London penetration depth in (BEDT-TTF) 2 superconductors

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1 J. Phy. IV France 114 (004) 1115 EDP Science, Le Uli DOI: /jp4: London penetration depth in (BEDF) uperconductor R.W. Giannetta 1, D.D. Lawrie 1, A. Carrington, R. Prozorov 3, J.A. Schlueter 4, A.M. Kini 4, U. Geier 4, J. Mohtaham 5, R.W. Winter 5 and G.L. Gard 5 1 Loomi Laboratory of Phyic, Univ. of Illinoi at UrbanaChampaign, 1110 W. Green, Urbana, Il 61801, USA rug@uiuc.edu Dept. of Phyic, Univ. of Britol, Britol, UK a.carrington@britol.ac.uk 3 Dept. of Phyic and Atronomy, Univ. of South Carolina, Columbia, SC 908, USA prozorov@mailap.org 4 Material Science Diviion, Argonne National Laboratory, Argonne, Il 60439, USA jachlueter@anl.gov 5 Department of Chemitry, Portland State Univerity, Portland, OR 9707, USA Abtract. Meaurement of the London penetration depth, λ(), are reported for crytal of uperconducting κ(e) ]Br ( C = 11.6 K) and β"(e) ( C = 5. K) at temperature down to 0.35 K. For κ(e) ]Br the uperfluid denity how the power law behavior characteritic of nodal quaiparticle with impurity cattering. he rate of change of uperfluid denity with temperature i higher than predicted by a weakcoupling d wave model and higher than oberved in the copper oxide. he inplane penetration depth conitently how a 3/ dependence while the interplane penetration depth varie a 1.. Meaurement in β"(e) alo how power law behavior conitent with nodal quaiparticle but with greater impurity cattering than in κ(e) ]Br. Key word. penetration depth order parameter organic uperconductor uperfluid denity. 1. INRODUCION he ymmetry of the order parameter i crucial to undertanding uperconductivity. he identification of an unconventional ymmetry can rule out certain mechanim for pairing. hi iue ha been central to high C uperconductor where dwave pairing i on a firm bai in the holedoped material and trongly uggeted in the electrondoped material. Organic uperconductor have many imilaritie to copper oxide and it ha been uggeted that unconventional pairing may alo hold [1]. Data from NMR [,3], thermal conductivity [4], tunneling [5], heat capacity [6] and penetration depth [7,8] have uggeted a dwave tate in the κ(e) X uperconductor where X = Cu(NCS) and ]Br. In thi paper we how data for both κ(e) ]Br and β"(e) crytal, both of which exhibit a power law dependence of the uperfluid denity indicative of a dwave pairing tate with impurity cattering. Many of the reult hown here were reported earlier [7,9].

2 1 JOURNAL DE PHYSIQUE IV 1.1 Reult Penetration depth, λ(), meaurement were performed with a 1 MHz tunnel diode LC reonator ued in everal previou meaurement [7]. Change in the ocillator frequency were proportional to change in the penetration depth, λ( ) λ( ) λ( ) G f = = min through a contant G whoe determination i decribed elewhere [7,9]. he ac magnetic field wa applied perpendicular to the conducting plane. hi geometry generate inplane creening current and i enitive to the inplane penetration depth, λ P (). Several ingle crytal of κ and β" material were tudied. he growth procedure have all been decribed previouly[10]. A uperconducting order parameter with line node in momentum pace exhibit a linearly increaing denity of quaiparticle tate. hee nodal quaiparticle give rie to a normalized uperfluid denity that i linear in temperature, for 0.3 c ( ) ( ) ( ) ( ) ρ λ λ λ λ α = P P = + P P = 1 C (1) <. For a gap function of the form max( kx ky) one ha α = 0.65 with max =.14k B c. Even for a tate obeying eq.(1) the penetration depth will vary a λ P ( ) : Since term can alo arie from impurity cattering, it i important determine ρ( ) in order to ditinguih phyically ditinct ource of behavior. Reonator perturbation method do not directly yield λ P () 0. o determine ρ it i therefore neceary to take λ P 0 from ome other meaurement uch a µsr [11]. () ρ ( ) κ(e) ]Br BCS.5 BCS λ 0 (µm) = / C λ() λ(0) (µm) κ(e) ]Br λ = Fig. 1. Superfluid denity of κ(e) ]Br uing three different value of λ(0) = 0.6,, 1.5 µm. Fit are to eq.(1). Alo hown: ρ S for iotropic wave order parameter uing (BCS) = 1.76 k B C and (BCS)/. Fig.. λ() veru 3/ for κ(e) ]Br. Fig. 1 how our meaurement of ρ in κ(e) ]Br. ρ plot were generated uing everal value of λ P () 0 and were fit to the form, ρ ( ) = 1 α ( + ), characteritic of a d C wave tate with unitary limit impurity cattering[1]. hi model ha been widely ued in the cuprate although a microcopic jutification for unitary limit cattering i till lacking. Auming λ P () 0 = 0.6 µm (a lower limit from µsr) we find α =.8 and */ c = By comparion, α (YBCO) = λ P 0 = 1.5 µm and */ c < 0.01 while α (BSCCO) = 0.7 and */ c A choice of () give α = 1.6. κ(e) ]Br i therefore a plauible candidate for a dwave uperconductor but with a large value of α. Since α: ( d dθ ) 1 node, our reult imply a gap function which increae very lowly a one move away from the nodal direction [13]. A imilar value of α wa alo

