Electronic texture of the thermoelectric oxide Na0.75CoO2

0.61 MB·

by  M. -H. Julien

Electronic texture of the thermoelectric oxide Na CoO
0.75 2
M.-H. Julien1∗, C. de Vaulx1, H. Mayaffre1, C. Berthier1,2, M. Horvati´c2, V. Simonet3,
J. Wooldridge4, G. Balakrishnan4, M.R. Lees4, D.P. Chen5, C.T. Lin5, P. Lejay3
1Laboratoire de Spectrom´etrie Physique, UMR5588 CNRS and
Universit´e J. Fourier - Grenoble, 38402 Saint Martin d’H`eres, France
2Grenoble High Magnetic Field Laboratory, CNRS, BP166, 38042 Grenoble, France
3Institut N´eel, CNRS/UJF, BP166, 38042 Grenoble Cedex 9, France
4Department of Physics, University of Warwick, Coventry CV4 7AL, UK and
5Max-Planck-Institut for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
8 From59Coand23NaNMR,wedemonstratetheimpactoftheNa+vacancyorderingonthecobalt
0
electronic states in Na0.75CoO2: at long time scales, thereis neither a disproportionation into 75%
0 Co3+ and 25% Co4+ states, nor a mixed-valence metal with a uniform Co3.25+ state. Instead, the
2
system adopts an intermediate configuration in which 30 % of the lattice sites form an ordered
n patternoflocalized Co3+ states. Above180K,ananomalousmobilityofspecificNa+ sitesisfound
a to coexist with this electronic texture, suggesting that the formation of the latter may contribute
J to stabilizing the Na+ ordering. Control of the ion doping in these materials thus appears to be

6 crucial for fine-tuningof their thermoelectric properties.
2

] Complexity, which underlies many physical properties separately. For the magnetic field Hkc (i.e. θ = 0◦),
l
e of correlated electron systems [1], often results from the a typical spectrum (Fig. 1) shows three distinct sites.
- spatial modulation of electronic states. Besides the ten- These are labeled Co1, Co2 and Co3 in increasing or-
r
t dency to form ordered patterns (such as stripes in high der of their magnetic hyperfine shift K =Korb+Kspin.
s
. temperature superconductors), electrostatic interactions The most interesting differences between these sites lie
t
a with dopant ions are increasingly recognized as a source in both (i) the value of the on-site orbital contribution
m of electronic inhomogeneity [2, 3]. Because the sodium Korb, which is proportional to the (on-site) Van-Vleck
- ions in Na CoO are mobile and can order, these bat- susceptibility, and (ii) the value of Kspin (”Knight shift”
d x 2
terymaterialsareemergingasexceptionalcandidatesfor in metals), which for a given nuclear site i is given by:
n
o exploring such phenomena [4]. One of the most impor-
[c ttaringtuiqnugespthioynsiscarlegparordpienrgtietshiosfsmysetteamllicisphwahseetshaetrxth>∼e0in.6- Kαspαi,ni =AααχsαgpαµinB(i) +XBχsαgpαµinB(j), (1)
j
1 are related to a coupling between the electronic degrees
v of freedom and the spatial distribution of Na+ vacan- where A is the on-site hyperfine coupling, χspin is the
5 cies [4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. On the one hand,
local spin susceptibility and j stands for the nearest Co
9
long range sodium vacancy ordering has been reported
0 neighbors to which the nucleus i may be coupled via a
but the ordering pattern appears to be controversial for
4 transferred hyperfine interaction B. α = c,ab is the di-
1. the moststudied concentrationx=0.75[13, 14, 15]. On rection of the principal axis of A and χ tensors, along
the other hand, electronic ’textures’, which may be de-
0 whichH isaligned. Equation1makesclearthat,ifB 6=0
8 fined as both the disproportionation of electronic (spin, and χspin(i) 6= χspin(j), the number of NMR sites with
0 charge and possibly orbital) states and the spatial cor- differentKspin(i)valuesmaybegreaterthanthenumber
: relation between these states, are much less experimen-
v of different magnetic sites (i.e. of different χ(i) values).
