NMR in the superconducting state of YBa2Cu3O7

Physiea C 185-189 (1991) 93-97 North-Holland

NMR in the Superconducting State of YBa2Cu307

J. A. Martindale, S. E. Barrett, C. & Klug, IC E. O'Hara, S. M. DeSoto, C. P. SHchter,(a) T. A. Friedmann and D. M. Ginsberg. Department of Physics, Materials Research Laboratory, and Science and Technology Center for Superconductivity, University of Illinoisat Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801 The authors report studies of the 63Cu spin-lattice relaxation times in YBa2Cu307 below the superconducting transition. They show t h a t the data m a y indicate t h a t the orbital pairing in the superconducting state is d-like, and t h a t at low temperatures and strong fields t h e fluxoid cores m a y dominate the relaxation mechanism. I. Introduction W e report studies of 63Cu spin-lattice relaxation times in YBa2Cu307 below the super-

conducting transition temperature. W e find interesting anomalies compared to the normal state. Above To the two relaxation rates 63Wla end 63Wlc of 63Cu when HO is parallelto the crystalline a and c axes respectivelyare strongly temperature dependent, but their ratio 63Wla/SZWlc is not (from symmetry 63Wlb--63Wla). Below Te we find 63W1a/63W1 c varies with temperature, and also that at temperatures well below Tc Wlc varies with the strength of the applied fieldHo. W e show that the temperature variation of 63W1a/63W1c may give information about the orbital pairing of the superconducting state, and that the variation of 63Wic with H o probably results from a role of the vortex cores. 2. The Situation a Year Ago. W e begin by discussing the experimental ~....,,..~v.,.=, ,,,=,~=~,u== u-,~,==,..6 =, )-ear ~eu. Fig. I shows 63Wla and 63WI¢ versus temperature 1 for a number of samples. The samples and their preparation are described in reference 1. The insert shows the ratio 63Wla/63Wlcin the normal state, demonstrating its temperature independence. Fig. 2 shows a type of plot which we have found useful because we find t h a t using it experimental data lie on a straight line. T h a t is, a

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Fig. 1 Main Figure: The 63Cu(2) spin-lattice relaxation rate 63Wla vs. temperature f~r Ho | a (0, Sample 1; ["], S~mple 4) and for H01 c (o, Sample 1; A, Sample 4). The vertical solid line is at 92I~ Inset: The normal state ratio Wla/Wlc vs. t e m p e r a t u r e for Sample 4 (e). The horizontal line is at Wla/Wle=3.73, and the vertical line is at 92IC good rule of thumb for describing ~ W l a (a = a,c) below Tc is 63Wla(0)/0 = AeB0

(I)

with 0 -= Tfre where A and B are independent of temperature. In utilizing this equation, one needs to take account ofthe fact t h a t Te is lower in the presence of a magnetic field t h a n when the field is absent.

13921-4534/911503.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.

94

J.A. Martlndale et ~ / NMR in the superconducting state of YBa2Cu307

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describing normal state data. We were greatly aided in this activity by their help. There appeared to be four possibilities: 1) Perhaps the antiferromagnetic correlation length ~ was

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anisotropic below To. This proposal had the difficulty t h a t it required breaking the spin rotation invariance of x"(q,w), the imaginary p a r t of the electron spin susceptibility. (2) Possibly the MMP parameters [3 and ~, which had been taken

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TITc Fig. 2. The eqCu(2) relaxation rate 63Wl a divided by TfP© vs. T/To. The lines through the data reveal the exponential dependence of this quantity. Fig. 3 shows the ratio R =- 63Wla/63Wlc . In the temperature range 0.5
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the functional farms fitting the data far Sample 4 in Fig. 2. The solid line is the range of our data. The square at Tfrc=l would be the ratio at this point (3.98) if the Wla'S were continuous across the transition. W e attempted to understand our data a year ago utilizing the Millis, Manien, and Pines ( M M P ) theory2 which has been so successful in

