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PHYSICAL REVIEW B 1 SEPTEMBER 1998-IIVOLUME 58, NUMBER 10

Pseudogap behavior in single-crystal Bi2Sr2CaCu2O81d probed by Cu NMR

K. Ishida, K. Yoshida, T. Mito, Y. Tokunaga, Y. Kitaoka, and K. AsayamaDepartment of Physical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japa

Y. Nakayama, J. Shimoyama, and K. KishioDepartment of Superconductivity, University of Tokyo, Bunkyo-ku, Tokyo 113, Japan

~Received 21 April 1998!

We report that the nuclear spin-lattice relaxation rate divided by temperature, 1/T1T, has a broad maximumaroundT* ;210 K and;100 K in underdoped and overdoped single crystals of Bi2Sr2CaCu2O81d ~Bi2212!with Tc579 and 77.3 K, respectively, showing the normal-state spin-gap behavior. One result is that the steepdecrease in the63Cu Knight shift,K(T), has been observed belowTK* ;200 K and;100 K, suggesting thenormal-state pseudogap behavior in quasiparticle density of states~DOS!, which is consistent with thepseudogap behavior belowTARPES* ;170 K revealed on underdoped Bi2212 from studies of angle-resolvedphotoemission spectroscopy. We propose that the spin-gap behavior in 1/T1T has the same origin as thepseudogap in the quasiparticle DOS.@S0163-1829~98!51534-2#

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In underdoped cuprates, there is considerable evidethat the pseudogap in the magnetic and electronic excitaspectra is already formed in the normal state aboveTc . Fromstudies of the magnetic excitation spectrum,1–5 the spin-gapbehavior was first reported and the pseudogap in the etronic excitation spectrum later from a variety of othprobes.6–11 Recent studies by Dinget al. and Harriset al. ofangle-resolved photoemission spectroscopy~ARPES! in un-derdoped Bi2Sr2CaCu2O81d ~Bi2212! revealed that thepseudogap withd-wave symmetry opens belowTARPES*;170 K and 225 K, respectively, and these authors sgested that the pseudogap develops into thed-wave super-conducting gap once phase coherence is established bTc .7–9 The result was interpreted as evidence in favor opreformedd-wave gap. TheTARPES* seems to increase abov;300 K in the underdoped Bi2212 withTc510 K.7

It was reported on underdoped YBa2Cu3O6.6 ~YBCO6.6)that the Knight shiftK(T) decreases upon cooling fromTmK ,4 whereas the spin-lattice relaxation rate dividedtemperature, 1/T1T, has a broad maximum aroundT*;150 K far aboveTc but belowTmK .1–3 Recently, this be-havior was also found in underdoped Hg-based compouwith mono- and three CuO2 layers.12–14The anomalous suppression in the spectral weight of the low-energy spinnamics belowT* is referred to as aspin-gapbehavior1 andwas confirmed by subsequent neutron experiments.5 How-ever, the 1/T1T in underdoped La22xSrxCuO4 ~LSCO! ~Ref.15! does not show the spin-gap behavior, but increasestinuously close toTc , whereas the spin susceptibility deduced from theK(T) in underdoped LSCO undergoes a cotinuous decrease belowTmK .15–17On the other hand, Loramet al. suggested from susceptibility and high-resolution scific heat measurements thatpseudogapis developed belowTmK upon cooling in the normal-state quasiparticspectrum.18 The anomalies aroundTm are also shown frommeasurements of Hall coefficients and thermoelectric poin LSCO.19 There is as yet no general consensus on a csistent interpretation of these magnetic anomalies relatethe Knight shift and 1/T1T.