i tally accessible and, not surprisingly, no electronic pat- Thus, the three 59Co NMR sites do not necessarily cor-
X
tern has yet been resolved. Nevertheless, the observa-
respond to three distinct electronic densities.
r tion of two, or more, magnetically distinct 59Co sites
a Additional information on the cobalt sites is provided
at the time scale (∼10−6 s) of nuclear magnetic res-
by the anisotropy and the temperature (T) dependence
onance (NMR) [16, 17, 18, 19, 20, 21] demonstrates
of K. H||ab spectra are too poorly resolved to directly
that some electronic disproportionationoccurs in metal-
extract the in-plane anisotropy and the K values for all
lic Na CoO with x ∼0.7. However, because of the dif-
x 2 sites. Nevertheless, neglecting the in-plane anisotropy,
ficulty in accurately determining the Na content x, and
K can be extracted from a combined knowledge of the
ab
the sensitivity of Na order to small variations in x or to ◦ ◦
line positions for θ = 54.7 and θ = 0 , which define
thesynthesismethod,acoherentpictureoftheelectronic
K = 1(2K +K ) and K respectively. The values of
states has yet to emerge. iso 3 ab c c
KorbandoftheeffectivetotalhyperfinefieldAhf foreach
We have obtained reproducible NMR spectra of 59Co sitearethenextractedfromlinearfitsof59Kab,c vs.23K
nuclei in high quality single crystals of Na CoO , data, as described in [19].
0.75 2
grown in three different groups [22, 23]. Our compre- For the Co1 site, the values of the orbital shift
hensive characterizationof the crystals will be published (Korb=2.36%, Korb = 2.35%) are almost the same as
ab c
2
acterizedby muchlargerandanisotropichyperfine fields
values (Ahf = 64 and 154 kG/µ and Ahf = 34.5 and
59 ab B c
Co data =0(cid:176) (H||c) 40 kG/µB, respectively), showing that the spin density
simulated
Co1+Co2+Co3 f=146.44 MHz is much larger. The difference between these sites and
Co1 also manifests itself in the much larger Korb values
ab
(a)
(2.55 % and 2.60 %, respectively). However, the phe-
* * * nomenological link between Korb anisotropy and the Co
Co1 valence proposed in Ref. [19] appears not to hold here:
Co2 (b) K values are similar and not strongly anisotropic for
Co3 orb
Co2 and Co3 (Korb=2.37 % and 2.39 %, respectively).
13.9 14.1 14.3 14.5 c
Magnetic Field [T] Thus, while the shift difference between the Co2 and
Co3mostlikelyarisesfromdifferentelectrondensitiesat
Co2 =54.7(cid:176) these sites, we cannot rule out the possibility that part
Co3 diff. Co1 f=82.0 MHz of the difference is due to distinct transferred hyperfine

fieldsfromtheirConearestneighbors. IfpresentatCo3+
=5 s (c)
sites, the transferred interaction should affect magnetic
7.8 8.0
=60 s sites as well.
7.7 7.8 7.9 8.0 8.1
The distinction between magnetic and non magnetic
Magnetic Field [T]
sites is even more striking in the spin-lattice relaxation
rates T−1. (T T)−1 is constant at the Co3+ (Co1) sites
FIG. 1: (a) Spectrum for Hkc (Circles) and T = 30 K, with (Fig.2c1). At m1agneticsites, onthe other hand, (T T)−1
the total simulation (line) resulting from the Co1, Co2 and 1
has a clear T dependence which can be ascribed to a
Co3 sites displayed in panel (b). Each site consists of seven
lines split by the quadrupole frequency 59ν . ν =0.57 MHz Curie-Weisslaw,typicalofspin-fluctuationsystems. Be-
c c
for Co1 is close to the value (0.68 MHz) for Co3+ sites in low∼50K,criticalfluctuationsaboveTM enhanceT1−1,
Na1CoO2 [24],andisdistinctlylowerthanνc =1.22MHzfor with a progressive loss of Co2 and Co3 signals.
