Infrared Conductivity and Charge Ordering in NaCoO2

0.29 MB·

by  S. Lupi

NaCoO/2005
Optical conductivity and charge ordering in Na CoO
x 2
S. Lupi, M. Ortolani, L. Baldassarre, P. Calvani
”Coherentia” - INFM and Dipartimento di Fisica,
Universit`a di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185 Roma, Italy
D. Prabhakaran, A. T. Boothroyd
Department of Physics, Oxford University, Oxford, OX1 3PU, United Kingdom
5
(Dated: February 2, 2008)
0
0 The infrared conductivity σ(ω) of NaxCoO2 is studied as a function of doping and temperature
2 for 0.5 ≤x≤ 1. Charge localization in CoO2 layers shows up through a far-infrared peak (FIP) in
n σ(ω),whichcoexists with asmall Drudecontribution. Long-rangeorderingat x= 0.5 isconfirmed
a tocreateafar-infraredgap,inadditiontotheFIP.Athighx,theformationofaSpin-DensityWave
J reportedbelow22KdramaticallyshiftstheFIPtohigherenergywhenxisincommensuratewiththe

1 lattice,indicatinganabruptdeepeningofthelocalizingpotential. Thein-planeE1u phononlifetime
3 isshowntobesensitivetoboth”freezing”andorderingofthemobileNa+ ions. Acomparisonwith
the behavior of the FIP shows that such ”freezing” is not the only origin of charge localization in

] theCoO2 layers.
l
e
- PACSnumbers: 74.25.Gz, 74.72.-h,74.25.Kc
r
t
s
.
t I. INTRODUCTION whereasNaCoO2 shouldbe a narrow-gapbandinsulator
a or a semiconductor. By increasingly adding Na+ vacan-
m
cies from x = 1, the electron ground state changes from
In low-dimensional, correlated electron systems,
- a Spin-Density-Wave (SDW) metal (for 0.75 ≤ x < 1)
d Coulomb, magnetic, and charge-lattice interactions are
n known to produce competitive ground states. For ex- to a Curie-Weiss metal (for x < 0.75). For x < 0.5 the
o metallic state is characterized by a more conventional
ample, in cuprates at low temperature one may observe
c Pauli paramagnetism. The two regions are separated by
either unconventional superconductivity, or charge/spin
[ the above described 0.5 system. Once intercalated with
ordering, or both. The recent discovery[1] of the ”wet”
1 superconductor NaxCoO2·yH2O added a new oxide to water molecules, NCO becomes superconducting below
v about 5 K for 1/4 < x < 1/3. The critical temperature
the listofthose whichexhibit suchintriguingproperties.
6 Theanhydrousparentcompoundofthesuperconduct- Tc[2, 8] of NaxCoO2·yH2O depends on y, also because
4 the intercalated H3O+ ions are likely to provide addi-
7 ing cobaltates, NaxCoO2 (NCO), has a hexagonal crys- tional doping to the CoO2 planes.[8]
1 tal structure (P63/mmc). Its ab planes are formed by
0 CoO2 layersseparatedbyNa+ ions. Suchionsarehighly The low-energy excitations of the CoO2 plane have
5 mobile among three different lattice sites: in Na(1) the beenstudiedbyAngle-resolvedPhotoemission(ARPES)
0 Na+ ion is placed at (0,0,1/4), above the Co site of the and infrared spectroscopy. ARPES detected, at x = 0.7,
/ alargehexagonal,hole-type,Fermisurfaceandastrongly
t CoO2 layers;inNa(2)itoccupiesthe (2/3,1/3,1/4)lat-
a renormalizedquasi-particleband. This latter crossesthe
tice point above the center of the triangular lattice of
m Fermi level in the k-space direction from M to Γ. This
the CoO2 layers; the third site Na(2)’ is similar to the
d- Na(2) one but Na+ is at (2x, x, 1/4). The occupation corresponds to a single-particle hopping rate of 8 meV,
consistently with the absence of quasi-free particles at
n probability of the above sites depends on both x and T.
