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PHYSICAL REVIEW B 1 DECEMBER 2000-IVOLUME 62, NUMBER 21

Muon-spin-relaxation study on the Cu-spin state of Bi2Sr2Ca1ÀxYx„Cu1ÀyZny…2O8¿d

around the hole concentration of 18 per Cu

I. WatanabeMuon Science Laboratory, RIKEN (The Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako, Saitama 351-0198,

M. Akoshima and Y. KoikeDepartment of Applied Physics, Graduate School of Engineering, Tohoku University, Aoba-yama 08, Aoba-ku, Sendai 980-8579

S. OhiraDepartment of Physics, Graduate School of Science, University of Tokyo, Hongo, Tokyo 113-8654, Japan;

Meson Science Laboratory, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK-M1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan;

and Muon Science Laboratory, RIKEN (The Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako,Saitama 351-0198, Japan*

K. NagamineMeson Science Laboratory, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK-M

1-1 Oho, Tsukuba, Ibaraki 305-0801, Japanand Muon Science Laboratory, RIKEN (The Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako,

Saitama 351-0198, Japan~Received 24 January 2000!

Muon-spin-relaxation (mSR) measurements were applied to the partially Zn-substituted Bi-2212 system,Bi2Sr2Ca12xYx(Cu12yZny)2O81d , to study the Cu-spin state in a wide range of the hole concentration,p.Singularity of the magnetic correlation between Cu spins atp; 1

8 per Cu has been confirmed clearly, provingthe existence of the so-called ‘‘1

8 effect’’ in the Bi-2212 system. The muon-spin depolarization rate of theZn-substituted sample withp; 1

8 per Cu (x50.3125 andy50.025) at 0.30 K has been found to exhibit nearlya root-square dependence on the magnetic field applied along the initial muon-spin direction. This fielddependence can be explained by assuming that a magnetically excited state of Cu spins moves in a one-dimensional direction producing fluctuating internal fields at the muon sites. The presentmSR measurementsmay support the existence of the stripe correlations of spins and holes in the Bi-2212 system also.

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I. INTRODUCTION

The so-called ‘‘18 effect’’ is now recognized as one of keproblems to elucidate the mechanism of high-Tc supercon-ductivity ~SC!. This effect is characterized by several fetures. One is that the SC is anomalously suppressed arthe hole concentration,p, is 1

8 per Cu.1,2 Another is that amagnetically ordered state of Cu spins appears as the Ssuppressed.3–7 The other is that this effect seems to belated to the structural phase transition from orthorhom~space group:Bmab, OMT phase! to tetragonal~space group:P42 /ncm, TLT phase!.8–10 In order to understand thmechanism of the18 effect, a stripe model on spins and holhas been suggested by Tranquadaet al.11 from neutron elas-tic scattering experiments on La22x2yNdySrxCuO4 in whichthe TLT structure appears below about 60 K.10,12Based uponthis model, dynamically fluctuating stripe correlationsspins and holes are statically stabilized in the TLT phaleading to the suppression of SC.11

On the other hand, it has been pointed out by Yamet al.13 from neutron inelastic scattering experimentsLa22xSrxCuO4 that incommensurate peaks relevant tostripe correlations are observed in a wide range ofp. This

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fact suggests that the dynamically fluctuating stripe corretions of spins and holes exist in a wide range ofp and arestatically stabilized atp; 1

8 per Cu by some pinning forceSince such incommensulate peaks are also observeY-123 ~Ref. 14! and Bi-2212 systems,15 the 1

8 effect is ex-pected to exist also in the Y and Bi systems as well if thare pinning centers in these systems. Actually, Akoshiet al.16 have found anomalous transport phenomenasuppression of the SC atx50.3125 (p; 1

8 per Cu! inthe partially Zn-substituted Bi-2212 samplesBi2Sr2Ca12xYx(Cu12yZny)2O81d , while no anomaly hasbeen observed in non-Zn-substituted Bi-2212 samples. AOMT-TLT structural transition appears at low temperatuin these systems, they have suggested that substitutedatoms operate as pinning centers of the stripe correlationspins and holes.

