Microsoft Word - preprint.doc
April 9, 2007, submitted to J. Phys. Soc. Jpn. 
Layered sodium cobaltate NaxCoO2
1) provides us with a 
fascinating playground to study the physics of strongly 
correlated electrons on the frustrated triangular lattice in a 
wide range of band filling.  Recent two important 
discoveries have accelerated the research of NaxCoO2: one 
is an unusually large thermoelectric power for x ~ 2/32) and 
the other is superconductivity below 4.5 K in a hydrated 
compound with x ~ 1/3.3)  Particularly, a lot of studies have 
focused on the hydrated superconductor to clarify the 
mechanism of the superconductivity and to understand 
underlying electronic states realized in the triangular lattice.  
In spite of extensive research, however, there still remain 
some controversial issues possibly resulting from difficulty 
in the chemistry of the compounds that put obstacles in the 
way of obtaining high-quality samples.4, 5)   
The electronic phase diagram of NaxCoO2 as a function 
of x has been proposed by several groups.  Foo et al. gave a 
typical one where a charge-ordered magnetic insulator exists 
at x = 0.5 with a "paramagnetic (PM) metal" on the left (x < 
0.5) and a "Curie-Weiss (CW) metal" on the right (x > 
0.5).6)  In contrast, Yokoi et al. found that the boundary 
between the two metals is located approximately at x = 0.6.7)  
The reason for this discrepancy is not known. Moreover, the 
origin of the change in metallic character has not yet been 
interpreted in a clear manner.  On the charge-ordered 
insulator at x = 0.5, it is known that the ordering of Na ions, 
which is already present at high temperature, triggers a 
magnetic as well as a metal-insulator transitions at low 
temperatures.6-8) 
The electronic states of NaxCoO2 near the Fermi level 
come from the Co d derived t2g state that splits into an a1g 
singlet and an e'g doublet.  These bands are filled 
progressively with x, because one Na+ ion donates one 
electron to the CoO2 layer.  According to band structure 
calculations,9-14) the a1g band always crosses the Fermi level, 
irrespective of band filling, which gives a large circular 
(cylindrical) Fermi surface (FS) around the Γ point in the 
Brillouin zone.  In addition, two important features on the 
FS are found in the local-density approximation 
calculations: one is a set of small hole pockets originating 
from the e'g band near the K points, which are expected to 
appear at low fillings such as x = 0.3.  The other is a small 
concentric electron FS around Γ coming from a dip in the 
band energy of the a1g state, which may appear at high 
fillings such as x = 0.7.  However, the absence of the latter 
was suggested for any doping levels by more sophisticated 
band structure calculations incorporating spin polarizations 
or the on-site Coulomb interaction U.11)  Experimentally, 
angle-resolved photoemission spectroscopy (ARPES) study 
on Na0.7CoO2 observed only a large circular FS around Γ 
and failed to detect the other FSs.15) Recently, Mochizuki 
and Ogata pointed out in their tight binding model that band 
dispersions and FS topology change sensitively with the 
thickness of the CoO2 layer:
16, 17)  the hole pockets near K 
would appear for a thinner CoO2 layer, while the small 
electron pocket around Γ would be present for a thicker 
CoO2 layer.  Thus, the current status is miles away from a 
complete understanding of the basic electronic structures of 
NaxCoO2. 
In this letter, we study systematically the transport and 
thermodynamic properties of NaxCoO2 using a series of 
polycrystalline samples.  The key point of the present study 
is a novel method used to prepare samples: most of samples 
studied so far were obtained by a soft-chemistry method at 
ambient temperature,3) which might cause an 
inhomogeneous distribution of Na ions or otherwise lead to 
Precise Control of Band Filling in NaxCoO2 
Daisuke YOSHIZUMI, Yuji MURAOKA**, Yoshihiko OKAMOTO, Yoko KIUCHI, 
Jun-Ichi YAMAURA, Masahito MOCHIZUKI1, ***, Masao OGATA2 and Zenji HIROI* 
Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581 
1RIKEN, Hirosawa, Wako, Saitama 351-0198 
2Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033 
Electronic properties of the sodium cobaltate NaxCoO2 are systematically studied through a precise 
control of band filling.  Resistivity, magnetic susceptibility and specific heat measurements are carried 
out on a series of high-quality polycrystalline samples prepared at 200°C with Na content in a wide 
range of 0.35 ≤ x ≤ 0.70.  It is found that dramatic changes in electronic properties take place at a critical 
Na concentration x* that lies between 0.58 and 0.59, which separates a Pauli paramagnetic and a Curie-
Weiss metals.  It is suggested that at x* the Fermi level touches the bottom of the a1g band at the Γ point, 
leading to a crucial change in the density of states across x* and the emergence of a small electron pocket 
around the Γ point for x > x*. 
