Mesoscopic phase separation in Na$_x$CoO$_2$ ($0.65leq xleq 0.75$)

a r X i v :c o n d -m a t /0312284v 1 [c o n d -m a t .s t r -e l ] 11 D e c 2003

Mesoscopic phase separation in Na x CoO 2(0.65≤x ≤0.75)

P.Carretta,M.Mariani,C.B.Azzoni and M.C.Mozzati

Department of Physics “A.Volta”and Unit`a INFM,University of Pavia,Via Bassi 6,I-27100,Pavia (Italy)

I.Bradari′c

Laboratory for Theoretical and Condensed Matter Physics,

The ”Vinˇc a”Institute of Nuclear Sciences,P.O.Box 522,11001Belgrade,Serbia

I.Savi′c

Faculty of Physics,University of Belgrade,Studentski trg 12-14,11000Belgrade,Serbia

A.Feher

Faculty of Science,P.J.Saf′a rik University,Park Angelinum 9,04154Kosice,Slovakia

J.ˇSebek

Institute of Physics,AS CR,Na Slovance 2,18221Prague 8,Czech Republic

NMR,EPR and magnetization measurements in Na x CoO 2for 0.65≤x ≤0.75are presented.

While the EPR signal arises from Co 4+magnetic moments ordering at T c ?26K,59Co NMR signal originates from cobalt nuclei in metallic regions with no long range magnetic order and characterized by a generalized susceptibility typical of strongly correlated metallic systems.This phase separation in metallic and magnetic insulating regions is argued to occur below T ?(x )(220?270K).Above T ?an anomalous decrease in the intensity of the EPR signal is observed and associated with the delocalization of the electrons which for T

PACS numbers:76.60.-k,76.30.-v,71.27.+a

I.INTRODUCTION

Na x CoO 2has been subject of an intense research activity in the past owing to its possible technological applicabilities as a battery electrode material 1.More recently it has attracted a renewed interest in view of its rich phase diagram and for the several aspects it shares in common with the superconducting cuprates 2.In particular,it has a layered structure formed piling up CoO 2layers containing Co 4+S =1/2ions 3and it becomes superconducting when the chemical pressure is modi?ed by intercalating water molecules between Na and CoO 2planes 4.On the other hand,while in the cuprates Cu 2+ions form a square lattice,in Na x CoO 2cobalt ions form a triangular lattice which induces geometrical frustration of the antiferromagnetic interactions 5.Moreover,Na x CoO 2,for x around 0.7shows an anomalous phase transition at T c ?26K,evidenced by a small peak in the speci?c heat.The low-temperature (T)ground state yields an extremely small macroscopic magnetization 6and it was argued 7,on the basis of μSR measurements,that it might correspond to a spin-density wave (SDW).Furthermore,slightly below room temperature,on the basis of NMR measurements alone,Gavilano et al.Ref.8suggested that charge ordering occurs.In this T range anomalies in 59

Co NMR spectra 9and a crossover from insulating to metallic-like behavior in the c-axes resistivity 10was observed for x ?0.5.Finally,a recent analysis of low-T thermal and transport properties suggested that for x around 0.7the electronic properties have to be described by a two-band model 11.

In the following,based on the analysis of NMR and EPR data,it will be shown that metallic and magnetic insulating domains coexist in Na x CoO 2for 0.65≤x ≤0.75.In particular,while EPR is sensitive to the magnetic domains with electrons localized on Co 4+d z 2orbitals,NMR spectra and relaxation measurements allow to investigate the spin dynamics in the metallic regions.The phase separation is argued to occur below T ?(x )(220?270K),the same temperature at which Gavilano et al.Ref.8suggested the occurrence of charge ordering.Above T ?the electrons which were localized on Co 4+d z 2orbitals can delocalize through an activated process.

In the next section the experimental results and technical aspects involved in the sample preparation,magnetization,EPR and NMR measurements will be given.The analysis of the EPR and NMR spectra providing evidence for a phase separation will be presented in Sect.III,together with the analysis of the generalized spin susceptibility within the metallic phase.The concluding remarks will be given in Sect.IV.