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Even in the NMR community, there is no consensus abthis issue. As a matter of fact, Yasuokaet al. insisted that thedecrease in 1/T1T below T* is ascribed to an opening ofpseudogap in the antiferromagnetic~AF! spin excitationspectrum, and estimated from the rapid decrease in 1/T1TbetweenTc and T* that anactivated-gapsize,DT1

, is in arange of 13–18 meV for various underdoped compound20

Although they stressed that this spin gap should not berectly related to the superconducting gap, they considethat the appearance of the spin gap is likely to be relatethe mechanism of high-Tc superconductivity. On the othehand, Williamset al. claimed that the reduction in Knighshift from TmK is due to the presence of a pseudogap withd-wave symmetryin the quasiparticle density of states~DOS!in the normal state.21 They analyzed the decreasing behavof K(T) over the entire temperature range by assuming acomprising the pseudogap (Eg) and the superconducting ga(Ds), D25Ds

21Eg2 and claimed that sinceEg scales to a

maximum value ofTc in various cuprates, the pseudogap athe superconducting gap have a similar energy scale. In tanalyses, however, the spin-gap behavior in 1/T1T was ig-nored completely. In addition, Bobroffet al. claimed fromthe 17O Knight shift, 17K(T) measurement on underdopeHgBa2CuO41d that 17K(T) extrapolates to zero atT.0,which indicates the opening of a pseudogap atT* .Tc .12

They considered that the pseudogap temperatureT* may bedefined as a crossover temperature between the decrebehavior and the flat high temperature part in17K(T). Thedifferent temperature dependence of 1/T1T and K(T) hasnever been interpreted in a consistent manner on a sfooting.

Since ARPES,7–9 tunneling spectroscopy,22,23and thermaland transport measurements24 are being carried out onBi2212 single crystals where the doping level varies frounderdoping to overdoping, it is important to compare tpseudogap behavior probed from various experimental teniques with those evidenced from theT1 and the Knight shiftdata. In this paper, we report Cu-NMR measurements inderdoped and overdoped Bi2212 single crystals withTc;79 and 77.3 K, respectively. In the underdoped Bi2212

R5960 © 1998 The American Physical Society

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broad peak in 1/T1T is observed atT* ;210 K and the steep

decrease inK(T) occurs belowTK* ;200 K, deviating from aT-linear-like gradual decrease below a much higher tempture,TmK . It is pointed out that the latter result is consistewith the ARPES results that the gap opens belowTARPES*;170 K reported by Dinget al.7 and 225 K by Harriset al.9

for samples with almost the same doping level. The remaable coincidence among these gaplike features leads us tconclusion that the spin-gap behavior in 1/T1T has the sameorigin as the pseudogap in the quasiparticle DOS evidenfrom the Knight shift and the ARPES results. Furthermowe suggest that the overdoped Bi2212 also revealspseudogap behavior aroundT* ;TK* ;100 K close toTc

577 K. The present NMR studies on the Bi2212 single crtals have provided detailed information about the naturethe pseudogap not only in the collective AF-spin excitatspectrum but also in the quasiparticle DOS.

Single crystals of Bi2212 were synthesized by the floatzone method. Underdoped (Tc579 K) and overdoped (Tc577.3 K) single crystals were prepared by annealing600 °C under P~O2!54.6731024 atm for one day at 400 °Cand under P~O2)52.1 atm for three days, respectively. Thtemperature width in the superconducting transition is ab3 K for both samples. The superconducting fraction inunderdoped and overdoped samples is nearly the same,the size of the diamagnetic shielding signal for each is coparable. From the dependence ofTc on carrier-hole concentration p per the CuO2 plane,25 p in the underdoped andoverdoped samples is estimated to be;0.125 and;0.225,respectively. Cu NMR measurements were performed atfrequency of 178.1 MHz using a 16 T~4.2 K! superconduct-ing magnet. The nuclear spin-lattice relaxation timeT1 wasmeasured by the saturation recovery method. Above 40single component ofT1 was determined by fitting the recovery of the nuclear magnetizationM (t) after saturation pulseto the theoretical relaxation function@M (`)2M (t)#/M (t)50.1exp(2t/T1)10.9exp(26t/T1). To investigate an evolution of magnetic behavior with respect to hole content,include the previous results of the 1/T1T and the Knight shiftin optimally doped Bi2212~Tc;86 K, p;0.20.!26,27 NMRdata in overdoped Bi2212 (Tc577 K) have already been reported by Walstedtet al.28 The present NMR results in thoverdoped Bi2212 are found to be consistent with theirsults.