KEYWORDS:  sodium cobaltate, resistivity, magnetic susceptibility, specific heat, Sommerfeld 
coefficient, Fermi surface, band filling 
*E-mail: hiroi@issp.u-tokyo.ac.jp 
**Present address: The Graduate School of Natural Science and Technology, Okayama University, 
1-1, Naka-3, Tsushima, Okayama 700-8530 
***Present address: Tokura Multiferroics Project, ERATO, Japan Science and Technology Agency (JST) 
a strong tendency for Na ordering at certain fractional 
compositions such as x = 0.5.  Particularly, the Na ordering 
strongly influences the electronic state of the (CoO2)
x- layer 
and may mask the intrinsic features.  We adopted 
alternatively a solid-state reaction at higher temperatures 
starting from two end members of Na0.35CoO2 and 
Na0.70CoO2 and succeeded in controlling x on a scale of 0.01.  
Moreover, since the high-temperature reaction favoured 
disordering of Na ions, more intrinsic properties of the 
(CoO2)
x- layer have been clarified.   
We prepared a series of polycrystalline samples of 
NaxCoO2 by a solid-state reaction of Na0.35CoO2 and 
Na0.70CoO2.  First, powders of Na0.70CoO2 were synthesized 
by a reaction of stoichiometric amounts of Na2CO3 and 
Co3O4 in air at 860°C.  Sodium deintercalation was then 
carried out in a 1.0 M Br2 solution in acetnitrile to obtain 
powders of Na0.35CoO2.  The Na content was determined by 
the inductively coupled plasma-atomic emission 
spectroscopy (ICP) method.  A dozen of samples with 
intermediate compositions were prepared by reacting the 
two powders of Na0.35CoO2 and Na0.70CoO2 in an 
appropriate ratio in a sealed quartz tube at 200°C for 24 
hours, followed by slow cooling to room temperature.  The 
Na content of the products was also examined by the ICP 
analysis.  The phase purity was confirmed by means of 
powder x-ray diffraction.  More detail on the sample 
preparation and characterization will be reported 
elsewhere.18)  Resistivity and specific heat were measured in 
a Quantum Design PPMS system, and magnetic 
susceptibility measurements were performed in a Quantum 
Design MPMS system. 
Figure 1 shows the systematic variation of resistivity ρ 
with x.  For clarity, each set of data is divided by the value 
at 250 K.  The ρ of x = 0.50 exhibits a smooth, 
semiconductor-like increase at low temperature with no 
anomalies for a metal-insulator transition, in contrast to the 
previous report where a soft-chemically prepared sample of 
x = 0.50 exhibits a sharp rise in ρ below 53 K.6, 7)  We 
examined our sample by electron diffraction and found that 
a superstructure coming from Na ordering was almost 
absent.18)  We think that this semiconducting behavior is due 
to a partial ordering of Na ions, because even at room 
temperature the Na ions tend to align.18)  As x increases 
from 0.50, such a semiconducting increase in ρ is 
progressively suppressed, and finally a metallic T 
dependence appears above 0.55.  Nevertheless, a small 
upturn is observed below 20 K, as shown in the inset to Fig. 
1, which may be ascribed to weak localization due to a 
random electrostatic potential from disordered Na 
distributions. 
Compared with the T dependence in ρ for x ≤ 0.58, which 
is always concave-downward, those of x ≥ 0.59 are 
apparently dissimilar; almost T linear for x = 0.59 and 
concave-upward for x = 0.66 and 0.70.  The last one shows a 
steep decrease below 30 K, which is similar as reported 
previously for x = 0.75.6)  Therefore, the  T dependence of 
ρ changes significantly across x = 0.58 ~ 0.59. 
Another related change is found in the evolution of 
magnetic susceptibility χ, as shown in Fig. 2.  The χ for x ≤ 
0.58 shown in the left panel is relatively small in magnitude 
and weakly T dependent, while, in distinct contrast, the χ for 
x ≥ 0.59 is large in magnitude and shows a characteristic 
CW divergence that is progressively enhanced with 
increasing x.  Hence, a substantial change in magnetism 
must occur across a critical Na concentration x* between 
0.58 and 0.59, accurately corresponding to the above results 
from resistivity. 