o For x = 0.5 the Na+ ions are already arranged at room high T.[9]
c temperature in a periodic structure, both along the ab Infrared spectra of NaxCoO2 have been reported by
:
v planeandthecaxis,withNa(1)andNa(2)equallylikely. several groups for different x.[10, 11, 12, 13] Strong
Xi At low T, Na0.5CoO2 becomes a charge-order insulator. electron-phononinteractionandananomalousDrudebe-
It has been suggested that, since the Na+ ions exert a haviorhavebeenfoundinx=0.57singlecrystals,where
ar strong unscreened potential on the CoO2 layers, in the thechargecarriershaveaneffectivemassofabout5elec-
x = 0.5 samples the charge-ordered state in the layers tronmassesandtheirscatteringrateΓ(ω)showsanω3/2
mirrors[2, 3] the periodic structure of the out-of-plane dependence.[10] Similar results have been found for x =
Na+ ions. Na+ order has been observed also for x6= 0.5 0.7, a sample close to a SDW instability.[11] At x = 0.5,
and seems more stable for commensurate doping (x = the charge order shows up in the optical conductivity
1/3; 1/2; 2/3; 3/4; 1).[3, 4]; σ(ω) through the opening of a gap at low temperature
The competition between charge mobility, localiza- around150cm−1.[12,13]Meanwhile,aFar-InfraredPeak
tion, and ordering, in addition to a doping-dependent (FIP)springsupat200cm−1,throughatransferofspec-
magnetic behavior, make the (x,T) phase diagram[5] of tral weight (SW) across the gap.
NaxCoO2 nearly as rich as that of La-Ca manganites.[6] However, an extended infrared study of charge lo-
Theory[7]showsthatCoO2 isaMott-Hubbardinsulator, calization and ordering in the (x,T) phase diagram of
2
NCO has not been published yet. Here we study the
1.0
in-plane infrared conductivity σ(ω) of six single crystals T = 295 K
of NaxCoO2 which cover the range 0.5 ≤ x ≤ 1.0. In 23300
this whole range, the carriers are shown to be close to 0.5 12

strong instabilities leading to localization and ordering.

These phenomena show up through a strong FIP which x=0.50 a
0.0
at 0.5 is associatedwith a far-infraredgap. For x≥ 0.75
the FIP is softer and coexists with a weak Drude term,
0.5
while no gap is detected. A dramatic shift of the FIP to
higher energies is observed, at high incommensurate x,
x=0.57 b
between 30 and 12 K. This should be the effect of the 0.0
spin-density-wavetransition reported to occur in similar
samples at 22 K.[5] Finally, by studying the phonon line
0.5
width,wealsoobtaininterestinginformationontherela-
tion between charge localizationin the CoO2 planes and ω) x=0.75 c
”freezing” of the out-of-plane Na+ ions. R( 0.0
0.5
II. EXPERIMENT AND RESULTS
x=0.85
d
0.0
Single crystals of NaxCoO2 (0.5 ≤x≤ 1.0) have been
grown by the floating-zone method in a four-mirror im-
0.5
age furnace under an oxygen/argon atmosphere at 106
Pa.[14] The reflectivity R(ω) of the six single crystals (x x=0.95 e
= 0.5,0.57,0.75, 0.85,0.95,and 1.0)has been measured 0.0
at quasi-normal incidence (80) between 320 and 8 K for
40 <ω < 20000 cm−1, by using a Michelson interferom- 0.5
eter and with radiationpolarizedalong the CoO2 layers.