We have applied muon-spin-relaxation (mSR) measure-ments to non-Zn-substituted and Zn-substituted sampleBi2Sr2Ca12xYx(Cu12yZny)2O81d aroundp5 1

8 per Cu andfound anomalous slowing-down behavior of Cu-spin fluctutions, indicating an enhancement of the magnetic correlabetween Cu spins in the Zn-substituted sample withp; 1

8 perCu.17–20 Although no clear three-dimensional~3D! long-range magnetic order of Cu spins has been observed

14 524 ©2000 The American Physical Society

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have concluded that the18 effect is likely to exist in theBi-2212 system also and that the18 effect is common tohigh-Tc cuprates with the CuO2 plane.

In our previous mSR study onBi2Sr2Ca12xYx(Cu12yZny)2O81d ,18 it has still been uncleawhether the Cu spins are dynamically fluctuating or staticafrozen at low temperatures in the Zn-substituted sampwith p; 1

8 per Cu. Also, the question whether the stripe crelations of spins and holes exist or not in the Bi-2212 stem is still open. In this paper, we report the results of zefield ~ZF! and longitudinal-field~LF! mSR measurements onon-Zn-substituted and Zn-substituted samples of the2212 system, Bi2Sr2Ca12xYx(Cu12yZny)2O81d , in a widerange ofp.

II. EXPERIMENT

Polycrystalline samples oBi2Sr2Ca12xYx(Cu12yZny)2O81d with y50 and 0.025 in awide range of 0.20<x<0.60 were prepared by the ordinasolid-reaction method. Raw materials of Bi2O3 , SrCO3,CaCO3, Y2O3, CuO and ZnO were mixed, preheated800°C for 12 h and pelletized. The pellet was sintered860°C–880°C for 24 h in air. The sintering process wcarried out once again so as to obtain homogeneous samAll of the samples were checked to be of the single phasex-ray diffraction measurements.

mSR measurements were carried out at the RIKEN-RMuon Facility at the Rutherford-Appleton Laboratory in thUK.21 A pulsed positive surface-muon beam with a mometum of 27 MeV/c was used. The direction of the initiamuon spin was parallel to the beam line. Forward and baward counters were located on the upstream and downstrsides in the beam direction. The asymmetry parameter,A(t),was defined asA(t)5@F(t)-aB(t)#/@F(t)1aB(t)#, whereF(t) and B(t) were total muon events counted by the foward and backward counters at timet, respectively. Thea isa calibration factor reflecting the relative counting efficiecies of the forward and backward counters. The initial asymetry was defined asA(0). Time evolution of the asymmetry parameter (mSR time spectrum! was measured in ZF anLF. The LF was applied along initial muon-spin polarizatio

III. RESULTS AND DISCUSSION

A. ZF-µSR

Figure 1 shows the ZF-mSR time spectra of non-Znsubstituted and Zn-substituted samples at about 20, 1.8,0.30 K. The time spectra show Gaussian-type depolarizabehavior in both non-Zn-substituted and Zn-substitusamples forx<0.25, i.e.,p. 1

8 per Cu, indicating that themuon spins depolarize only by randomly distributed stanuclear-dipole field.22 At p; 1

8 per Cu, the time spectrum oZn-substituted sample changes from the Gaussian-type toexponential-type below about 10 K, suggesting a changthe magnetic property of the Cu spins. On the other handchange of the time spectrum from the Gaussian-type isserved in the non-Zn-substituted sample even atp; 1

8 perCu. Forx>0.50, i.e.,p, 1

8 per Cu, the depolarization behavior changes to the exponential-type and a part of the in

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asymmetry is lost at low temperatures in both non-Zsubstituted and Zn-substituted samples.

As mentioned in the previous paper,18 the difference ofthe muon sites in a sample has to be taken into account inanalysis of time spectra. Thus the two-component functioadopted;

A1e2l1t1A2e2l2t3GZ~D,HLF ,t !. ~3.1!

