearly observedin ¬-(ET)2Cu(NCS)2, but not the twofold symmetry in­-(BETS)2GaCl4. The absence of the fourfold symmetry in­-(BETS)2GaCl4 may be related to the stronger interlayercoupling than in the case of ¬-(ET)2Cu(NCS)2. Test for the

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at various currents, where T ¼ 4:2K and H ¼ 8:5T. The resistance curveshave a sharp minimum at � ¼ 0° (H k c).

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Fig. 3. (Color online) ª-dependence of interlayer resistance at 4.2K undera magnetic field of 8.5T for various values of º. The curves are measured inintervals of �� ¼ 10° from ¹80° (top curve) to 120° (bottom). The curvesare vertically shifted for clarity. The peak structure at � ¼ 90° is clear at all ºvalues, showing the vortex dynamics in all the in-plane field directions.

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FFR in highly 2D superconductors with d-wave pairingsymmetry is needed to clarify the relation between vortexdynamics and SC gap structure.

Acknowledgment This study was partly supported by a Grant-in-Aid forScientific Research (C) (No. 25400383) from the Japan Society for the Promotionof Science (JSPS).

+yasuzuka@cc.it-hiroshima.ac.jp†Present address: Department of Applied Physics, Hokkaido University,Sapporo 060-8628, Japan.1) C. C. Tsuei and J. R. Kirtley, Rev. Mod. Phys. 72, 969 (2000).2) C. Pfleiderer, Rev. Mod. Phys. 81, 1551 (2009).3) K. Ishida, Y. Nakai, and H. Hosono, J. Phys. Soc. Jpn. 78, 062001

(2009).4) K. Kuroki, J. Phys. Soc. Jpn. 75, 051013 (2006).5) M. Sigrist and K. Ueda, Rev. Mod. Phys. 63, 239 (1991).6) T. Sakakibara, A. Yamada, J. Custers, K. Yano, T. Tayama, H. Aoki,

and K. Machida, J. Phys. Soc. Jpn. 76, 051004 (2007).7) Y. Matsuda, K. Izawa, and I. Vekhter, J. Phys.: Condens. Matter 18,

R705 (2006).8) G. E. Volovik, JETP Lett. 58, 469 (1993).9) I. Vekhter, P. J. Hirschfeld, J. P. Carbotte, and E. J. Nicol, Phys. Rev. B

59, R9023 (1999).10) A. B. Vorontsov and I. Vekhter, Phys. Rev. B 75, 224501 (2007).11) A. B. Vorontsov and I. Vekhter, Phys. Rev. B 75, 224502 (2007).12) Y. Higashi, Y. Nagai, M. Machida, and N. Hayashi, Physica C 471, 828

(2011).13) Y. Higashi, Y. Nagai, M. Machida, and N. Hayashi, Physica C 484, 97

(2013).14) J. R. Clem and M. W. Coffey, Phys. Rev. B 42, 6209 (1990).15) A. E. Koshelev, Phys. Rev. B 62, R3616 (2000).16) S. Yasuzuka, K. Saito, S. Uji, M. Kimata, H. Satsukawa, T. Terashima,

and J. Yamada, J. Phys. Soc. Jpn. 82, 064716 (2013).

17) H. Kobayashi, T. Udagawa, H. Tomita, K. Bun, T. Naito, and A.Kobayashi, Chem. Lett. 22, 1559 (1993).

18) H. Kobayashi, H. Tomita, T. Naito, A. Kobayashi, F. Sakai, T.Watanabe, and P. Cassoux, J. Am. Chem. Soc. 118, 368 (1996).

19) P. A. Goddard, S. J. Blundell, J. Singleton, R. D. McDonald, A.Ardavan, A. Narduzzo, J. A. Schlueter, A. M. Kini, and T. Sasaki,Phys. Rev. B 69, 174509 (2004).

20) C. Mielke, J. Singleton, M.-S. Nam, N. Harrison, C. C. Agosta, B.Fravel, and L. K. Montgomery, J. Phys.: Condens. Matter 13, 8325(2001).

21) M. A. Tanatar, T. Ishiguro, H. Tanaka, and H. Kobayashi, Phys. Rev. B66, 134503 (2002).

22) K. Clark, A. Hassanien, S. Khan, K.-F. Braun, H. Tanaka, and S.-W.Hla, Nat. Nanotechnol. 5, 261 (2010).

23) M. Chaparala, O. H. Chung, Z. F. Ren, M. White, P. Coppens, J. H.Wang, A. P. Hope, and M. J. Naughton, Phys. Rev. B 53, 5818 (1996).

24) S. Uji, T. Terashima, M. Nishimura, Y. Takahide, T. Konoike, K.Enomoto, H. Cui, H. Kobayashi, A. Kobayashi, H. Tanaka, M.Tokumoto, E. S. Choi, T. Tokumoto, D. Graf, and J. S. Brooks, Phys.Rev. Lett. 97, 157001 (2006).

25) D. Feinberg and C. Villard, Phys. Rev. Lett. 65, 919 (1990).26) P. A. Mansky, P. M. Chaikin, and R. C. Haddon, Phys. Rev. Lett. 70,

1323 (1993).27) K. Oshima, H. Urayama, H. Yamochi, and G. Saito, J. Phys. Soc. Jpn.

57, 730 (1988).28) M. A. Tanatar, T. Ishiguro, H. Tanaka, A. Kobayashi, and H.

Kobayashi, J. Supercond. 12, 511 (1999).29) J. Wosnitza, J. Hagel, J. S. Qualls, J. S. Brooks, E. Balthes, D.

Schweitzer, J. A. Schlueter, U. Geiser, J. Mohtasham, R. W. Winter,and G. L. Gard, Phys. Rev. B 65, 180506(R) (2002).

30) T. Arai, K. Ichimura, K. Nomura, S. Takasaki, J. Yamada, S. Nakatsuji,and H. Anzai, Phys. Rev. B 63, 104518 (2001).

31) K. Izawa, H. Yamaguchi, T. Sasaki, and Y. Matsuda, Phys. Rev. Lett.88, 027002 (2001).

32) L. Malone, O. J. Taylor, J. A. Schlueter, and A. Carrington, Phys. Rev.B 82, 014522 (2010).

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