3 ISCOM found in recent uceptibility meaurement by Pinteric et. al.[8]. hoe author uggeted that the admixture of an wave component (d + ) would hift the kpace poition of the gap node and give a larger value of α. o obtain α =.8 would require an wave component approximately 0.7 time the maximum dwave gap, for which there i no obviou jutification. Fig.1 how that an order parameter of the form or d + i would require an extremely mall wave component. We etimate that any finite gap on the Fermi urface would need to be le than 3% of the BCS value BCS = 1.76 k B C. Fig. 1 how ρ for both a BCS energy gap and for = ½ BCS. In either cae, ρ i eentially temperature independent below / C = 0.1. Our meaurement for κ(e) Cu(NCS) gave very imilar reult. 3 λ P : power law with remarkable For all ample tudied, the penetration depth obeyed a conitency, a hown in Fig.. Although there i no phyically motivated order parameter that would give 3/, it i a power law that arie from Boe excitation obeying a quadratic power law (e.g. magnon). It ha alo been hown that a dwave pair fluctuation model would exhibit a 3/ term in the uperfluid denity [14]. However, we find that to fit ρ to a 3/ power law require a very large value of λ P () 0 ( = 6 µm) and no linear term. Other reearcher have reported a 3/ law for CeCoI 5 which wa attributed to a combination of trongcoupling uperconductivity and nonlocality [15]. Nonlocality i unlikely to be applicable to the organic uperconductor, however. A 3/ power law can of coure be cloely approximated by a combination of and, but the convere i not true. Neither YBCO nor BSCCO generally fit to a 3/ power law. We peculate that thi power law may indicate a cattering rate peculiar to thee material that i highly conitent owing to the quality of the ample. By aligning the ac magnetic field parallel to the conducting plane we meaured the interplane penetration depth, λ. For a dwave uperconductor with coherent interlayer tranport one ha ( ) 1 : β with β = 1. Incoherent coupling between plane can lead to β = which i widely ρ oberved in the cuprate [16]. Higher power can alo arie depending upon detail of the interlayer tranport and impurity cattering [17,18]. We conitently oberved β=1.1.3 in κ(e) ]Br again giving trong upport to the dwave picture. he large difference in creening between the actual ample and a perfect diamagnet of the ame dimenion alo allowed u to extract () λ 0 85µ m directly from the change in frequency of the reonator a the ample wa extracted from the coil, in itu. We etimate an error of 15% in thi meaurement [7]. 4/3/003 15:48: ρ = λ(0) inter = 85 µm 0.8 λ(0) = 5.0 µm.0 µm ρ (interplane) ρ β"(e) µm 0.5 µm Fig. 3. Interplane uperfluid denity veru temperature in κ(e) ]Br (/ c ) Fig 4. Inplane uperfluid denity in all organic β"(e) veru (/ C ), for everal different value of λ(0). More recently we reported penetration depth meaurement in ingle crytal of the uperconductor β"(e) (c = 5. K). hi material ha both organic cation and anion. It ha been uggeted that pairing occur through charge fluctuation and the order parameter hould have d xy ymmetry [19]. Our meaurement average over inplane direction and would not ditinguih d from d ymmetry. We found that 3 λ P : over a large temperature range, xy x y