II.EXPERIMENTAL RESULTS

A.Sample Preparation

Na x CoO2(x=0.65,0.70and0.75)samples were prepared following the”rapid heat-up”method12,13.A stoichio-metric mixture of99.99%purity Co3O4and Na2CO3was thoroughly ground,and placed in a furnace and preheated at750C for12hours.The obtained samples were reground and annealed for15hours at850C in air,followed by slow cooling to room temperature.X-ray powder di?raction measurements con?rmed all samples to be single phase of hexagonalγ-Na x CoO214,15.The lattice parameter a was estimated around2.827?A for all samples,while c=10.939(3),10.907(4)and10.892(4)?A for x=0.65,0.70and0.75,respectively,in good agreement with the values reported in literature(see Fig.1).

B.Magnetization

Magnetization measurements were performed using a Quantum Design XPMS-XL7SQUID magnetometer.The ?eld cooled magnetization(M)for T≥T c?26K was observed to increase linearly with the magnetic?eld intensity (H).The temperature dependence of the susceptibilityχ=M/H,after correcting for the core electrons diamagnetism, for x=0.65,0.7and0.75,is reported in Fig.2.One notices thatχincreases on cooling and shows a small kink at T c?26K in all samples.The magnitude ofχwas observed to increase sizeably upon decreasing x.The susceptibility measurements were repeated on the x=0.75sample after4months and no ageing e?ect was noticed,except for a small increase in the low-temperature susceptibility due to possible contamination from paramagnetic impurities.

C.EPR measurements

EPR spectra were recorded with an X-band spectrometer equipped with a standard microwave cavity and a variable temperature device.The room temperature derivative of the EPR powder spectra for x=0.65,0.7and0.75is shown in Fig.3.The spectra are broad and slightly asymmetric,with a g?2,typical of Co4+ions with a distorted octahedral coordination and a low-spin S=1/2con?guration.One notices a remarkable decrease in the intensity of the EPR signal with increasing Na content.The intensity of the EPR signal was calibrated with respect to the one of a reference paramagnetic salt and it was found that even for x=0.65only about8%of all Co sites contribute to the EPR signal. This reduced intensity at room temperature should not be associated with a poor penetration of the microwave inside the grains.In fact,at room temperature the estimated skin depth is18μm,close to the average grain size.Only at low temperature the shortening of the skin depth can lead to a poor irradiation.The low EPR signal originates from a reduced fraction of Co4+sites.The intensity of the EPR signal(see Fig.4),which in principle is proportional to the contribution to the static uniform susceptibility of the irradiated Co4+ions,shows an anomalous decrease above T?(?240K for x=0.7and?270K for x=0.65)and vanishes around500K.At low temperature the signal intensity passes through a maximum around125K,then decreases and vanishes abruptly at T c,indicating that at this temperature a transition to a phase with long range order among Co4+moments occurs.The temperature dependence of the EPR linewidth shows a minimum around115K characteristic of two-dimensional(2D)antiferromagnets17,18 (see the inset to Fig.3).

D.NMR Spectra and relaxation

NMR spectra and spin-lattice relaxation measurements were carried out using standard radio-frequency(RF)pulse sequences.23Na echo signal was maximized with aπ/2?τ?πpulse sequence while59Co echo signal was maximized with aπ/2?τ?π/2sequence.The23Na(see Fig.5)and59Co NMR powder spectra were obtained from the Fourier transform of half of the echo signal and from the envelope of the echo magnitude,respectively.

23Na NMR spectra of the central line,associated with the1/2??1/2transition,were observed to progressively shift to higher frequency and to broaden on cooling(see Fig.6).However,the shape of the low-T spectra was not reproducible.Even after a temperature cycle in helium atmosphere,where the sample was warmed from35K up to 280K and after50minutes cooled back to35K,a change in the spectrum was noticed(see Fig.5).This evidences that the modi?cations are not due to ageing e?ects but rather re?ect intrinsic di?erences in the microscopic environment around the nuclei.In some cases a nearly symmetric line shape was observed whereas in other measurements two distinct peaks were visible19(see Fig.5).The two peaks of23Na central line should not be ascribed to the two

singularities expected for a quadrupolar perturbed NMR powder spectrum20since,as will be shown hereafter,the temperature dependence of the spin-lattice relaxation rate measured at the two peaks is di?erent.Also59Co NMR spectra show analogous modi?cations after the sample has undergone a temperature cycle between35K and room temperature.