The final alignment of the reflectivity set-up has been x=1 f
0.0
2 3 4
performed with the interferometer under vacuum by us- 10 10 10
ingremotelycontrolledmotors,torecoverthemechanical ω (cm-1)
stressoftheopticsduetointerferometerevacuation. The
crystals have been cleaved before each measurement to FIG. 1: In-plane infrared reflectivity of NaxCoO2 for 0.5 ≤
obtain a fresh and shiny surface. The reference was ob- x ≤ 1, at different temperatures. For the sample with x =
tainedby evaporatinga goldorsilverfilm, depending on 0.57, the lowest two temperatures are 90 and 20 K.
the frequency range, onto the sample via a hot filament
placed in front of it.
The reflectivity is shown at different temperatures in 0.95 crystals instead (Figs. 1-a, -d, and -e, respectively),
Fig. 1. That of the x= 0.57 sample has been already high-frequency spectral weight is transferred mainly to
published.[10]Atroomtemperature,R(ω)shows,forany a bump around 400 cm−1. A shallow minimum appears
Na content, an overall metal-like behavior, indicated by in R(ω) around 150 cm−1. At lower frequencies the re-
its increase for decreasing frequencies. A pseudo-plasma flectivity increasesagainto 1. All samplesshow astrong
edgeisalsoevidentaround5000cm−1,foranyxbut0.5, phonon absorption around 590 cm−1. This corresponds
independentlyofthenominaldoping. Asimilareffecthas to a ”layer-sliding” E1u mode related to the hexagonal
beenobservedinhigh-Tccuprates. Therein,the pseudo- P63/mmc structure, which results from the in-plane Co-
plasmaedgecouldhardlybeattributedtofree-carrierab- Ostretchingmotionmixedwithasmallcomponentofthe
sorption,likefortheplasmaedgeofconventionalmetals. Navibrationparalleltotheplane.[17]Theotherinfrared-
It was instead explained by an additional term centered active phonon mode, predicted at about 200 cm−1, is
in the mid-infrared, having both peak frequency and in- not observed. At high energy, the band peaked at 8000
tensity roughly independent of doping.[16] At x = 0.5, cm−1 has been attributed to a charge-transfertransition
on the other hand, (Fig. 1-a), the pseudo-plasma edge betweenthe 2p-Ostatesandthe 3d-Coelectronic states,
is smeared compared to the other samples. Correspond- whilethataround15000cm−1 toa3d-3dtransitionacti-
ingly, a lower value of the reflectivity is observed in the vated by a weak hybridization between 3d-Co and 2p-O
far- and mid-infrared range at all temperatures. states. [10, 11, 12]
As T decreases, R(ω) monotonously increases below The optical conductivity σ(ω) was then obtained
1500 cm−1 in the x = 0.57, 0.75, and 1 samples (Fig. from R(ω) through standard Kramers-Kronig transfor-
1-b, -c, and -f, respectively), through a transfer of spec- mations. R(ω) was extrapolated to zero frequency by
tral weight across that frequency. In the 0.5, 0.85, and using a standard Hagen-Rubens behavior and, at high
3
absorption peak is centered around 200 cm−1 at room
3000
a T = 295 K x=0.50 temperature. Its intensity increases by lowering T down
230
2000 160 to 30 K, whereas its characteristic frequency shifts to
1000 3102 about100cm−1. However,bothat12and8K(thelatter
one is not shown in Fig. 2-c for sake of clarity) spectral
0 b x=0.57 weight is lost below 100 cm−1 and transferred to higher
2000 frequencies. This effect is amplified both in the x = 0.85
and0.95samples(Figs.2-dand-e,respectively). Therein
1000
a strong FIP develops at nearly 100 cm−1 below about
0 160Kandshiftsto200cm−1below30K.Onemaynotice
c x=0.75
that,below22K,aSpin-Density-Wave(SDW)instability
2000
has been reported for 0.7 ≤ x ≤ 0.9. [5, 19]. The FIP
-1m) 1000 peak is separated from the quasi-particle contribution,
c
1 0 clearlyvisibleforthex=0.75and0.95samplesbelow50
−Ω d x=0.85 and 80 cm−1 respectively, by a minimum similar to that
ω) ( 2000 previously reported[20] at low T in a sample with x =
σ( 1000 0.7. Finallythenominallyx=1sample,atvariancewith
thetheoreticalpredictions[7],showsametallicσ(ω)that,
0
e x=0.95 at low frequencies, increases by lowering T. However,
2000 this unexpected behavior will be explained in the next
Section by the possible presence of a few Na defects in
1000
the nominally x = 1 crystal.