to be independent of temperature in the superconducting state, were in fact temperature dependent. This possibility, however, was severely constrained by the obse:'vatians of Hammel et al3 that the ratio 63Wlc/17W1©, comparing 63Cu and 170 relaxation rates, was independent of temperature below Tc. (3) Perhaps 63Cu w a s relaxed by Cu orbital magnetism, not by Cu electron spins. Estimates af the orbital mechanism by Millis and Monien made that seem unlikely. (4) Lastly, perhaps t h e effect was a result of the application of the strong H0 (8.3 T). We checked this latter possibility at 77 K using sample 4, for which 8.3 T NMR data is shown in Fig. 3. First we made a zero field measurement of Wlc. This measurement can be dane easily since in zero field one simply has the usual NQR spectrum. Because of the n a t u r e af the electric field gradient, the NQR relaxation measures Wlc. The result af the NQR experiment on sample 4 is plotted in Fig. 3 and is seen to fall an the same curve as the NMR data. To m e a s u r e Wla, one needs a magnetic field perpendicular to the c axis. We did this using Ha = 0.446 T. This field is so much lower than the 8.3 T field that it should reveal any H0 dependence provided we used the value of Tc appropriate ta that field. 63Wla measured in this manner likewise agreed with the high field data for 63Wla. Therefore, at 77K it was clear t h a t the difference in anisotropy between the superconducting and normal states was a real effect, not simply an artifact of the strong Ha.

.I,4. Mw~zztale et al. / NMR in the superconducting $mte of YBa2Cu¢97

In looking at our data in Fit;. 2, it is apparent that the best straight line fits using Eq. 1 to the data have different slopes between the NMR and the NQR Wit. T h e difference is not large, but did seem real. Was it an effect of Ho which became progressively more important the lower the temperature, was it a sample difference or was it in fact not real?

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3. Recent Experiments Accordingly, we decided to redo the experiments all on one sample to study both the temperature dependence and magnetic field dependence. The results are shown in Fig. 4. 1 0t

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Fig. 5. Normalized 63Wla divided by Tfre versus Tfrc for Ho = 0.45 T (-) and Ho = 8,31 T (m). I

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Fig. 4 Spin-latticerelaxation rate versus temperature for 63Cu(2) for differentmagnetic field strengths and orientations. The solid symbols are for HO ± c (63WI a) and the open symbols for Ho flc (63Wlc). ~g. 5 shows the data ¢^- t..~xT, m~ ,,o (normalized to values at Tc) and Fig. 6 shows normalized ]n(Wlc/'r) vs T f r c. It is clear that Wla (T/To) is only very weakly dependent on H0, whereas Wit (T/Tc) has a strong dependence on H0 at lower temperatures. We thus examined separately the low field temperature dependence LVL

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Fig. 6 Normalized 63Wic divided by T/"rcversus Tfrc for HO=0 T (0),Ho=4.14 T (A),and HO = 8.31T

(D). of 63Wla/63~Vlc, then the low temperature Ho dependence of 63W!c. Fig. 7 shows the low field ratio 63Wla?s~V~c. As one lowers T through T¢, the ratio first drops. as we had earlier shown, then at lower temperatures rises, eventually going to values which exceed the ratio in tr.e normal state.

96

Jdl. Martlndale et aL

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in the superconducting state of YBa2Cu307

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Their theoretical calculation is shown on Fig. 7. Also shown are a calculation by J.P. Lu, 7 and one by Lu and D. Pines. 8 These are also based on a BCS wave function without and with antiferromagnetic enhancement.

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Fig. 7 The anisotropy ratio 63Wla/e3Wlcversus temperature. The open diamonds are our weak field (0.45 T) data. The curves are the theoretical fits of Lu (dotted line), of Lu and Pines (dashed line), and of Bulut and Scalapino (solid line). The vertical line is at TfTcf92.5K. M. Takigawa et al.4 also realized the possibilitythat there might be anomalous effects in our data arising from the magnetic field,and measured 63Wla/S3Wlc at low fields. Their data and ours are in agreement. 4. Theoretical Models In the meanwhile, two theoretical analyses of the anisotropy in the superconducting state have appeared which are able to explain the data. One, by Bulut and Scalapino,5 is based on their model of the superconducting state. They write the complex electron spin susceptibilityZ (q,e~)as