It must be mentioned that neither59Co nor23Na spectra show any sizeable change when the sample is cooled below T c.As can be seen in Fig.7the59Co NMR spectrum of the central line is practically identical above and below T c.This is a clear indication that the59Co nuclei giving rise to the NMR signal,corresponding to the majority of cobalt nuclei, are in regions with no long range magnetic order.It must be mentioned that the observation of59Co nuclei belonging to Co4+ions,the ones yielding the EPR signal,is prevented by the extremely fast nuclear relaxation.Hence,EPR and NMR in Na x CoO2are complementary.The?rst probes the local susceptibility of Co4+rich regions which show a long range magnetic order below26K,the second allows to investigate the static and dynamic magnetic properties of the metallic regions with non-magnetic cobalt ions.

The paramagnetic shift?K of23Na NMR central line shows the same temperature dependence ofχmeasured with the SQUID magnetometer.In fact,one can write

Aχ(q=0,ω=0)

?K=

e T and O2p orbitals,through an activated process.This leads to an activated transport along the c-axes10and to a polaronic-like motion o

f the electrons,as pointed out by Rivadulla et al.Ref.21.When the electrons are promoted to the conduction band the number of Co4+sites is progressively reduced,the intensity of the EPR signal diminshes with temperature(see Fig.3)and,?nally,for T>500K the majority of the electrons are itinerant.Hence,one can derive the T-dependence of Co4+sites density directly from the EPR data.

In order to estimate the number of Co4+sites one has?rst to take into account that the EPR signal intensity depends on the T-dependent static uniform susceptibility and on the microwave screening,which is relevant at low-T. The T-dependence of the spin susceptibility was assumed to be the one of a2D triangular antiferromagnet22,with a Curie-Weiss temperatureΘ?135K.This value is suggested by the minimum in the T-dependence of the EPR linewidth,which usually occurs at a temperature slightly belowΘ17,18.The maximum in the T-dependence of the EPR intensity around125K is not the one characteristic of the susceptibility of a2D triangular antiferromagnet, which should occur around0.35Θ?47K(see the dotted line in Fig.4).Also the decrease of the EPR intensity below 100K is too fast to originate from the T dependence of the susceptibility of a2D triangular antiferromagnet.In fact, the pronounced reduction of the low-T EPR intensity results from the decrease of the skin-depth d with temperature, which is proportional to the square-root of the electrical resistivity.In order to take into account this e?ect we have assumed for simplicity spherical grains,with an average radius of30μm,and that a grain is fully irradiated over a distance equal to d(18μm at room temperature).Taking into account the T-dependence of Na x CoO2resistivity reported in literature we have derived the curve shown in Fig.4for the expected integrated EPR intensity.The experimental data are observed to follow rather well the expected behavior below T?,pointing out that for T≤T?the density of Co4+sites is T-independent.The reduction of the EPR intensity above T?,with respect to the estimated one allows to derive the temperature evolution of the fraction of electrons localized on Co4+a T1orbitals(see Fig.11). If?is the energy di?erence between the a T1level and the conduction band,the statistical population of Co4+ions should be given roughly by n Co4+(T)/n Co4+(T?T?)=1/(1+N eff exp(??/T)),with N eff an e?ective density of states for the itinerant electrons.Although the data in Fig.11can be?tted rather well for a value of??0.3eV a more quantitative estimate would require the knowledge of the T-dependence of?and therefore this value should be taken just as an order of magnitude.