◦
Co2and1.14MHzforCo3. (c)Spectrumforθ=54.7 where
Although a snapshot of Na CoO would certainly
0.75 2
thequadrupolesplittingvanishes,andT=50K.Co2andCo3 show 75% of Co3+ and 25% of Co4+ states, this de-
linesaremuchbroaderandmoreshiftedthanforHkc. These
scription evidently does not apply at long time scales:
two lines have a much shorter spin-spin relaxation time T2
than the Co1 line, so they can be isolated from the latter by Firstly, the characteristics of the magnetic sites are dif-
subtractingspectratakenattwodifferentvaluesoftheNMR ferentfromthoseofthehighlyoxidizedcobalt(nominally
pulse spacing τ (Inset). Note that, for θ = 54.7◦, the Co1 Co4+) measured in the x = 0 member CoO [26]. Sec-
2
lineisactually splitintoCo1a andCo1b sublines. Thiseffect ondly,integrationoftheNMRsignalintensity(corrected
arisesfromeitherin-plane(hyperfineormagnetic)anisotropy
for T decay) over the whole spectrum shows that the
2
or from differences in the Co nearest neighbors at the Co1 Co3+ sites represent only 30±4 % of the total number
sites. For simplicity, we report here only the properties of
of sites throughout the T range. The magnitude of this
the more intense, less shifted, Co1a line (the maximum Kiso
difference between Co1a and Co1b is 5 to 10 times smaller number, as well as its reproducibility in different sam-
thanthedifferencebetweentheCo1andtheCo2orCo3sites). ples, demonstrates that pinning by extrinsic impurities
or defects cannot explain the Co3+ localization. There-
fore,longrangemagneticorderbelow22Kdoesnotarise
those reported for the Co3+ site in Na CoO [24, 25]. from a minority of localized magnetic moments, as often
1 2
As argued in [19, 21], the isotropic character of K is assumed: The spin density is not concentrated on 25%
orb
also consistent with the filled t shell of the Co3+ ion. of the lattice sites but is spread over ∼70% of them.
2g
Clearly,the Co1site correspondsto non-magnetic Co3+. A knowledge of the local magnetization in the cobalt
This assignment may, at first sight, appear to be in con- planesallowsustocomputethe hyperfinefieldattheNa
tradiction with Kspin(Co1)6=0. We cannot rule out the sites. Our computer simulations, an example of which
possibility that the effective valence of the Co1 ion is is displayed in Fig. 3c, show that any random distribu-
slightlyhigherthan+3,i.e. t2g holeshaveasmallbutfi- tion of magnetic and non magnetic Co sites produces a
niteprobabilityofresidingontheCo1sites. However,the very large number of magnetically distinct 23Na NMR
quasi-isotropic Ahf = 28 kG/µB, as well as the different sites, leading to a broad, featureless, spectrum. This
T1 vs. T behavior (see later) for this site would suggest is because the 23Na nuclei are coupled to a large num-
that most of the hyperfine field may be transferred from ber of Co sites: 2 (6) first neighbors and 12 (14) second
its magnetic nearest neighbors (i.e. the second term of neighborsfortheNa(1)andtheNa(2)sites,respectively.
equation 1). Thus, it must be concluded that there are These simulations are at odds with the central transi-
localizedsitesinthecobaltplaneswhicharepermanently tions of the 23Na spectrum at T = 59 K, which con-
occupied by six t2g electrons. sists of only three clearly separated main resonances, in
The Co2 and Co3 sites, on the other hand, are char- which six lines with different K values (and negligible
3
59Co
23Na
59Co
FIG.3: (a)Centrallines(1/2↔-1/2transitions)ofthespec-
23Na trumintwodifferentsinglecrystalsatT =30K.(b)Fittosix
lines, having a similar quadrupole frequency 23ν ≃1.9 MHz
c
to within ± 10 %. (c) Simulated 23Na NMR spectrum (line)
obtained by a Gaussian broadening of the histogram com-
puted for randomly distributed magnetic and non-magnetic
Co sites. Assuming two different types of magnetic sites fur-
therincreasesthenumberoflines. Hyperfinecouplingstofirst
neighbors a and to second neighbors b = a/2 were assumed
to beidentical for theNa(1) and Na(2) sites.