Looking in more detail, the χ of x = 0.35 decreases 
gradually with decreasing T from 300 K, exhibits a 
minimum at 120 K and then shows a CW divergence at low 
Fig. 1.  Evolution of the temperature dependence of 
resistivity ρ normalized to the value at 250 K for 0.50 ≤ 
x ≤ 0.58 (left) and 0.59 ≤ x ≤ 0.70 (right). 
Fig. 2.  Magnetic susceptibility χ measured on heating in a 
magnetic field of 10 kOe for  0.35 ≤ x ≤ 0.58 (left) and 
0.59 ≤ x ≤ 0.70 (right).  Note the difference in the 
vertical scale. 
temperature.  This low-temperature CW component may be 
due to a minor portion of spins that come from defects or 
impurities and are noninteracting with majority spins. The 
positive slope above 120 K suggests the existence of a peak 
in χ at a higher temperature.  In fact, the 0.50 and 0.52 
samples seem to show a broad maximum near 300 K.  
Moreover, a broad peak is clearly observed at around 150 K 
for x = 0.56.  The peak is possibly further shifted to a lower 
T for x = 0.58 and becomes obscure.  This broad peak 
indicates the development of antiferromagnetic (AF) short-
range order on cooling.  Then, its systematic shift to lower 
temperatures implies that the characteristic energy of AF 
spin fluctuations or effective superexchange Jeff decreases 
with increasing x.  Since the density of spins (1-x) decreases 
as x increases, we expect that Jeff between nearest-neighbour 
spins also decreases, consistent with the observed behavior 
in χ.  For x ≥ 0.59, on the other hand, the Weiss temperature 
deduced from fitting the data to the CW law χ = C/(T - Θ) is 
always negative in sign (AF) and gradually increases from -
156 K (x = 0.59) to -99 K (x = 0.70).  This fact indicates that 
AF fluctuations are suppressed or additional ferromagnetic 
interactions are enhanced with increasing x. 
In order to demonstrate more explicitly the dramatic 
changes across x*, the ρ and χ data of x = 0.58 and 0.59 are 
compared in Fig. 3.  The ρ of 0.58 is proportional to T2 in a 
wide T range below 70 K, as shown in the inset, provided 
that the low-temperature upturn is ignored.  Such T2 
behavior is what one expects generally  for a strongly 
correlated electron system.  In contrast, the T dependence in 
ρ of 0.59 is rather unusual, showing an almost linear 
variation in a similarly wide T range below 80 K.  Hence, 
there must be a substantial difference in the scattering 
mechanism of carriers between the two samples. 
On the other hand, it is apparent from Fig. 3 that χ is 
enhanced enormously from 0.58 to 0.59.  Moreover, the T 
dependence above 50 K changes from linear to CW-like.  
This T linear behavior for 0.58 may be accidental as a few 
contributions of different origins coexist. The unusual T-
linear dependence in ρ for 0.59 must be related to the 
appearance of the CW component in χ: additional magnetic 
scattering can be the source. 
To evaluate the change in the T dependence of χ, the 
slope at 100 K is plotted in Fig. 4, following the previous 
analysis done by Yokoi et al.7)  The slope is close to zero or 
takes small negative values for x ≤ 0.58, while it decreases 
almost discontinuously to a relatively large negative value at 
0.59, followed by a further decrease with increasing x.   
Another experimental evidence to support the existence 
of a critical x value has been obtained from specific heat 
measurements.  The x dependence of the Sommerfeld 
coefficient γ determined from the intercept of the C/T versus 
T2 plot is shown in Fig. 4.  Obviously, there is a change in γ  
at x*: γ increases slightly with x for x ≤ 0.58 and suddenly 
rises at x* by 17 %, from 16.8 mJ K-2 mol-1 for 0.58 to 19.7 
mJ K-2 mol-1 for 0.59.  Then, it increases rapidly to be 
saturated at 31.5 mJ K-2 mol-1 for x = 0.70.  Note that the γ 
of 0.50 is finite because of the metallic nature of our sample 
in the absence of charge order.  Since γ is proportional to the 
density of states (DOS), we conclude that the DOS at the 
Fermi level suddenly increases above x*. 