4 14 JOURNAL DE PHYSIQUE IV but conitently croing over to a lower power law exponent at the lowet temperature obtainable. In Fig. 4 we plot the inplane uperfluid denity for a range of plauible λ P () 0 value. For all curve, the aymptotic dependence i ρ = 1 c. A power law can arie from a pin triplet, pwave tate but we know of no meaurement that ugget triplet pairing in thi material [0]. Auming inglet pairing, a power law would imply a dwave tate with */ c > 0.5 and thu very trong cattering. It could alo imply a very inhomogeneou ample with a pread of tranition temperature. However, the latter cae i unlikely in that the value we oberve for dλ d are extremely conitent, within 10% from ample to ample. Since the penetration depth i determined by the quaiparticle energy, power law behavior can indicate gap node but not the phae of the order parameter directly. It i poible to indirectly detect the phae through penetration depth meaurement. For ample urface perpendicular to nodal direction, quaiparticle in a dwave uperconductor uffer a ign change in the pair potential upon pecular reflection. Barah et. al. have hown that thi lead to a ingular denity of urface Andreev bound tate at zero quaiparticle energy and a correponding paramagnetic term λ : 1 at very low temperature [1]. he competition between the and term from nodal quaiparticle and the 1/ term from Andreev bound tate give a minimum in λ P below min = g( θ) ξ λ where g 1 i a meaure of amount of crytalline urface normal to the nodal direction and ξ i the coherence length[1]. Recently, Carrington et. al.[] verified thee prediction in YBCO crytal where min : 10K. A imilar 1/ term wa oberved earlier in irradiated film of YBCO where urface favorable for bound tate were purpoely created [3]. For κ(e) ]Br, thi theory predict K. he obervation of λ : 1 would provide a definitive tet of dwave pairing in the min 0.1 organic uperconductor. In concluion, we find that the κ(e) ]Br data i conitent with a dwave order parameter in the preence of impurity cattering but with a larger value of dρ S d than predicted 1.5 in a weakcoupling model. All ample conitently howed a near perfect fit to λ :. β"(e) uperconductor exhibited ρ = 1 c behavior, again conitent with nodal quaiparticle but with much greater impurity cattering. Acknowledgement We wih to thank Ro McKenzie for ueful converation. Work at UIUC wa upported through NSF DMR Reearch at Argonne National Lab wa upported by Department of Energy, Office of Baic Energy Science, Diviion of Material Science, Contract No. W31109ENG38. Reference [1] R.H. McKenzie, Science 78 (1997) 80 [] H. Mayaffre et. al., Phy. Rev. Lett. 75 (1995) [3] S.M. DeSoto et. al., Phy. Rev. B 5 (1995) [4] S. Behnia, K. Behnia, and A. Deluzet, Phy. Rev. Lett. 81 (1998) [5]. Arai et. al., Phy. Rev. B 63 (001) [6]Y. Nakazawa and K.Kanoda, Phy. Rev. B 55 (1997) R8670R8673 [7] A. Carrington et. al., Phy. Rev. Lett. 83 (1999) and reference therein. [8] M. Pinteric et. al. Phy. Rev. B 66 (00) [9] R. Prozorov et. al., Phy. Rev. B 63 (001) [10] U. Geier et. al., Jour. Am. Chem. Soc. 118 (1996) [11] L.P.Le et. al., Phy. Rev. Lett. 68 (199) [1] P.J. Hirchfeld and N. Goldenfeld, Phy. Rev. B 48 (1993) R419R4 [13] D.Xu, S.K. Yip and J.A. Saul, Phy. Rev. B 51 (1995) [14] Q.J. Chen, I. Koztin, B. Janko, K. Levin, Phy. Rev. Lett. 81 (1998) [15] I. Bonalde et. al., Phyica B: Condened Matter. 39(Part ) (003) [16] A. Hoeini et. al. Phy. Rev. Lett. 81 (1998) and reference therein. [17] R.J. Radtke, V.N Kotur, K. Levin, Phy. Rev. B 53 (1996) R5R55 [18]. Xiang and J.M. Wheatley, Phy. Rev. Lett. 77 (1996)

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