0
f x=1
2000
III. DISCUSSION
1000
0 A. Electronic conductivity
0 200 400 600 800
ω (cm-1)
A FIP at finite energy associated with an optical gap,
FIG. 2: Real part of the infrared conductivity of NaxCoO2 as in the present and previously reported [12, 13] σ(ω)
for 0.5 ≤ x ≤ 1, at different temperatures. For the sample ofthe x= 0.5sample, isusually observedinthe infrared
with x= 0.57, thelowest twotemperaturesare 90and 20K. conductivityofcharge-orderedmaterials.[21,22]Accord-
The arrows mark the strong displacement below 30 K of the ing to the Charge-Density-Wave (CDW) theory, [21, 22]
FIP in both samples with high and incommensurate doping the optical gap will measure the energy needed to excite
(x = 0.85, 0.95). one charge from its superlattice state (in NaxCoO2, the
Co3+-Co4+ periodic structure) to E . In turn, a FIP in
F
σ(ω), in the absence of full gap opening, reflects a co-
frequencies, by a Lorentzian fit. An alternative high- existence of localized charges, not necessarily long-range
frequency extrapolation based on the reflectivity[15] of ordered,anditinerantcarriers. Inthiscase,asithappens
NdCoO3 gavethesameresultswithinerrors. Theresults here for the samples with x = 0.75and 0.95,a minimum
are shown in Fig. 2 for all samples, at selected tempera- separating the Drude term from the localization peak
tures. Itexhibitsastrongtemperaturedependenceupto may appear in the optical conductivity.
800 cm−1, while its low-frequency behavior is certainly At x = 0.5 the energy gap here is on the order of
non-monotonouos vs. x. At x = 0.50 (Fig. 2-a) an over- 150 cm−1, to be compared with the 800-1000 cm−1
damped FIP is centered around 400 cm−1 both at 295 foundin the charge-stripestate ofthe layeredperovskite
and 230 K. Below that frequency a flat background is La1.33Sr0.67NiO4. [23, 24] This shows that charge order-
present, indicating incoherent charge transport at high ing in Na0.5CoO2 affects smaller energy regions around
temperature in the CoO2 layers. The peak increases in EF. However, the strong depression of σ(ω) below 150
intensity by decreasing T. Between 230 and 160 K, the cm−1 is consistent with the presence of a gap over the
transferofspectralweightfromthein-gapstatestowards entire Fermi surface. The samples with x = 0.75, 0.85,
thepeakopensagapinthefar-infraredσ(ω)around150 and 0.95 show a metallic dc conductivity down to the
cm−1, in agreement with the results of Refs. [12, 13]. lowest temperatures.[5] However, as already mentioned,
The x = 0.57 sample (Fig. 2-b), the only one exhibiting σ(ω) shows at x = 0.75 (Fig. 2-c) a minimum around
a metal-like behavior, was extensively discussed in Ref. 50 cm−1, which deepens by lowering T. A similar mini-
10. mum (Fig. 2-e) appears around 80 cm−1 in the x = 0.95
On the other hand, for x≥ 0.75,the far-infraredσ(ω) sample. Both these minima separate a quasi-free parti-
looks like a combination of those for the charge-ordered cle term from a FIP at about 100 cm−1, as observed in
0.5 and the metallic 0.57 samples. At x = 0.75 a broad certain cuprates.[25] This FIP is much softer than the
4
corresponding one for the x = 0.5 sample, but shows a
2000
similar temperature dependence. Both at x = 0.75 and x=0.50 x=0.57
fit T = 295 K
0.95 the periodicity of magnetic correlations, measured fit 70
by magnetic neutron scattering, [26, 27] should rule out (÷2) σσ((ωω)) T = 2 9750 K
the occurrence of long-range Co3+-Co4+ order in these 1000
samples. ThereforethesoftFIPcanbeassignedtolocal-
izedcharges,eitherdisorderedorwithshort-rangeorder,
coexisting with itinerant carriers in the CoO2 layers. 0