The observation of an EPR signal below T?suggests that,although the electrical resistivity has a metallic behavior11, there is still a sizeable fraction of electrons localized on Co4+a T1orbitals at low T and,hence,T?cannot signal a conventional metal to insulator transition21.The absolute value of the fraction of Co4+sites for T?T?,estimated from the EPR measurements,is around8%for x=0.65and progressively decreases upon increasing the Na content. This trend is exactly the one of the magnetic entropy estimated from speci?c heat measurements carried out on samples of the same batch24(see Fig.12).In particular,the x dependence of the intensity of the speci?c heat peak at T c scales with the EPR intensity upon increasing x(see the inset to Fig.12).Moreover,the magnitude of the magnetic entropy24also indicates that for x=0.65a fraction around8%of S=1/2ions contribute to the total entropy.This is a neat con?rmation that the magnetic transition yielding the speci?c heat peak at26K is due to the ordering of localized Co4+magnetic moments.AlsoμSR measurements suggest that only a small fraction of the sample becomes magnetic.In fact,Sugiyama et al.Ref.7observed that for x=0.75no more than20%of the muons injected in the sample go into(or close to)magnetically ordered regions for T≤T c.This is not by itself an indication of a SDW phase since in that case,although one might expect a reduced value of the sample magnetization,all the sample should show a long-range order.

On the other hand,59Co NMR relaxation measurements and spectra,due to cobalt nuclei in metallic regions,show no sign of magnetic ordering.These observations clearly point towards a phase separation between antiferromagnetic insulating and metallic regions for T

The di?erence in the NMR spectra after temperature cycling above T?can be due to a di?erent topological arrangement of the insulating and metallic domains.In the case of23Na NMR spectra,the fast relaxing nuclei yielding the high frequency shoulder(see Fig.5))are the ones closer to Co4+ions,while the most intense peak should be associated with23Na nuclei well inside the metallic regions.Since no e?ect of thermal cycles was noticed on the intensity of the EPR signal the ratio of the insulating over metallic volume should not change after the temperature cycles.Then,a di?erent ratio in the intensity of the two components of23Na NMR spectra should originate from a modi?cation in the surface/volume ratio of the insulating regions.An increase in the intensity of the high frequency shoulder should be caused by an average decrease in the size of the insulating domains and vice-versa.Now,why the topology of the metallic and insulating domains should be a?ected by the temperature cycles?One possibility is that at high temperatures,due to their relatively high mobility,Na+ions modify their arrangement and lead to a modi?cation in the Coulomb potential.In particular,one should expect that the metallic domains are attracted by Na+ionic potential,while the Co4+rich insulating domains are repulsed.

A lower boundary for the size L of the magnetic domains can be estimated by taking into account that T c is x-independent and,therefore,is not a?ected by?nite size e?ects.Then at T c the in-plane magnetic correlation length

ξCo4+(T c)?L.By taking forξCo4+(T)the T-dependence expected for a2D triangular antiferromagnet and the in-plane exchange coupling J=2Θ/3?90K,one?nds22that at T c the correlation length is less than3lattice steps.

ξCo4+(T c)can be estimated also by taking a mean?eld expression for T c?J⊥ξ2

Co4+(T c),with J⊥?10?2J?0.9K10

the interplanar exchange coupling among Co4+magnetic moments.One?ndsξCo4+(T c)?5.4lattice steps.Hence,it must be concluded that L?6lattice steps.Although an upper estimate for L cannot be made it must be remarked that one can conclude that the phase separation is not macroscopic,i.e.due to chemical inhomogeneities,but mesoscopic.First of all,it would be rather singular that all data reported in literature on Na x CoO2samples prepared in di?erent ways indicate the same T c and a similar magnitude of speci?c heat peaks6,11.Second,if the insulating magnetic domains where macroscopic the EPR signal intensity should not su?er from microwave irradiation problems. Third,the intensity of23Na and59Co NMR spectra should not be a?ected by thermal cycles if the separation was macroscopic.

Finally,it is important to observe that the phase separation is already present at T?J.This clearly indicates that the antiferromagnetic coupling among Co4+ions cannot be the driving force for this phase separation and that alternative explanations should be envisaged25.