The first term represents muons which are bound to the ogen ions of the CuO5 pyramid and depolarize mainly badditional fields from the Cu spins. The second termscribes the other muons bound to the oxygen ions in theplane. Since the oxygen ions in the BiO plane are far awfrom the CuO2 plane, the influence of internal fields from thCu spins is rather small near the BiO plane. Therefomuons bound in the BiO plane depolarize mainly by radomly distributed static nuclear-dipole fields.GZ(D,HLF ,t)

FIG. 1. Zero-fieldmSR time spectra of the non-Zn-substitute(y50) and Zn-substituted (y50.025) Bi-2212 system,Bi2Sr2Ca12xYx(Cu12yZny)2O81d , in a range of 0.20<x<0.60 atabout 20, 1.8, and 0.30 K. Solid lines show the best fit of Eq.~3.1!.The value ofp is about1

8 per Cu atx50.3125 where the superconductivity is anomalously suppressed~Ref. 16!.

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14 526 PRB 62WATANABE, AKOSHIMA, KOIKE, OHIRA, AND NAGAMINE

is the static Kubo-Toyabe function, whereD/gm is the dis-tribution width of nuclear-dipole fields at the muon sites22

gm is the gyromagnetic ratio of the muon spin (2p313.554 MHz/kG).HLF is LF. In the case of ZF-mSR, weput zero inHLF . A1 andA2 are the initial asymmetries anl1 andl2 are the depolarization rates, respectively. Whenl1is close tol2 at high temperatures, which means that tinfluence of internal fields from the Cu spins is small, itdifficult to apply the two-component fitting. In this case,single-component analysis using only the second termadopted for convenience. Solid lines in Fig. 1 are the besof Eq. ~3.1! to the time spectra.

The ratio ofA1 to A2 means the ratio of the number omuons stopping around the CuO2 plane to those around thBiO plane. It has been found that this ratio is not affectedthe Y-substitution and is similar to that formerly estimatby Nishidaet al.23 in an insulating Bi-2212 sample withx51.0 andy50.

Figure 2 shows thex dependence, namely, thep depen-dence of the muon-spin depolarization rate of non-Zsubstituted and Zn-substituted samples at 0.30 and 1.8Detailed temperature-dependence of the depolarizationaroundp5 1

8 per Cu was reported in the previous paper.18 Inthe case of the two-component analysis, the fast depolation rate,l1, is plotted. In the case of the single-componeanalysis,l2 is plotted. Forx>0.50, there is no big differencin the muon-spin depolarization behavior between non-substituted and Zn-substituted samples. The depolarizarate decreases rapidly with decreasingx. For x<0.40, thedepolarization rate in non-Zn-substituted samples becosmall and independent ofp. On the other hand, the depolaization rate of Zn-substituted samples shows a minimaroundx50.40 and exhibits a maximum atx50.3125 (p; 1

8 per Cu! where the SC is anomalously suppressed. Inoverdoped region ofx<0.25, depolarization rates of botZn-substituted and non-Zn-substituted samples are smal

FIG. 2. Y-concentration dependence, namely,p dependence ofthe zero-field muon spin depolarization rate of~a! non-Zn-substituted samples (y50) and ~b! Zn-substituted samples (y50.025) of Bi2Sr2Ca12xYx(Cu12yZny)2O81d at 0.30 and 1.8 K.The depolarization rate is anomalously enhanced aroundx50.3125 (p; 1

8 per Cu! in the Zn-substituted samples. Solid lineare guides to the eye through the depolarization rate obtained aK. The broken lines show thex dependence ofTc determined byAkoshimaet al. from transport measurements withy50 and 0.025~Ref. 16!.

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Figure 3 displays the temperature dependence of inasymmetries of Zn-substituted samples withx50.50 and0.60. The initial asymmetries decrease with decreasing tperature below about 10 K and become constant below a1 K. Taking into account themSR results on the insulatingBi-2212 sample23 and those on the La systems,3–7 the de-crease of the initial asymmetry shows the appearancemagnetically ordered state of the Cu spins at low tempetures forx>0.50. The magnetic transition temperature is dtermined from Fig. 3 to be about 4 and 10 K withx50.50and 0.60, respectively. The magnetic transition temperaincreases with increasingx, namely, with decreasingp.Therefore, this magnetically ordered state is concluded torelated to the antiferromagnetically ordered state in the inlating Bi-2212 sample withx51.0.23 Large values of thedepolarization rate forx>0.50 is concluded to be due tstrong internal fields from the ordered Cu spins.