One of the puzzles of NMR in superconductors has been the absence of the ~ccalled coherence peak9 seen just below 'Pc. This peak, when contrasted with the precipitous drop in ultrasonic absorption, 10 was one of the first proofs of the pairing condition. One of the successes of both the Bulut-Scalapino, and the Lu, Lu-Pines calculations is that they successfully reproduce the experimental data namely the temperature dependence including the absence of the coherence peak (as described by Eq. 1). However, as Lu points out, a successful fit of the anisotropy is dependent on coherence. Fig. 8 shows the variation of Wit with H0 at T/Pc = 0.2. We see that there is an extra relaxation rate proportional to H0. Since the number of vortex lines per unit area of the sample is proportional to H0, this result suggests the extra relaxation arises from the vortices. 0.008

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(2) 0.004

where zo(q,w) is calculated using BCS theory, with a lifetime broadening r, and U is taken as an edjustable parameter to give antiferromagnetic enhancement. They then consider various BCS solutions. Since the Knight shift data6 indicates a spin singlet pairing, they make this assumption. They find that to produce the upturn at low temperatures they must take an orbital d-state pairing. The data can not be fit by an crbital s state.

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Fig. 8.63Wlc at W/Tc = 0.2 versus magnetic field

strength, demonstrating the linear dependence of 63V-flc on n 0.

J.,4.Martindale et at / NMR

in the supet~ndzwting state of YBa,Cu30 ~

Indeed, at 8.31 T, assuming a 16.5 ~ radius for the vortex core, II w e find that 3.4% of the sample is contained in the cores. But the extra relaxation rate at 8.31 T is 2.8% of the relaxation rate 63Wlc one would have at this temperature of the normal state 63Wlc at Tc is extrapolated to T/T e = 0.2 using the Korringa law TIT = constant. These numbers can be understood if one assumes that either (1) nuclei in the corns are relaxed by the normal electrons, then exchange energy by mutual spin flips with nuclei outside the cores or (2) the cores are quite mobile on a time scale of the nuclear spin lattice relaxation time (1/Wle) so that every nucleus spends equal time "inside" a vortex core. Which interpretation is correct (or whether still another one is needed) awaits further experimentation.

,~',

(T~A.F., D.M.G.); and the Science and Teclmolo~Center for Superconductivity Grant Number DMR-88-09854 (C.P.S., D.M.G.). REFERENCT~ a) Also at Department of Chemistry.

1) S.E. Barrett, J. ,~ Martindale, D. J. Durand, C. H. Pennington, C. P. Slichter, T. Friedmann, J. P. Rice, and D. M, Ginsberg. Phys. Rev. Lett. 66 108-111, (1991) 2) A . J . Millis, H. Monien, and D, Pines, Phys. Rev. B 42, 167 (1990).

3) P . C . Hammel et al., Phys. Rev. Lett. 68, 1992 (1989). 4) M. Takigawa, J.L. Smith, and W. L. Hutt, (preprint) 5) N. Bulut and D. Scalapino (preprint)

An important consequence of the discovery of a strong field dependence is the recognition that all relaxation data taken in strong fields may be more characteristic of the normal than the superconducting state. In particular, 170 data needs to be reexamined, as do any conclusions deduced about the superconducting state from 170 relaxation.

6) S. E. Barrett, D. J. Durand, C. H. Pennington, C. P. Slichter, T. A. Friedmarm, J. P. Rice, and D. M. Ginsberg. Phy ~ Rev. B. 41, 6P2~6296 (1990).

ACKNOWLEDGEMENT The authors are grateful for discussion with D. Pines, A. J. Millis, H. Monien, J. P. Lu, P. Monthoux, D. Thelen, N. Goldenfeld, T. Imai, N. Bulut and D. Scalapino. We are grateful to M. Takigawa for communicating his results prior to publication. Two of us (S. E. Barrett and K. E. O'Hara) would like to acknowledge support from IBM and NSF, respectively. This work has been supported through the University of niinois Materials Research Laboratory by a grant from the Department of Energy Division of Materials Research under Grant Number DEFG0291ER45439 (C.P.S., J.A.M., C.A~K.); the National Science Foundation Division of Materials

10) H. E. Bommel, Phys. Rev. 96, 220 (1954), l~ W. Morse, H. V. Bohm, Phys. Rev. 108, 1094 (1957).

7) J . P . Lu (preprint) 8) J . P . Lu and D. Pines, Private Comrntm. 9) L.C. Hebel, C. P. Slichter, Phys. Rev. 113, 1504 (1959).

11) U. Welp et al., Phys., Rev. Let~ 62, 1908 (1989).