Unusual temperature dependence of the London penetration depth in all-organic beta``-(ET)_2

a r X i v :c o n d -m a t /0009118v 1 [c o n d -m a t .s u p r -c o n ] 8 S e p 2000

Unusual temperature dependence of the London penetration depth in all-organic

β′′?(ET )2SF 5CH 2CF 2SO 3single crystals

R.Prozorov and R.W.Giannetta

Loomis Laboratory of Physics,University of Illinois at Urbana-Champaign,1110West Green St.,Urbana,Illinois 61801.

J.Schlueter and A.M.Kini

Chemistry and Materials Science Division,Argonne National Laboratory,Argonne,Illinois 60439.

J.Mohtasham,R.W.Winter,G.L.Gard

Department of Chemistry,Portland State University,Portland,Oregon 97207.

(February 1,2008)

The temperature dependence of the in-plane,λ (T ),and interplane,λ⊥(T ),London penetration depth was measured in the metal-free all-organic superconductor β′′?(ET )2SF 5CH 2CF 2SO 3(T c ≈5.2K).?λ (T )∝T 3up to 0.5T c ,a power law previously observed only in materials thought to be p ?wave superconductors.λ⊥is larger than the sample dimensions down to the lowest temperatures (0.35K),implying an anisotropy of λ⊥/λ ≈400?800.74.70.Kn,74.25.Nf

Despite intensive study,neither the pairing mechanism nor the symmetry of the order parameter has been con-clusively established in organic superconductors of the κ?(BEDT ?T T F )2X class.(Henceforth “BEDT-TTF“will be abbreviated by ”ET”.)For the most thoroughly investigated materials,κ?(ET )2Cu (NCS )2(T c ≈9.5K)and κ?(ET )2Cu [N (CN )2]Br (T c ≈12K),there is some evidence for a d ?wave pairing [1,2].However,recent penetration depth measurements revealed an un-usual fractional power law variation,?λ(T )∝T 3/2,un-like that of any other superconductor [2].While this exponent is consistent with a novel three-?uid model [3],it is also suggestive of a magnetic excitation.In this paper we report penetration depth measurements in β′′?(ET )2SF 5CH 2CF 2SO 3,a recently synthesized all-organic superconductor free of metallic ions and in which magnetism is likely to be negligible.This mate-rial is a strongly two dimensional,extreme type II su-perconductor with T c ≈5.2K .It is metallic between 10and 150K and semiconducting from 150and up to 410K [4].The upper critical ?eld parallel to the conducting planes exceeds the Pauli limit by 18%raising the possibil-ity of either an inhomogeneous pairing state [5,6]or spin triplet order parameter [7].We determine the London penetration depth for supercurrents both along (λ )and perpendicular (λ⊥)to the conducting planes.The pene-tration depth is extremely anisotropic,with λ⊥roughly 800times larger than λ .Notably,λ ∝T 3which might imply an energy gap with nodes,but is di?cult to recon-cile with either p or d ?wave models in two dimensions.We suggest that this power law may arise from the un-usual phonon spectrum in this material.

Single crystals of β′′?(ET )2SF 5CH 2CF 2SO 3were grown at Argonne National Laboratory by an electrocrys-tallization technique described elsewhere [8].The high

conductance layers correspond to the ab plane and the c ?axis is normal to the planes.This designation is similar to cuprates,while di?erent from the κ?(ET )2X ma-terials.The room-temperature interplane resistivity is roughly 700?cm while the in-plane resistivity is about 0.2?cm [9].Two crystals -0.5×0.5×0.3mm 3and 0.8×0.6×0.3mm 3were used for measurements.Each had a transition temperature of approximately 5.2K.A third crystal was used to measure the absolute penetra-tion depth.The penetration depth was measured with an 11MHz tunnel-diode driven LC resonator [10].Samples were mounted on a movable sapphire stage with temper-ature controllable from 0.35K to 50K.The low noise level,?f min /f 0≈5×10?10,resulted in a sensitivity of ?λ≤0.5?A for our samples.An rf ?eld was applied either perpendicular to the conducting planes to probe ?λ (T )or along the a ?axis to probe ?λ⊥(T ).

The resonator frequency shift due to superconducting sample,?f ≡f (T )?f 0,is given by [10]:

?f

2V 0(1?N )

1?

λλ

(1)

where f 0is the frequency in the absence of a sam-ple,V s is the sample volume,V 0is the e?ective coil volume and N is the e?ective demagnetization fac-tor.The apparatus and sample -dependent constant ?f 0≡V s f 0/(2V 0(1?N ))was measured by removing the sample from the coil in situ [10].For λ?R ,tanh R/λ≈1and the change in λwith respect to its value at low temperature is ?λ=?δfR/?f 0,where δf ≡?f (T )??f (T min ).In the parallel orientation (H ab ),however,we had to use the full expression,Eq.(1)to estimate λ⊥due to the weak screening in that direction.