Accordingly, rapid decrease of the depolarization ratex,0.50 means disappearance of the magnetically ordestate of Cu spins. As mentioned above, the depolarizarate exhibits a minimum aroundx50.40 and a maximumaroundx50.3125 (p; 1

8 per Cu! in Zn-substituted samplesIn addition, fast depolarization is no longer observed fox<0.25. These results clearly suggest that the anomaslowing-down behavior of Cu spins aroundx50.3125 in theZn-substituted samples is not due to a residual componenthe magnetically ordered state which is observed in thederdoped region ofx>0.50 but due to a singular effect ap; 1

8 per Cu. This proves that the18 effect exists in the Bi-2212 system also.

B. LF-µSR

1. LF -µSR for xÐ0.5

Figure 4 shows the LF dependence of time spectrumthe Zn-substituted sample withx50.60 at 0.30 K. The ob-servable relaxing part of the time spectrum recovers byapplication of LF of about 50 G. In order to recover the loinitial asymetry, LF of about 2000 G is needed. The timspectrum in LF of more than 50 G is independent oft. Theflat time spectrum in LF means that there is no influencedynamically fluctuating internal fields at the muon sites. T

1.8

FIG. 3. Temperature dependence of the initial asymmetryZn-substituted samples withx50.50 and 0.60 in zero field. Themagnetic transition temperatures are estimated from the midpointhe change of the initial asymmetry to be about 4 and 10 K fox50.50 and 0.60, respectively.

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PRB 62 14 527MUON-SPIN-RELAXATION STUDY ON THE Cu-SPIN . . .

fact proves that all of the Cu spins in the Zn-substitusample withx50.60 are completely frozen at 0.30 K. Thsimilar LF dependence of the time spectrum has beenserved at 0.30 K in the Zn-substituted sample withx50.50.These results are consistent with the conclusion that a mnetically ordered static state appears at low temperaturex>0.50, as mentioned in Sec. III A.

The static internal field at the muon site can be rougestimated from the LF dependence of the initial asymmeas shown in Fig. 5. The LF dependence is analyzed usingfollowing equation on the assumption that the magnitudethe internal field at each muon site is unique but its directis random:24–26

A~`!5A~0!S 3

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wherex5HLF /H loc . H loc is the local field which is producedby the magnetically ordered Cu-spins at the muon site.A(`)is the residual asymmetry left after a long time. The solines in Fig. 5 are the best fit of Eq.~3.2!. The internal field

FIG. 4. Longitudinal-field dependence of the time spectrumthe Zn-substituted sample withx50.60 at 0.30 K. The flat tail ofthe time specrum in LF means that the Cu-spin fluctuationsalmost frozen.

FIG. 5. Longtudinal-field dependence of the initial asymmeof Zn-substituted samples withx50.50 and 0.60 at 0.30 K. Solidlines are the best fit of Eq.~3.2!.

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at the muon site is estimated to be 300627 and 373631 Gfor x50.50 and 0.60, respectively. These values are simto that obtained in an insulating Bi-2212 sample withx51.0 andy50.23 Accordingly, Cu spins with 0.5mB areexpected to be statically ordered at low temperatures insubstituted samples ofx>0.50.

Figure 6 shows the LF dependence of the time spectof the Zn-substituted sample withx50.60 at 11 K which isjust above the magnetic transition temperature. The LFpendence is completely different from that obtained at 0K ~Fig. 4!. The tail of the time spectrum is quenched by tapplication of LF of 50 G, but the exponential-type depolaization is still observed even in LF of 2000 G. This is thevidence that the Cu spins are dynamically fluctuating atK. The reason why the LF dependence was measured atis that the ZF time spectrum is very similar to that of tZn-substituted sample withx50.3125 at 0.30 K. So that, thcomparison of the LF dependence attracts interest, as widiscussed in Sec. III B 2.

2. LF -µSR at xÄ0.3125

LF was applied to the Zn-substituted sample withx50.3125 at 0.30 K as shown in Fig. 7 in order to investigamagnetic properties of Cu spins. The time spectrumquenched gradually with increasing LF, but long-time deplarization is still observable even in LF as high as 3950The existence of this long-time depolarization in LF suggethat dynamically fluctuating components of internal fielstill remain at the muon sites.