Figure 1 shows theT dependence of the Knight shift paallel to thec axis, Kc(T) in the underdoped and overdopeBi2212. TheKc in the underdoped Bi2212 decreases lineain the range 200 K2300 K, whereas it undergoes a markdecrease belowTK* ;200 K, exhibiting a small anomaly aTc . In contrast, theKc in the overdoped Bi2212 decreasgradually below;100 K from a constant value in tempertures higher than 100 K and steeply belowTc577.3 K. TheKc at 4.2 K consists of the orbital contribution from th3dx22y2 orbit, the superconducting diamagnetic contributiand the spin shift originating from the residual densitystates~RDOS! in the superconducting state. The presenceRDOS was verified from the observation ofT1T5 constantbehavior at low temperatures.26 By subtracting suchT-independent contributions from the measured Knight sdataKobs, the T-dependent part of the Knight shiftDK(T)

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5Kobs2K~4.2 K! is shown in Fig. 2, together with the datin the optimally doped Bi2212 reported previously.26,27 Inthe optimally doped Bi2212, since the accuracy of the63CuKnight shift is poor, theD17K(T) deduced from the17OKnight shift data reported by Takigawa and Mitzi are alplotted for comparison.27 For each compound, the decreasibehavior inDK(T) is different, reflecting their different doping level.

In order to characterize the respectiveT variation inDK(T) upon cooling, we plot in Fig. 3 the temperaturderivative change inDK(T), dK(T)/dT as a function oftemperature. From the respective behavior for the unddoped and optimally doped Bi2212 in Fig. 3, two charact

FIG. 1. T dependence of the Knight shift parallel to thec axis(Kc) in underdoped and overdoped Bi2212. Arrow indicatesTc foreach compound.

FIG. 2. T-dependent spin partKcs~Cu! in Kc in underdoped,optimally doped, and overdoped Bi2212. TheT-dependent spin parKs~O! in the 17O Knight shift in optimally doped Bi2212 reporteby Takigawaet al. is also plotted by open circles~Ref. 27!. Theanomalies atTc , TK* , andTmK are indicated by arrows~see text!.

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R5962 PRB 58K. ISHIDA et al.

istic temperatures ofTmK andTK* are defined as the tempertures wheredK(T)/dT begins to increase from zero anincrease steeply from a finite value, respectively. In thetimally doped Bi2212,TmK;203 K andTK* ;123 K are de-duced. In the underdoped Bi2212,TmK shifts to a tempera-ture higher than room temperature andTK* ;200 K. By

FIG. 3. T dependence ofT derivatives of the spin part in63CuKnight shift for ~a! underdoped,~b! optimally doped, and~c! over-doped Bi2212. Open circles in~b! are theT derivatives in the17OKnight shift reported by Takigawa~Ref. 27!. Arrows show theanomalies atTc , TK* , andTmK .

FIG. 4. T dependence of 1/T1T in underdoped, optimally dopedand overdoped Bi2212. Arrows indicateTc andT* for each com-pound.

-contrast,TK* and TmK in the overdoped Bi2212 cannot bexactly distinguished from one another as seen in Fig. 3

We turn to the nuclear-relaxation behavior in both tsamples. Figure 4 shows theT dependence of 1/T1T in theunderdoped and overdoped Bi2212 together with the datthe optimally doped Bi2212.26 The 1/T1T in the underdopedBi2212 reveals a broad maximum aroundT* ;210 K andcontinues to decrease without any clear change atTc . Thevalue of 1/T1T at Tc has decreased to 34% of its value atT* ,which is lower than the underdoped YBa2Cu3O6.6 ~63%!~Ref. 3! and YBa2Cu4O8 ~57%!,29 and is comparable withthat in the underdoped HgBa2CuO41d with Tc580 K~27%!.13 In the optimally doped and the overdoped Bi221T* is reduced to;130 K and;100 K, respectively. In con-trast to the underdoped Bi2212, the steep decrease in 1T1Tis clear belowTc for both the samples. A striking result ithat T* is close toTK* for the underdoped and optimalldoped Bi2212. Even in the overdoped Bi2212,T* is close toTmK;TK* . These results provide evidence that the spin-gbehavior in 1/T1T below T* has the same origin as thpseudogap behavior in the quasiparticle DOS belowTK* .

