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VOLUME 76, NUMBER 22 P H Y S I C A L R E V I E W L E T T E R S 27 MAY 1996

rance

Spin Gap in HgBa2Ca2Cu3O81d Single Crystals from 63Cu NMR

M.-H. Julien,1 P. Carretta,1,* M. Horvatic,1 C. Berthier,1,2 Y. Berthier,2 P. Ségransan,2 A. Carrington,3 and D. Colson41Grenoble High Magnetic Field Laboratory, Centre National de la Recherche Scientifique

and Max-Planck-Institut für Festkörperforschung, Boıˆte Postale 166, 38042 Grenoble Cedex 9, France2Laboratoire de Spectrométrie Physique, Université Joseph Fourier Grenoble 1 (URA 08 CNRS), Boıˆte Postale 87,

38402 Saint-Martin d’Hères Cedex, France3Commissariat à l’Energie Atomique, Département de Recherche Fondamentale sur la Matière Condensée,

Laboratoire de Cryophysique, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France4Commissariat à l’Energie Atomique, Service de Physique de l’Etat Condensé, Saclay, 91191 Gif sur Yvette Cedex, F

(Received 17 October 1995)

We report on63Cu NMR spectra,T1 andT2G measurements in single crystals of underdoped, three-layered, HgBa2Ca2Cu3O81d, with Tc . 115 K. We show clear evidence for the opening of a spin gapbelow T p . 230 K, the highest temperature reported so far. Also, the characteristic energy of the spinfluctuations is found to be higher than in YBa2Cu3O61x ; both features are presumably related to thevery highTc in this compound. BelowT p, 63T1 has the same temperature dependence in the three CuO2

planes, which is difficult to explain within a pure interlayer spin pairing. [S0031-9007(96)00319-5]

PACS numbers: 74.25.Nf, 74.72.Jt, 76.60.–k

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A comprehensive description of the magnetic propties of high-Tc superconductors, particularly the differebehaviors observed in underdoped and overdoped cpounds [1], is considered a stringent test for any micscopic theoretical description of these materials. Onethe key features of the underdoped regime is the opeof a gap in the spin excitations (hereafter spin gap) atemperatureT p well aboveTc. First unambiguously seein YBa2Cu3O72d (YBCO) by inelastic neutron scatterin(INS) [2], this gap corresponds to a progressive tranof low frequency excitations atQAF spya, pyad to-wards higher energies. The NMR fingerprint of the sgap is a decrease of the63Cu nuclear spin-lattice relaxation rate63sT1d21 [3] without any reduction of the spinspin relaxation rates63T2Gd21 [4]. In underdoped YBCOand La22xSrxCuO41d, the uniform spin susceptibilityx0

[5,6], the resistivity [6,7], the Hall coefficient [6,7], anthe electronic specific heat [6,8] show systematic anolies below a characteristic temperatureT0, which is greaterthan bothT p andTc. However, it is unclear if this originates from a loss of spin excitations atq 0, or fromfeatures in the density of states [9,10]. We note thatT0varies strongly with hole dopingnh [5–8] and is insen-sitive to Zn doping [11,12], whereasTp depends moreweakly on nh, but is depressed by Zn [12]. Clearly,careful distinction has to be made between the behavof the dynamic spin susceptibility atq 0 andq QAF .

Despite considerable theoretical and experimework, a thorough understanding of the influence ofnh

and the number of CuO2 planes per unit cell on the spigap is still lacking. Early attempts to describe the phdiagram as a function ofnh were based on the formatioof a resonating valence bond state in the 2Dt-J (ort-t0-J) model [13]. A quite different approach, bason a scaling analysis of the 2D quantum Heisenbantiferromagnet (2DQHAF) phase diagram [14], has b

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proposed by Pines and collaborators [15]. FollowiMillis and Monien [16], several authors have also sugested that the transverse magnetic coupling withinCuO2 bilayer plays a central role in the opening of thspin gap [17].

In this Letter, we present an investigation of63Cu NMRin underdoped HgBa2Ca2Cu3O81d (Hg-1223) single crys-tals, having aTc . 115 K. We show that a spin gapopens belowTp as high as 230 K, and that the charateristic energy of the spin fluctuations is higher thanunderdoped YBCO. This is argued to be related tohigher Tc. The T dependence ofT1 is the same for in-ner and outer planes, which questions the pure interlaspin-pairing picture.