A clear shift to higher frequencies is observed in the x=0.75 x=0.85
)
1
FIP when T is lowered from 30 K to 12 K (data at 8 K, -m
virtually superimposed to those at 12 K, have not been 1 c
reported): the FIP displaces to about 120, 200, and 200 −Ω 1000
cm−1 for x = 0.75 0.85, and 0.95, respectively. Those ) (
ω
energies areclose to that of the FIP in the 0.5 sample at (
σ
12 K, showing that further ordering takes place for the
0
high-doping materials below 30 K. Between 30 and 12 x=0.95 x=1
K,moreover,a Drude-Lorentzfit to σ(ω) showsthat the
quasi-particletermloosesabout60%ofits SW,bothfor
x= 0.75and0.95. Atx =0.85,instead,the Drudeterm 1000
is not resolved down to 40 cm−1. Since this material
shows a metallic dc conductivity at low T,[2] one may
infer that here the Drude term is weak and squeezed at
very low frequencies. 0
500 500 600
The above strong effects on the low-energy charge dy- ω (cm-1)
namicsatlowT showthat the SDWtransitionatT
SDW
= 22 K [5, 19] further gaps the Fermi surface. From
the FIP shift one can estimate for the charges an addi- FIG. 3: Real part of the infrared conductivity corresponding
tional binding energy ESDW of about 100 cm−1. This to the E1u in-plane phonon at 295 (open symbols) and 70 K
(full symbols). Thin and thick solid lines are Drude-Lorentz
value is comparable with that measured for the SDW of
fitsto data for 295 and 70 K, respectively (see text).
Bechgaard salts (TMTSF)2X (X=PF6, ClO4).[22] One
thus obtains E /k T ∼ 6, a value consistent
SDW B SDW
with a strong-coupling Spin-Density-Wave. Moreover,
0.95. AssumingthattheholesareonlyduetoNadoping,
E is of the same order as both the in-layer and c-
SDW theactualNa+contentofthenominallyx=1samplecan
axis magnetic exchange interactions which characterize
be estimated from the ratio SW(x = 1)/SW(x = 0.95)
theA-typeantiferromagneticstructure.[26,27]Therefore
to be 0.98.
the shift to higher energy ofthe FIP peak, belowT ,
SDW
may be due to a stronginteractionof the chargecarriers
withthein-layerferromagnetically-orderedspins. Onthe
other hand, in the x = 0.5 material, the FIP frequency B. Phonon absorption
monotonously decreases down to 8 K, indicating the ab-
sence of any SDW instability in this system. Therefore Several authors have attributed the origin of charge
the charge ordering showed, above 30 K, by the 0.5 sys- ordering in NaxCoO2 to the out-of-plane ordering of the
tem or the charge localization in the x = 0.75, 0.85 and Na+ ions[2,8]. Indeed,theirpartiallyscreenedCoulomb
0.95samples,mustbeduetoaphysicalmechanismother potentialmayaffectthemobilityofthechargecarriersin
than the SDW instability andmay be correlatedboth to theCoO2layers. The”freezing”oftheNa+ latticebelow
the pinning potential of the out-of-plane Na+ ions and acertaintemperaturewouldfavorapinningofthecharge
to the Hubbard repulsion between charge-carriersin the carriers. One may not expect any direct observation of
CoO2 layers. Na+ ordering in the infrared. However, as discussed in
Finally, σ(ω) at x = 1 unexpectedly does not show the Introduction, the ”layer sliding” E1u phonon mode
an insulating behavior, as instead predicted by band (wellevidentintheσ(ω)ofallsamplesaround590cm−1,
theory,[7]butispoorlymetallicandincreasesbylowering seeFig.2)containsasmallcomponentofthe Na+ vibra-
T (Fig. 2-f). A FIP also appears at the lowest frequen- tion parallel to the plane.[17] Therefore, the lifetime of
cies, between200and160K.These observationsmay be thismodemaybesensitivetoorderingphenomenaatthe
explained with a small number of Na+ vacancies, which Na+ sites.