From the comparison among LF dependences of the tspectra shown in Fig. 4, 6, and 7, it is found that decouplbehavior of the Zn-substituted sample withx50.3125 ob-tained at 0.30 K~Fig. 7! is quite different from that of theZn-substituted sample withx50.60 at 0.30 K~Fig. 4! butexhibits more or less similar tendency to that at 11 K~Fig.6!. Taking into account that the depolarization behaviorthe Zn-substituted sample withx50.3125 at 0.30 K is simi-lar to that of the Zn-substituted sample withx50.60 at 11 Kin which the Cu spins are regarded as being dynamicfluctuating, it is concluded that the Cu spins in the Z

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FIG. 6. Longitudinal-field dependence of the time spectrumthe Zn-substituted sample withx50.60 at 11 K. Solid lines showthe best fit of Eq.~3.1!.

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14 528 PRB 62WATANABE, AKOSHIMA, KOIKE, OHIRA, AND NAGAMINE

substituted sample withx03125 are still dynamically fluctuating at 0.30 K.

3. Dynamical property of the Cu spins

Time spectra of the Zn-substituted sample withx50.3125 at 0.30 K are analyzed using Eq.~3.1! and the bestfit results are shown by the solid lines in Fig. 7. Values ofl1,obtained from the fitting, are shown in Fig. 8. It is found thl1 decreases with increasing LF in the relationship ofl1}(HLF)n with n520.6. The LF dependence ofl1 of theZn-substituted sample withx50.60 at 11 K is also shown inFig. 8. In this case,l1 decreases with increasing LF, but idependence above about 100 G is much weaker than ththe Zn-substituted sample withx50.3125.

There may be a possibility that magnetic momentslocally induced around substituted Zn ions and fluctu

FIG. 7. Longitudinal-field dependence of the time spectrumthe Zn-substituted sample withx50.3125 at 0.30 K. Solid linesshow the best fit of Eq.~3.1!.

FIG. 8. Longitudinal-field dependences of the depolarizatrate,l1, of the Zn-substituted sample withx50.3125 at 0.30 K andof the Zn-substituted sample withx50.60 at 11 K. The solid line isthe best fit showing nearlyl1}HLF

20.5. The broken line is the best fishowing the 1D13D diffusion model.

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slowly to produce dynamically fluctuating internal fieldsthe muon sites. If this is the case, induced magnetic momweakly interact with each other through the dipole-dipointeraction and the LF dependence ofl1 can be described bythe Redfield’s equation as follows:27

l152gm

2 H loc2 tc

11gm2 HLF

2 tc2

, ~3.3!

wheretc is the correlation time of muon spins. However, E~3.3! shows a convex shape as a function ofHLF in a log-logplot, so that this function cannot discribe the experimenresult ofl1 vs HLF . Therefore, this model is not suitable foexplaining the Cu-spin state of the Zn-substituted samwith p; 1

8 per Cu.HLF

20.5 dependence of the dynamical depolarization rwas observed by Nagamineet al.28 and Ishidaet al.29 in low-dimensional materials such as polyacetylene with odimensional~1D! chains of molecules. In this case, dynamcally fluctuating internal fields at the muon sites weunderstood to be produced by the 1D diffusion of a muoinduced soliton state. According to Butleret al.,30 in casethat a spin-excited state diffuses in a crystal making flucating internal field, the LF dependence of the dynamicalpolarization rate reflects the dimensionality of the diffusiof the spin-excited state. That is, the depolarization rateproportional to HLF