Next we discuss the gradual decrease inDK(T) as tem-perature decreases fromTmK to T* . Since 1/T1T continues toincrease betweenTmK and T* where DK(T) decreasesgradually as seen in Figs. 2 and 4, the likely cause forgradual decrease inK(T) is associated with the developmeof AF-spin correlations towardsT* , which is also suggested

FIG. 5. Hole contentp dependence of characteristic tempertures below which an anomaly appears in various measurem~see text!.

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from the recent theoretical studies.30,31 In the gaplessquantum-spin systems such as one dimensionalS51/2 linearspin-chain Sr2CuO3 ~Ref. 32! and three-leg spin-laddeSr3Cu2O5,33 the gradual decrease in susceptibility was oserved as temperature decreases. This means that the grdecrease in static susceptibility in the underdoped and omally doped Bi2212 is not always related with the openof the pseudogap. Rather, the sharp decrease in63K(T) be-low TK* , where 1/T1T starts to decrease, should be ascribto the opening of the pseudogap. We note that an extraption of pronounced decrease inDK(T) in the normal statenear Tc intercepts to the temperature axis atT.0 in theDK(T) vs T plot in Fig. 2. This feature is consistent with th17O Knight shift data in underdoped HgBa2CuO41d single-layer cuprates.12

To summarize the present NMR results, we presenFig. 5 the hole content dependence ofT* , TK* , and TmK

together with various characteristic temperatures at whichanomaly was observed by other experimental probes.et al. reported that the in-plane resistivity starts to devidownward from aT-linear-like behavior belowTr* and thatthe uniform susceptibilityx(T) starts to decrease gradualbelow Tmx .24 As seen in Fig. 5, it is obvious thatT* ;TK*;Tr* ;TARPES* , which increase with decreasing hole conteThis agreement in various characteristic temperaturesgests strongly that the pseudogap opens not only in thespin excitation spectrum at low energy aroundQ5(p,p) butalso in the quasiparticle DOS. Furthermore, the tunnespectroscopy on the same optimally doped Bi2212 revthat the normal-state pseudogap opens in the quasipaDOS around 120 K close toT* ; 130 K.23 Convincing evi-

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dence is increasing to indicate that the pseudogap in thesiparticle DOS and the spin gap observed in 1/T1T has thesame origin in a series of Bi2212 single crystals wheredoping level varies from underdoping to overdoping. Bcontrast, other characteristic temperatures,TmK andTmx , be-low which the Knight shift and the susceptibility decreagradually, respectively, have nothing to do with thpseudogap formation, but provide a signature for the deopment of AF-spin correlations.

It is still a key issue whether the pseudogap is associawith a spin gapsignaling a non-Fermi-liquid state based onconcept of a spin-charge separation,34 or a normal-state precursor of thed-wave superconducting gap35 or a precursor toa spin density wave state.30,36At the present stage, we canndetermine an origin of the pseudogap. However, we sugfrom the present NMR result that the pseudogap andsuperconducting gap are the same in origin, sinceanomaly of 1/T1T in the underdoped Bi2212 is not observeat Tc .

In order to settle the above issue, it is important to inspwhetherT* , TK* , andTARPES* continue to increase when thholes are decreased near the superconducting to nonmeand magnetic phase boundaries. To check this, we remthat further systematic experiments are planned on the sBi-based single crystals.

We thank O. Narikiyo and K.Miyake for stimulating discussions. This work has been partially supported by NEfor the Industrial Science and Technology Frontier Prograand by a Grant-in-Aid for Scientific Research in Priority Aeas~‘‘Anomalous metallic state near Mott transition’’! fromthe Ministry of Education, Science, Sport and Culture.

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