1

0246

D f (H z )

T (K)

FIG.1.Frequency variation in parallel (?f ⊥)and perpen-dicular (?f )orientations of the magnetic with respect to su-perconducting https://www.sodocs.net/doc/073080628.html,ual notation in terms of current ?ow is used.Inset:zoom of ?f ⊥(T ).Note substantial di?erence in shielding ability for two orientations.

Figure 1shows the frequency variation measured in two orientations for zero DC magnetic ?eld.For (H ab )the rf screening is controlled by λ⊥(T )and is much weaker than in the (H c ?)orientation,where the relevant screening length is λ (T ).Since all three crystal dimen-sions were roughly comparable,this indicates that λ⊥is several hundred times larger than λ .The inset shows an expanded view of the ?f ⊥(T )curve.From the to-tal frequency variation and using Eq.(1)we estimate λ⊥(0)≈800μm .

To date,there have been no reported measurements of the zero temperature penetration depth,λ (T =0).We recently developed a new method to determine λ (T =0)that relies upon the change in screening of an Al-coated sample as the temperature is reduced from above T c (Al )to below T c (Al )[11].The inset to Fig.2shows the data obtained in a single crystal of YBCO.The method yields a value of 0.145±0.01μm which is within 5%of literature values.The mainframe of Fig.2shows the method applied to β′′?(ET )2SF 5CH 2CF 2SO 3.Since T c of this material is only 5.2K,its penetration depth is still changing at 0.35K and the method is less reliable than for cuprate superconductors.We estimate a value of λ (T =0)=1?2μm ,in rough agreement with values for other ET compounds [2],and leading to an anisotropy of 400-800.Our measurements provide only the average of ?λ (T ).Microwave conductivity measurements revealed a small in-plane anisotropy of approximately 1.35with a maximum along the b axis [4].

Figure 3shows the low temperature variation of ?λ (T )observed in two samples of β′′?(ET )2SF 5CH 2CF 2SO 3.Data for sample 2is o?set for clarity.The horizontal axis is T 3showing that ?λ(T )∝T 3with a slope of 0.07μm/K 3.The cubic

power law is obeyed up to ～T c /2.The Al coated sam-ple,shown in Fig.2also showed ?λ(T )∝T 3,but below T c (Al )the signal from β′′?(ET )2SF 5CH 2CF 2SO 3is screened by the Al coating.Both the n =3exponent and the wide range over which it holds are unusual and have not been observed in cuprate superconductors.To highlight the di?erences among superconductors,we plot in Fig.4the normalized low temperature variation of the penetration depth in κ?(ET )2Cu (NCS )2(uppermost curve),β′′?(ET )2SF 5CH 2CF 2SO 3(middle curve)and polycrystalline Nb for comparison.Solid lines are the ?ts to T 3/2,T 3

and

010203040

T/T

c

D l

||

(μm )T 3 (K 3

)

FIG.3.?λ (T )measured in two di?erent crystals.(Data for sample 2is o?set for clarity).Solid lines show ?ts to T 3power law.

It is also possible that a small tilt of the c ?axis relative to the ?eld may induce interplane supercurrents and cre-ate an admixture of both λ (T )and λ⊥(T )in the data.If the applied ?eld is tilted by θrelative to the c ??axis the additional contribution to the observed frequency shift is given by [10],

?f tilt =

f 0V s

d +λ⊥

ature dependence to the e?ective mass and thus a power law to the London penetration depth over and above that due to the super?uid fraction[19].For example,a phonon density of states g(E)varying as E2may give rise to a T3power law for an s-wave superconductor,in the ab-sence of vertex corrections.Under most circumstances vertex corrections raise the power to T5making the ef-fect extremely small,but this may not be true here.Our data suggest that strong coupling calculations involving a realistic phonon spectrum may be relevant for organic superconductors.We also wish to stress the desirability of NMR measurements inβ′′?(ET)2SF5CH2CF2SO3to help determine the parity of the order parameter.

ACKNOWLEDGMENTS

We wish to thank M.B.Salamon for useful discussions and for providing results on Sr2RuO4prior to publica-tion.Research at Urbana was supported through State of Illinois ICR funds.Research at Argonne was sup-ported by the U.S.Department of Energy,O?ce of Basic Energy Sciences,Division of Materials Sciences,under contract No.W-31-109-ENG-38.Research at Portland State University was supported by NSF grant No.CHE-9904316and the Petroleum Research Fund,ACS-PRF 34624-AC7.