Small single crystals of Hg-1223 were grown usingsingle-step synthesis as described in Ref. [18]. A msaic of 23 of them (total weight,1 mg), with commonc axis, was made in order to increase the NMR signac susceptibility measurements (Hac . 1 Oe, appliedkab)on this mosaic revealed a broad superconducting transbetween 134 and 110 K. However, specific heat measments on selected crystals showed that the bulkTc waswithin the range 113–116 K (see inset in Fig. 1), andthe transition observed in the susceptibility or in thesistivity is presumably due only to surface inhomogenity. We emphasize that no sign of oxygen distributicould be detected from the NMR measurements since wdefined lines and no distribution of the relaxation rawere observed. All experiments were carried out by stdard spin-echo pulse sequences in a field of 15 T.H0kab, we identified the lines corresponding to the twcopper sites (Fig. 1): Cu(2) in the outer planes and Cuin the inner plane. ForH0kc, the lines could not be separated. We found that the Cu(1) lines were much narrowthan the Cu(2) ones, probably because the inner planmore distant from the Hg-O layer which is the source

© 1996 The American Physical Society


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FIG. 1. Field sweeps of the63Cu(1) and63Cu(2) lines: (1y2,–1y2) (filled circles) and (3y2, 1y2) transitions (open circles)Inset: Anomaly atTpeak 113 K in the electronic part of thespecific heat, for one crystal from the mosaic (an approximphonon background has been subtracted).

most of the disorder in the structure. From the positionthe NMR lines we estimated the63Cu quadrupolar couplingfrequencies:63n

Cus1dQ 9.7 6 0.1 MHz, 63n

Cus2dQ 13.7 6

0.1 MHz.Figure 2 presents the MHS (i.e., the line positio

corrected for the quadrupolar shift) arising fromT -dependent spin contributionKs sA 1 4Bdxsq 0, v 0dygmB and from aT-independent orbital termKorb; A and B are the on-site and transferred hyperficoupling constants, respectively. The decrease ofKs

below T0 . 370 K is characteristic of underdoped samples [1]. Note that theT dependence of63Ks is nearlythe same for the two nonequivalent sites, as foundTl2Ba2Ca2Cu3O102d [19]. The shifts get slightly closeras T decreases (Fig. 2), and we can tentatively concluthat the inner plane is slightly less doped than the ouones. There rests some uncertainty, however, ashyperfine coupling constants are not accurately known

To proceed with a more quantitative analysis, wesume that the hyperfine on-site tensorA does not changesignificantly among the cuprates, so that the valuesYBCO [20], Aab 70 kOe andAc 2332 kOe, are ap-plicable to Hg-1223. This assumption is supportedthe fact that the orbital shifts measured here,Korb

ab 0.19%, Korb

c 1.16%, are similar to those for YBCO[20]. From the anisotropy ofKs, we can then estimate thaBCus2d 136 kOe andBCus1d 146 kOe (absolute values615%). These values are much higher than for YBC(B 83 kOe), revealing a stronger hybridization betweCu and O orbitals. This might imply that the in-plane sperexchangeJ between copper spins should be higherHg-1223. A possible reason for this is that Hg-based marials have the flattest CuO2 planes of all cuprates; i.e., thCu-O-Cu bond angles are the closest to180± [21]. Theabsolute values ofx0 deduced fromKs at T 350 K,

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FIG. 2. 63Cu magnetic hyperfine shift data. Inset: Spin paof the MHS (triangles, right scale in%), and in-plane resistivitydivided by T (solid line, left scale inmV cm K21) fromRef. [25].

x0 5.3 3 1025 and4.4 3 1025 emuymole for the outerand inner planes, respectively, are close to that measufor YBa2Cu3O6.63 (6.0 3 1025 emuymole at 300 K [22]),and theT dependence is quite similar.

A test for theA andB values is the anisotropy ofT1:µ1

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where Fc,ab Ac,ab 1 2Bscosqx 1 cosqyd and vL is theNMR frequency. Using a phenomenological form of thsusceptibilityx 00sq, vd . x

00AFsq, vd [23,24], with the AF

part approximated by a Gaussian (with a width equalthe correlation lengthjya), we find (for jya . 2) thats63T1d21

ab ys63T1d21c 2.2 6 0.1, in remarkable agreemen

with experiment (2.17 6 0.10).The inset to Fig. 2 shows previously reported da

for the in-plane resistivityrab for single crystals withthe same bulkTc as those reported here [25].rab

deviates from linearity belowT0 . 370 K, the sametemperature at which we estimate thatx0 starts todecrease. Furthermore, it is striking to observe the almperfect scaling ofKab andrabyT , from T0 down to a fewtens of a kelvin aboveTc.