20.5 in the case of 1D diffusion,C2D

2 ln(HLF) in the case of two-dimensional~2D! one andC3D–HLF

0.5 in the case of 3D one, whereC2D and C3D areconstants. Actually, these LF dependences of the dynamdepolarization have been observed also in conducting pmers by Prattet al.31

l1 of the Zn-substituted sample withx50.3125 at 0.30 Knearly exhibitsHLF

20.5 dependence as shown in Fig. 8. Thuon the analogy of mSR results of low-dimensionamaterials,28,29,31a model can be supposed that a magneticaexcited state of the Cu spins like a soliton or a magnon sdiffuses in a 1D direction within the CuO2 plane producingfluctuating internal fields at the muon sites. This model mbe understood by assuming the existence of the 1D stcorrelations of spins and holes also in the Bi-2212 systemthis case, the movement of the spin-excited state whicsupposed from the presentmSR study is restricted to be inthe 1D spin and/or hole chains. In addition, the spatial regwhere the stripe correlations exist is also expected to min parallel or perpendicularly to the stripe direction, becauthe stripe correlations are periodic in the 1D direction withthe CuO2 plane. These motions are like the 1D diffusioTherefore, the observation ofHLF

20.5 dependence ofl1 in thepresentmSR study is expected to support the existence ofstripe correlations also in the Bi-2212 system atp; 1

8 perCu. Actually, this scheme is supported by a recent neutinelastic scattering experiment on the Bi-2212 system whis suggestive of the existence of the stripe correlations.15

Consequently, the following scenario seems to be reasable atp; 1

8 per Cu in the Bi-2212 system. As there is npinning center in non-Zn-substituted samples, spinsholes fluctuate in high frequencies out of themSR time win-dow which is typically between 1026 and 10211 sec. OnceZn is partially substituted for Cu, the substituted Zn ions

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PRB 62 14 529MUON-SPIN-RELAXATION STUDY ON THE Cu-SPIN . . .

as pinning centers of the stripe correlations of spins aholes and tend to make them static.

Finally, it is worthwhile mentioning the LF dependencel1 of the Zn-substituted sample withx50.60 at 11 K. It hasbeen found that the LF dependence ofl1 cannot be ex-plained by a single-component diffusion model of a spexcited state as in the case of the Zn-substituted samplex50.3125 at 0.30 K. After trial and error, it has been fouthat a 1D13D diffusion model is the best to explain the Ldependence ofl1, as shown by the broken line in Fig. 8This suggests a possibility of the existence of the stripe crelations of spins and holes in the underdoped region aHowever, more detailedmSR or other experiments are required to reveal the detailed Cu-spin state in this region.

IV. SUMMARY

ZF- and LF-mSR measurements were applied to non-Zsubstituted and Zn-substituted samples of the Bi-2212 stem, Bi2Sr2Ca12xYx(Cu12yZny)2O81d , in a wide range ofpin order to examine the existence of the so-called1

8 effectand the stripe correlations of spins and holes. A magneticordered state of the Cu spins has been confirmed attemperatures forx>0.50, i.e.,p, 1

8 per Cu. The magneti-cally ordered state disappears forx<0.40. It has been confirmed from the ZF-mSR measurements that the muon-spdepolarization rate exhibits a local maximum aroundx50.3125, i.e.,p; 1

8 per Cu in Zn-substituted samples anthat the magnetic correlation between Cu spins is enhan

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around thisp region. These results prove that the18 effect

exists in the Bi-2212 system also.The LF dependence of the time spectrum of the Z

substituted sample withx50.3125 at 0.30 K has been founto be similar to that of the Zn-substituted sample withx50.60 at 11 K in which the Cu spins are still dynamicalfluctuating. In addition, the long-time depolarization behaior has remained even in LF of 3950 G, suggesting the etence of dynamically fluctuating internal fields at the musites. Therefore, it is concluded that the Cu spins in thesubstituted sample withx50.3125 are dynamically fluctuating even at low temperatures as low as 0.30 K.

The LF dependence of the dynamical depolarization rof muon spins in the Zn-substituted sample withx50.3125at 0.30 K has been found to be nearly proportional toHLF

20.5.This LF dependence can be understood by assuming theistence of the 1D diffusion of a magnetically excited statethe Cu spins which is producing fluctuating internal fieldsthe muon sites. This model may support the existence of1D stripe correlations of spins and holes in the Bi-2212 stem also.

ACKNOWLEDGMENTS

A part of this study, especially sample preparation acharacterization, was supported by a Grant-in-Aid for Scitific Research from the Ministry of Education, SciencSports and Culture, Japan, and also by CREST of Japanence and Technology Corporation.

.

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