B.Spin dynamics in the metallic domains

The magnetization and NMR data allow to probe the static and dynamic magnetic properties of the metallic regions which do not undergo a phase transition.The total static uniform susceptibility measured with the SQUID is the sum of two termsχ=χCo4++χNF L,the?rst due to the magnetic domains and the second due to the metallic ones. One notices(see Fig.2)thatχCo4+is rather small and can account just for the small shift in the high T absolute value ofχ(x),but not for the sizeable increase on cooling.In fact,also in the x=0.75sample,whereχCo4+is negligible, an increase ofχupon cooling is observed.This increase indicates that strong correlations among the electrons are present and that the metallic regions cannot be treated as a weakly correlated Fermi liquid.Also speci?c heat C measurements show a low temperature upturn in C/T11characteristic of2D electron systems with antiferromagnetic correlations26.Following Moriya et al.Ref.27one would expect a high-T Curie-Weiss behavior both for the uniform static susceptibilityχ(0,0)and in1/T1T.However,if one plots1/χ(0,0)vs.T,withχ(0,0)the one measured with the SQUID one observes a non-linear behavior(see Fig.13).We remark that here there is no sense in subtracting a T-independent Pauli-like contribution since the electrons are strongly correlated.Also if one plots the inverse of the spin contribution to23Na NMR shift?K=Aχ(0,0)/gμB N A one observes a non-linear temperature dependence. Therefore,one has to resort to a form of the generalized spin susceptibility which can describe the non-Fermi-liquid (NFL)behavior.Recently,based on inelastic neutron scattering results,combined with heuristic arguments a response function of two-dimensional(2D)character has been used to describe the NFL behavior in the proximity of a quantum critical point28,29:

χ?1

NF L

(q,ω,T)=k B (T?iω/a)α

Θ′/T|Q|2 the correlation length.In particular a valueα?0.7was observed to justify the behavior of CeCu5.9Au0.1gener-alized susceptibility28,30.In the light of these?ndings one can resort to the above form ofχNF L(q,ω)to analyze magnetization and1/T1results.From Eq.2one?nds that

χNF L(0,0,T)=

c

is the one expected for a NFL and one can verify if,by using the form ofχNF L(q,ω)reported above andα=0.7, the T-dependence of1/T1is reproduced.From Eq.2,by recalling that31

1

2N

k B T A2 q χ′′NF L(q,ωL)

T1=

γ2

aα

1+(qξ)2α ?2

FIG.1:The x-dependence of the c-axes length is reported for the Na x CoO2powder samples investigated in this work and for other samples reported in the literature.

FIG.2:Temperature dependence of the susceptibilityχ=M/H,for H=40Gauss,in Na x CoO2powder samples(x=0.65,0.70 and0.75).The dotted line shows the contribution to the susceptibility from Co4+magnetic moments for x=0.65,as derived from EPR measurements(see the dotted line in Fig.4).In the inset the?eld dependence of the magnetization at280K is shown for the x=0.65sample.

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24details on the speci?c measurements and on the analysis will be published by A.Feher et al.elsewhere.

24See for example T.Takahashi,Y.Maniwa,H.Kawamura and G.Saito,J.Phys.Soc.Jpn.55,1364(1986)

25see for example Intrinsic Multiscale Structure and Dynamics in Complex Electronic Oxides,Eds.A.R.Bishop,S.R.Shenoy and S.Sridhar,World Scienti?c Pub.(2003)

26H.v.L¨o hneysen,M.Sieck,O.Stockert and M.Wa?enschmidt,Physics B223-224,471(1996)

27see T.Moriya,Acta Physica Polonica B34,287(2003)and references therein.

28Q.Si,S.Rabello,K.Ingersent and J.L.Smith,Nature413,804(2001).

29A.Schr¨o der,G.Aeppli,R.Coldea,M.Adams,O.Stockert,H.v.L¨o hneysen,E.Bucher,R.Ramazashvili and P.Coleman, Nature407,351(2000).

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32J.M.Tranquada et al.,Nature375,561(1995)

FIG.3:Derivative of the EPR signal in Na x CoO2for x=0.65,0.70and0.75,at T=293K.The intensity was normalized to the same reference value for all Na contents.In the inset the T-dependence of the linewidth of the EPR absorption signal for x=0.65is reported(the line is a guide to the eye).