introduce holes in the otherwise full e1g- ag electronic Figure 3 shows that this is indeed the case. Therein,
bands. Indeed the SW of the x =1 sample, obtained by σ(ω) is reported for the six samples at different T in the
integratingσ(ω)uptothepseudo-plasmaedge(ω=5000 E1u region (500 - 600 cm−1), together with the Drude-
cm−1), is about 40 % of the corresponding SW at x = Lorentz fit above mentioned. This latter provides the
5
monic phonon-phonon interactions and disorder in the
x=0.50 Na+ lattice. The last two terms depend on T. Assum-
40
ingthatdifferentdecaychannelsareindependentofeach
50 other, the phonon line width can be written as
20
0 Γph(T)=Γ0+Γph−ph(T)+ΓNa(T). (1)
0
x=0.57 40 where Γ0 is the contribution of structural disorder, both
50 in the CoO2 layers and in the Na+ lattice, Γph−ph(T) is
20 due to the inharmonic phonon-phonon interaction, and
Γ (T)isrelatedtothermaldisorderanddiffusioninthe
Na
0 Na+ lattice. Also in oxides, Γph−ph(T) is well described
0 by the usual law a(T/Θ)3,[28] where a is a constant and
x=0.75
40 Θ is the Debye temperature. If we assume, according to
diffraction results, that in samples with commensurate
50
20 doping (x =0.5, 0.75 and 1.0) the Na+ ions are already
frozenat roomtemperature, Γ (T) = 0. Therefore,for
) Γ Na
-1m 0 N those samples one has
Γ(cph500 x=0.85 40 a (cm)-1 Γph(T)=Γ0+a(T/Θ)3. (2)
20
Satisfactory fits to Eq. 2, shown by the dashed lines in
the left panels of Fig. 4, can be obtained for all samples
0
0 x=0.95 wthiethsacmomema/eΘns3u=rat3exd1o0p−in7gcbmy−v1aKry−i3n.gAΓs0Θon≃ly3a8n0dKu,s[i2n8g]
40
isnotexpectedtodependappreciablyontheNacontent,
50 one obtains an x-independent a = 15±4 cm−1. The fit
20 also gives Γ0 = 25±5 cm−1 for all samples, but for x =
0.5 where Γ0 = 10±2 cm−1. Such a narrow line is then
0
associatedwiththe long-rangeNa ordercharacteristicof
0 the 0.5 sample. It is also consistent with that extracted
x=1.0
40 from thermal conductivity measurements.[5]
50 As shown in Fig. 4, at the incommensurate x = 0.57,
20 0.85 and 0.95 one observes clear deviations from Eq. 2,
especially above 200 K. In those samples, Na+ thermal
0 disorderprobablygivesacontributiontoΓ (T)alsobe-
Na
-10 low300K.Moreover,onemaynoticethattheincreaseof
0 100 200 300 0 300
Γ below100Kforx=0.57(andprobablyforx=0.85
ph
T (K) and0.95)isduetoFanointeractionbetweenthisphonon
modeandthequasi-particlecontinuum,asdiscussedina
previous paper.[10] Since Γ (T) is not known, we can-
FIG. 4: Temperature dependence of the E1u phonon broad- Na
ening Γph(T) (left panels, full symbols), and its fit (dashed not predict the temperature behavior of Γph(T) in the
incommensurate systems. However, therein a freezing
lines) to Eq. 2 (see text). In the right panels an estimate of
ΓNa(T)(seeEq.1)tothephononbroadeningΓph(T)isshown temperatureforNa+ diffusioncanbedeterminedbysub-
for all samples. Herethe solid line is just a guide to theeye. tractingfromthe experimentalΓph(T)thatgivenby Eq.