In Fig. 3 we show theT dependence ofs63T1T d21, forboth sites andH0kab along with preliminary data for thenuclear spin-spin relaxation rates63T2Gd21. For the lattermeasurementsH0 waskc as the spectrum was too broafor H0kab, and so eachs63T2Gd21 value is an average ofthe Cu(1) and Cu(2) sites. However, in light of the63Ks

and s63T1d21 data, we do not expect a large differencin the magnitude and theT dependence ofs63T2Gd21

for the two Cu sites. This assumption has indeed beconfirmed in optimally doped Hg-1223, therefore jusfying our analysis [26]. Whiles63T1T d21 increases withdecreasingT and starts to drop atTp . 230 K, s63T2Gd21

continues increasing and eventually saturates be

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FIG. 3. Nuclear spin-lattice relaxation rate divided by tempatures63T1T d21 measured withH0kab for the Cu(1) and Cu(2)sites, and the nuclear spin-spin relaxation rates63T2Gd21, mea-sured withH0kc. The dotted lines are guides to the eye. InsThe quantity63sT1TyT2Gd vs temperature.

,200 K. The combination of these two behaviodemonstrates unambiguously the opening of a sgap [27].

The first remarkable point is that the decrease ofsT1T d21

occurs at a temperature much higher than in all otsystems studied so far (typically120 # T p # 165 K), sug-gesting that the higherTc at optimal doping in Hg-1223(T max

c , 160 K under pressure [28]) is related to the highT p. Indeed, the ratioTpyT max

c is approximately the samas in YBCO, which clearly favors superconductivity meated by spin fluctuations. Until now, the only compounin whichT0, Tp, andTc were so well separated belongedthe low doping regime of YBCO. Thus our findings prvide a new element in the spin gap phenomenology, whputs constraints on theoretical descriptions of the cupraA relationship betweenT p and Tmax

c finds natural basisin the resonating valence bond [13] and quantum diso[15] models. However, data in more strongly underdopsamples are needed to discriminate between these twoliquid pictures.

Secondly, this first clear observation of a spin gap ithree-layered compound does not seem to be in favorpure interlayer spin pairing, since in that case one expea faster decrease ofsT1T d21 for the inner plane. Indeedextending to three layers the simple RPA calculationCuO2 planes coupled by a weakJ' [29], we found thatthe dynamic susceptibility should be different in the innand outer layers, in contradiction with our experimenresult. However, we cannot rule out thatJ' is strongenough to ensure a common spin temperature in the tplanes, thus more detailed calculations for a three-layesystem are desirable. Note that our results do not excthe possibility thatJ' is primarily important to stabilizethe spin-gap state.

There are several possible approaches in the descriof the relaxation rate data. Several authors [23,30] h

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used mean-field dynamic spin susceptibilities for a neaantiferromagnetic Fermi liquid (NAFL) in which the correlation lengthj varies asT21y2 and the dynamic criticalexponentz 2 (z relates the characteristic frequencythe spin fluctuationsvSF to j; vSF ~ j2z). This leads,for large values ofj, to a constant ratio for the quantitT1TysT2Gd2. These models contain no parameters whcan describe the spin gap state. Sokol and Pines [15] hproposed that the transition between the underdopedthe overdoped regime corresponds to the crossover fthe quantum critical regime (QC) of the 2DQHAF, witz 1, to a NAFL. In the QC regime, the ratioT1TyT2G

should be constant.All the above descriptions share the same problem

that they postulate aT dependence of the correlatiolength and require rather large values ofj, in contradictionwith the inelastic neutron scattering results for YBC[2]. We therefore use a numerical analysis where wefully investigate the effect of differentjya values [31].Neglecting the quasiparticle contribution:

sT1T d21c

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whereDq QAF 2 q, the functionsg and h contain theq dependence ofx 0 andvSF , andgs0d hs0d 1. Forsimplicity, we takeg 1yh to be Gaussians. For a givepair of experimental values ofsT1T d21 and sT2Gd21, wecan then computevSF and x

0QAF

as a function ofjya.We find thatvSF fsjdT1TyT2G, with jfsjd slowly in-creasing withj in the range1 # jya # 2, and reachinga constant value forjya $ 2. We conclude therefore thaif T1TyT2G is T independent whilej varies withT , thenvSF ~ j21 (i.e., thez 1 regime) even forjya as lowas 2. Experimentally we see that the ratioT1TyT2G (insetFig. 3), seems to become constant above 250 K, aspected in the QC regime of a doped 2DQHAF [15].