All the above results indicate that the electronic structure 
of NaxCoO2 does not change smoothly with x, but there is a 
well-defined boundary at x*.  It is found that the critical 
concentration lies between 0.58 and 0.59, not at 0.5 as 
reported by Foo et al.,6) but close to 0.60 as reported by 
Fig. 4. x dependences of the slope in χ at 100 K (top) and 
the Sommerfeld coefficient γ (bottom).  Crosses in the 
bottom panel represent the data reported by Yokoi et 
al.7)  Dotted lines serve as guides to the eye. 
Fig. 3.  Comparisons of resistivity (left) and magnetic 
susceptibility (right) between x = 0.58 and 0.59.  Inset in 
the left panel shows a ρ - ρ0 versus T
2 plot for 0.58, 
where ρ0 is the residual resistivity and is 1.83 mΩ cm.  
Inset in the right panel shows the T dependence of 
inverse χ for 0.59. 
Yokoi et al.7)  The sharp boundary breaks the phase diagram 
into two regions: a Pauli paramagnetic metal with a 
relatively small DOS for x < x*and a CW metal with an 
enhanced DOS for x > x* (Fig. 5).  A main reason why we 
observed such sharp changes in properties at x* in the 
present study may be ascribed to the high quality of our 
samples prepared at high temperature as well as the reduced 
influence of the Na ordering. 
On the basis of these experimental lines of evidence, we 
are now ready to consider what is going on with x in 
NaxCoO2 in terms of band structures.  As x decides filling in 
the t2g band, it is reasonable to assume that the band 
structure changes at a certain filling in the rigid band picture.  
According to band structure calculations,9-13) there is a dip 
around the Γ point in the a1g band, though it has not yet been 
detected experimentally.15)  Then, it is likely that at x* the 
Fermi level with energy E* touches the bottom of the a1g 
band exactly at the Γ point, as schematically depicted in Fig. 
5.  An approximate profile of DOS expected from the band 
structure is also illustrated in Fig. 5, which is constant below 
E* due to the two dimensionality and exhibits a 
discontinuous jump at E*, followed by a further increase 
above E*.  This profile of DOS is qualitatively in good 
agreement with the observed x dependence of γ shown in 
Fig. 4.  A minor difference between them may come from 
the actual three dimensionality of the band structure that 
splits the a1g band into two.
9, 12)  On the other hand, the top 
of the e'g band must be below the Fermi level even at the 
lowest filling, because no enhancement in γ is observed for 
0.35 ≤ x < x* in Fig. 4.  
Furthermore, one expects a distinct change in the 
topology of the FS at x*:  an additional small electron pocket 
should appear for x > x*.  Because of this small electron 
pocket, strong ferromagnetic correlations are expected for x 
> x*, which has been predicted theoretically10, 13, 19) and 
evidenced by neutron diffraction20, 21) and other 
experiments.22-24)  The observed change from a PM metal to 
a CW metal is obviously attributed to the emergence of this 
small electron FS. 
It seems difficult to estimate the accurate value of x* 
from band structure calculations, because the band structure 
is highly sensitivity to the crystal structure or the effect of 
electron correlations.9-14)  However, Korshunov et al. 
estimated x* (xm in their report) to be 0.56 based on a tight-
binding fit to an LAPW calculation, which is close to our 
value.13, 14)  They pointed out that taking account of electron 
correlations would push it up to 0.68,13, 14) which suggests 
that electron correlations may not be so important in 
NaxCoO2. 
Concerning superconductivity found in the hydrated 
compound, Sakurai et al. found that superconductivity  
appears at two specific Co valences of +3.48 and +3.40.4, 5) 
Interestingly, the latter corresponds to x = 0.60 in NaxCoO2, 
just above our x*.  Kuroki and his coworkers pointed out 
theoretically that the presence of the two concentric FSs 
around the Γ point leads to an enhanced spin fluctuation and 
thus gives rise to an extended s-wave superconductivity in 
the hydrated compound.25)  We think that superconductivity 
would show up at just above x* even in nonhydrated 
NaxCoO2, if the influence of disordered Na ions is 
appropriately taken away.  The other Co valence of +3.48 
corresponds to x = 0.52 in NaxCoO2, which is a simple PM 
metal.  However, a neutron diffraction experiment found 
that hydration squashes the CoO2 layer.
26)  It is theoretically 
predicted that this structural change with hydration pushes 
the e'g band above the Fermi level, leading to an 
enhancement in DOS and thus the occurrence of a spin-
triplet superconductivity.16, 17)  Therefore, the two 
superconducting states may be associated with the two 
corresponding FSs with enhanced DOS. 