2, which holds for Γ (T) = 0 (commensurate doping).
Na
The resulting Γ (T) is shown by open symbols in the
Na
phonon parameters: intensity S2 , frequency ω and left panels of Fig. 4, where the solid line is only a guide
ph ph
broadening Γ . The results are rather accurate as the to the eye. Therein we also show the fit residual, which
ph
vibrational absorption, at any x, is well distinguished for commensurate samples is obviously zero. In Fig. 4
from the electronic background. Γ (T) vanishes around 150 K for all samples with in-
Na
TheresultinglinewidthΓ (T)isshowninFig.4(left commensurate Na content. Such a freezing temperature
ph
panels)asafunctionofT andx. Onemaynoticethatthe is in qualitative agreementwith the value (200 K) found
T dependence ofΓ (T)is strongerforthe incommensu- by diffraction measurements in polycrystalline samples
ph
rate doping levels x = 0.57, 0.85 and 0.95 than for its with x> 0.7.[30]
commensurate values. Several effects may influence the The present data also provide information on the in-
phonon broadening: disorder in the CoO2 layers, inhar- terplay between the above detected Na+ ”freezing” and
6
the signatures of charge localization in the infrared con- ergy for exciting one charge out of the Co3+-Co4+ or-
ductivity. The FIPalreadypresentatroomtemperature dered ground state. At x = 0.75, 0.85 and 0.95, the gap
forcommensuratedoping(x = 0.5andx=0.75)develops is partially filled by Drude conductivity which is sepa-
between 230 and 160 K in the incommensurate systems rated by a minimum from a far-infrared peak, centered
with x = 0.85 and 0.95. In the same samples and tem- at about 100 cm−1 at 30 K. This FIP provides evidence
perature range, as shown above, the phonon line width that charge localization (or short-range charge order),
has an anomalous T-dependence due to increasing local- competeswithtransport,sincemetallicconductionisob-
ization of the Na+ ions. On the other hand, the FIP is servedatlowT alsoforx>0.5. Moreover,the magnetic
not observed at all when the incommensurate doping is ordering reported in the literature below 22 K and at-
0.57, even if Na+ ions freeze at the same temperature tributed to a Spin-Density-Wave instability induces, for
as in the other two samples. It seems then that charge incommensuratex=0.85and0.95,astrongrenormaliza-
localization - and possibly short-range charge order - is tion of the charge dynamics in the CoO2 planes. Indeed
driven by the freezing of out-of-plane Na+ when the Na the far-infrared peak hardens dramatically below 30 K
concentrationishighandthechargesdensityislow(x= (by about 100cm−1) pointing towardsa strong coupling
0.85 and 0.95). This mechanism becomes much less effi- of the charge and spin degrees of freedom. In contrast
cient when the Na+ concentration is low and the charge with these results, the x = 0.57 sample shows a metallic
density is high (x = 0.57). conductionateachT,describedby ananomalous-Drude
behavior in the far-infrared σ(ω).
We have also shown that a correlation exists between
IV. CONCLUSION the far-infraredpeak and the out-of-plane localizationof
Na+ ions, monitored by the E1u infrared-active phonon
In conclusion, we have carried out a systematic study lifetime. In particular, the temperature where the FIP
of the optical conductivity of the NaxCoO2 system in develops in the infrared conductivity is in reasonable
the x ≥ 0.5 part of its phase diagram. It is confirmed agreement with the Na+ freezing temperature, as ex-
that charge ordering opens, at x = 0.5, a far-infrared tracted from the phonon line width. This mechanism,
gap about 150 cm−1 wide. As a result, a peak appears however,appearsto be effective only for low chargeden-
around 200 cm−1, which corresponds to the lowest en- sity and high Na+ concentration.
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