FIG. 2: (a) 59K for the Co1, Co2 and Co3 sites, in two field
orientations. The grey area represents the phase with mag-
netic order below T = 22 K. (b) 23K for θ = 0◦. The
M DFT calculationsoftheNa/Copatternsandofthe23Na
symbol colors refer to lines in Fig. 3b. The vertical dashed
line denotes the temperature of 180 K, where the 23Na line shifts, which are underway.
splits. (c) (59T1T)−1 for the Co1 and the Co2 plus Co3 sig- Surprisingly,the23Naspectrumcollapsesintotwovery
nals (Co2 and Co3 central lines cannot be separated in T1 close lines above 180 K (see shifts in Fig. 2b), as if the
measurements performed on central lines with Hkc). Con- cobaltplaneswereelectronicallyhomogeneous. However,
tinuous lines are fit results: (T1T)−1 = 4.5 s−1K−1 (black), the observationofdistinctCo1,Co2andCo3sites above
(T1T)−1 = 8+800/(T +35) s−1K−1 (red). Below ∼ 50 K,
critical fluctuations above T enhance T−1, with a progres- 180 K tells us that this is not the case. Thus, the aver-
sivelossofCo2andCo3signaMls. (d)Corre1spondingT−1data. agingofthe hyperfinefields mustbe due toNa+ ionsoc-
1
(e)23T−1 dataforthethreemain23Nalines(calibratedfrom cupying several distinct sites within the NMR time win-
1
the 23Na resonance in aqueous NaCl solution). The symbol dow. The Na+ jump frequency has to be largerthan the
colors refer to NMR lines in Fig. 3b. All T1 values were ob- frequency separating the NMR lines with a fine struc-
tained by fitting the recovery curves to standard expressions ture (∼10 kHz), but smaller than the typical frequency
for magnetic relaxation.
of faster probes, such as X-ray diffraction (XRD), for
which Na+ order is already well-defined at ∼250 K [15].
This direct observation of slow Na motion with localiza-
23ν differences)arediscernible(four ofthem arelabeled tion around 180 K rationalizes the anomalies observed
c
asNa(i,...,iv)onFig.3b). Thesmallnumberofhyperfine in the T dependence of magnetic [28], lattice [15], and
fields at the Na sites demonstrates that the different Co possibly charge ([29] and references therein), properties
states are spatially ordered [27]. At the same time, the of this material.
specific spectral shape imposes an unprecedented set of SincetheNMRtimescaleisbasicallyidenticalfor59Co
constraints on any model of the Co and Na+ patterns in and 23Na, the observation that Co electronic differenti-
Na CoO . However, computational uncertainties con- ation coexists above 180 K with Na motional averaging
0.75 2
cerning the 3D stacking, which is crucial for 23Na and is striking. This implies either that electronic dispropor-
59CoNMRspectra,preventusfromdeterminingwhether tionation at the Co sites is completely unrelated to the
the in-plane pattern depicted in Fig. 4 [13], or another Na positions, which would contradict theoretical expec-
pattern,is correct. The problemshouldbe solvedby full tations [9, 10, 11, 13] or that excursions of the Na+ ions
4
lingiondopinginthesematerials(eitherbydilutedoping
ofionsofdifferentmobilityorviananoscaleelectrochem-
ical manipulations on Na CoO surfaces [32]) should re-
x 2
sult in an improved thermoelectric performance. More
generally, control of ionic textures in battery materials
appears to be an exciting route for tailoring electronic
properties.
This work was supported by the ANR NEMSICOM
and by the IPMC Grenoble.
FIG. 4: Na+ ordering pattern proposed for x = 0.75 in
Ref.[13]. SodiumionsatNa(1)positions(red)mayhoponto
[*] Correspondence to: [email protected]
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1
180 K follow the same trends. T−1 for this line is ap- [14] H.W.Zandbergenet al.,Phys.Rev.B70,024101(2004).
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ticipateanomalousphononmodes,possiblyanalogousto
167601 (2004), where Co3+/4+ states were assumed.
rattling phonons of thermoelectric skutterudites and su-
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x 2
essentialingredientsofthe thermoelectriceffect, control- [32] O.Schneegansetal.,J.Am.Chem.Soc.129,7482(2007).