FIG.4:The T-dependence of the integrated EPR signal is reported for the x=0.65and x=0.7Na x CoO2powder samples. The solid lines show the behavior expected on the basis of the T-dependence of the static uniform susceptibility and of the microwave skin-depth(see text).The dotted line shows the behavior of the static uniform susceptibility which should be followed if no shielding of the microwaves was present.

FIG.5:23Na central line NMR powder spectrum in Na0.75CoO2,for H=6Tesla.Top The spectrum at35K is reported before(dotted line)and after(solid line)having warmed the sample at280K in helium atmosphere for50minutes.Bottom The spectrum at16K is reported for two di?erent runs performed few weeks apart.

FIG.7:59Co(left)and23Na(right)central line NMR powder spectra in Na0.75CoO2,for H=16kGauss,for T above and below T c.The intensity of23Na signal is reduced to about half of its actual value since the length of theπ/2RF pulse, calibrated on59Co signal,was kept constant while sweeping the frequency.

FIG.8:The paramagnetic shift of23Na central line is plotted as a function of the macroscopic susceptibility,measured with a SQUID magnetometer,for the x=0.75Na x CoO2sample.

FIG.9:The recovery of23Na central line Fourier transform intensity after a saturation RF pulse(y(t)=1?m(t)/m(∞)). The circles show the recovery of the low frequency peak,whereas the squares show the recovery of the high frequency shoulder (see Fig.5.

FIG.10:T-dependence of23Na1/T1in Na0.75CoO2for H=6Tesla,derived from the recovery of the echo amplitude after a saturating RF pulse.In the inset these1/T1values are compared to the ones derived from the recovery of the Fourier transform high-frequency peak(closed circles)or low-frequency shoulder(open circles)(see Fig.5and Fig.9).

FIG.11:T-dependence of the fraction of Co4+ions in Na0.65CoO2,normalized to its value for T?T?.Above T?a marked decrease is evident.The solid line shows the best?t for a gap between localized and itinerant states??0.3eV(see text). In the inset the x-dependence of T?is reported with a schematic view of the portion of the x-T phase diagram where phase separation(PS)is observed.

FIG.12:x-dependence of the fraction of Co4+sites in Na x Co2,normalized to its absolute value for x=0.65(n Co4+(0.65?0.08). The open diamonds show the values estimated from the integrated EPR intensity while the closed circles show the values derived from the estimated entropy due to localized S=1/2spins24.In the inset the T-dependence of the ratio C/T,with C the speci?c heat,is reported.The decrease in the speci?c heat at T c?26K with increasing x is evident.

FIG.13:The inverse of the spin susceptibility measured with a SQUID magnetometer is reported against T(top)and T0.7 bottom for x=0.75.The non-linearity in the former plot and the linearity in the latter one are evident.

FIG.14:T-dependence of59Co(top)and23Na NMR1/T1T in Na0.75CoO2,for H=6Tesla,compared to the theoretical behavior(dotted line)expected for an exponentα=0.7(see text).The theoretical curve for59Co was derived using a hyper?ne coupling constant A=63kOe.

FIG.6:T-dependence of23Na central line NMR shift in Na x CoO2for x=0.65and x=0.75.In the inset the T-dependence of the full width at half intensity of23Na central line is reported.These data were taken when23Na central line was nearly symmetric with no shoulders.

10.80

10.85

10.90

10.95

11.00

11.05

c (A n g s t r o m )

x

0.000

0.001

0.002

0.003

M /H (e m u /m o l e )

T (K)

D e r i v a t i v e o f

E P R S i g n a l (A r b . U n i t s )

H (Gauss)

5

10

15

20

25

30

E P R A r e a (A r b . U n i t s )

T (K)

67.2

67.467.667.868.0

4008001200160067.2

67.4

67.6

67.8

68.0

500

1000

1500

2000

A m p l i t u d e (A r b . U n i t s )

ν (MHz)

T= 16 K

T=35 K

K

?

T (K)

4000

8000

12000

16000

A m p l i t u d e (A r b . U n i t s )

ν (MHz)

0.0006

0.0008

0.0010

0.0012

?K

103

χ (emu/mole)

0.01

0.1

1

y (t )

t (ms)

1/T (s )

T (K)

n (x )/n (x =0.65)

x