Within a model of spin fluctuation induced pairingMonthoux and Pines [32] found that, for the NAFL casTc is determined by an expression analogous to the usBCS one with the Debye energy replaced by the prodj2vSF (i.e., the range of energy in which the pairininteraction is effective). By analogy, in the QC regimthe relevant energy scale is likely to beVSF jvSF .As discussed above, this quantity is experimentally wdefined even ifj is not known; we calculate that for Hg1223 VSF 95 meV and for YBa2Cu3O6.63 [33] VSF 75 meV. It is clearly seen that the magnetic enerscaleVSF is higher for the Hg compound, although th


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magnitude and theT dependence of the uniform spisusceptibility are quite comparable. Note that the analof our data within the framework of Ref. [15] leadsthe same conclusions (VSF 77 meV for Hg-1223, and64 meV for YBa2Cu3O6.63), and to a value ofjya 3.5at 370 K.

In conclusion, we have demonstrated by NMR relaation rate measurements the opening of a spin gap atq QAF at a temperatureTp . 230 K in underdoped singlecrystals of HgBa2Ca2Cu3O81d. The Cu sites in inner andouter planes present the sameT dependence ofT1, whichseems incompatible with the interlayer spin-pairing snario. Quantitative analysis of the ratioT1TyT2G showsthat the magnetic energy scale in this compound is higthan in the underdoped YBCO system. This is consistwith a higher value of the transferred hyperfine fieldB,possibly leading to a higher value ofJ [34]. These fea-tures and the fact that Hg-1223 exhibits the highest vaof Tc (when optimally doped), as well as the highest vaof T p (when underdoped), seem to be a strong indicatof the role of antiferromagnetic spin fluctuations in tpairing mechanism of the cuprates.

We thank H. Monien, D. Pines, A. Sokol, and J. Coopfor helpful discussions. M. H. J. acknowledges P. A. Land A. J. Millis for useful comments on this work.

*Present address: Department of Physics “AlessanVolta,” University of Pavia, Via Bassi, 6-27100 PaviItaly.

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[8] J. W. Loramet al., Phys. Rev. Lett.71, 1740 (1993).[9] X.-G. Wen and P. A. Lee, Phys. Rev. Lett.76, 503 (1996).

is

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o

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K. Kukobi, and H. Fukuyama, J. Phys. Soc. Jpn.60, 3072(1991); P. A. Lee and N. Nagaosa, Phys. Rev. B46, 5621(1992); G. Stemmann, C. Pépin, and M. Lavagna, PhRev. B 50, 4075 (1994).

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[17] M. U. Ubbens and P. A. Lee, Phys. Rev. B50, 438 (1994);A. J. Millis and H. Monien, Phys. Rev. B50, 16 606(1994); L. B. Ioffeet al., JETP Lett.59, 65 (1994).

[18] D. Colsonet al., Physica (Amsterdam)233, 231 (1994).[19] Z. P. Hanet al., Physica (Amsterdam)226C, 106 (1994).[20] M. Takigawaet al., Phys. Rev. B43, 247 (1991).[21] O. Chmaissemet al., Physica (Amsterdam)217C, 265

(1993).[22] M. Horvatic et al., Phys. Rev. B48, 13 848 (1993).[23] A. J. Millis, H. Monien, and D. Pines, Phys. Rev. B42,

167 (1990).[24] We find that the quasiparticle contribution [x

00QPsq, vd

px0yG0, with G0 300 meV (i.e., the usual value foYBa2Cu3O7)] is negligible to within 5%.

[25] A. Carrington et al., Physica (Amsterdam)234C, 1(1994); although the resistiveTc is of order 130 K in thiscrystal subsequent specific heat meaurements have sthat the bulkTc 116 6 1 K.

[26] K.-i. Magishi et al. (to be published).[27] Y. Itoh et al., J. Phys. Soc. Jpn.63, 22 (1994). These

authors have ascribed the simultaneous decrease ofs63T1T d21 and 63T21

2G in Tl2Ba2CuO61d to a band effect.So, in the absence ofT2G data the results of Ref. [19] arnot conclusive for the spin-gap opening.

[28] M. Nunez-Regueiroet al., Science262, 97 (1993). C. W.Chu et al., Nature (London)365, 323 (1993).

[29] A. J. Millis and H. Monien, Report No. condmaty9506088.

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[31] J. A. Gillet et al., Physica (Amsterdam)235C–240C,1667 (1994).

[32] P. Monthoux and D. Pines, Phys. Rev. B49, 4261 (1994).[33] M. Takigawa, Phys. Rev. B49, 4158 (1994).[34] In parallel to this work, similar conclusions regardin

the B coupling and the characteristic energy in optimadoped Hg-1223 have been reached by the authorsRef. [26].

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