In summary, we have studied the electronic properties of 
NaxCoO2 with varying x, using a series of high quality 
samples prepared at high temperature.  Dramatic changes in 
various quantities and thus in the electronic structure are 
found at a critical Na concentration x* between 0.58 and 
0.59.  This provides strong evidence of the presence of an 
electron pocket around the Γ point for high band fillings of x 
> x*.  The intrinsic phase diagram of the (CoO2)
x- layer is 
rather simple, as depicted in Fig. 5, in the absence of an 
electrostatic potential superimposed from the Na layers 
above and below. 
Fig. 5. Schematic representation of the band structure of 
NaxCoO2.  Band dispersions along the Γ-K line (left), an 
expected profile of density of states (middle) and an x-T 
phase diagram (right) are depicted.  The critical Na 
content x* in the phase diagram corresponds to a band 
filling with the Fermi energy equal to E*, as shown by a 
broken line, where the Fermi level touches the bottom of 
the a1g band at the Γ point.  Hexagons represent the 
Brillouin zone with the Γ point at the center and the K 
points at the corners. A small electron Fermi surface 
appears for the Fermi energy above E* in addition to a 
large Fermi surface around Γ.  In the phase diagram, a 
Curie-Weiss metal exists above x*, while a Pauli 
paramagnetic metal below x*.  A charge-ordered 
insulator reported at x = 0.5 is excluded in this phase 
diagram, because it is extrinsic, coming from the Na 
ordering. 
Acknowledgment 
We thank M. Ichihara for his help in electron microscopy 
observations. 
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7) M. Yokoi et al.: J. Phys. Soc. Jpn. 74 (2005) 3046. 
8) G. Gaparovi et al.: Phys. Rev. Lett. 96 (2006) 046403. 
9) D. J. Singh: Phys. Rev. B 61 (2000) 13397. 
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13) M. M. Korshunov et al.: JETP Letters 84 (2007) 650. 
14) M. M. Korshunov et al.: Phys. Rev. B 75 (2007) 94511. 
15) M. Z. Hasan et al.: Phys. Rev. Lett. 92 (2004) 246402. 
16) M. Mochizuki and M. Ogata: J. Phys. Soc. Jpn. 75 (2006) 
113703. 
17) M. Mochizuki and M. Ogata: J. Phys. Soc. Jpn. 76 (2007) 
013704. 
18) D. Yoshizumi et al.: in preparation. 
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26) J. W. Lynn et al.: Phys. Rev. B 68 (2003) 214516.

  Electronic properties of the sodium cobaltate NaxCoO2 are systematically
studied through a precise control of band filling. Resistivity, magnetic
susceptibility and specific heat measurements are carried out on a series of
high-quality polycrystalline samples prepared at 200 C with Na content in a
wide range of 0.35 =< x =< 0.70. It is found that dramatic changes in
electronic properties take place at a critical Na concentration x* that lies
between 0.58 and 0.59, which separates a Pauli paramagnetic and a Curie-Weiss
metals. It is suggested that at x* the Fermi level touches the bottom of the
a1g band at the gamma point, leading to a crucial change in the density of
states across x* and the emergence of a small electron pocket around the gamma
point for x > x*.

Microsoft Word - preprint.doc
April 9, 2007, submitted to J. Phys. Soc. Jpn. 
Layered sodium cobaltate NaxCoO2
1) provides us with a 
fascinating playground to study the physics of strongly 
correlated electrons on the frustrated triangular lattice in a 
wide range of band filling.  Recent two important 
discoveries have accelerated the research of NaxCoO2: one 
is an unusually large thermoelectric power for x ~ 2/32) and 
the other is superconductivity below 4.5 K in a hydrated 
compound with x ~ 1/3.3)  Particularly, a lot of studies have 
focused on the hydrated superconductor to clarify the 
mechanism of the superconductivity and to understand 
underlying electronic states realized in the triangular lattice.  
In spite of extensive research, however, there still remain 
some controversial issues possibly resulting from difficulty 
in the chemistry of the compounds that put obstacles in the 
way of obtaining high-quality samples.4, 5)   
The electronic phase diagram of NaxCoO2 as a function 
of x has been proposed by several groups.  Foo et al. gave a 
typical one where a charge-ordered magnetic insulator exists 
at x = 0.5 with a "paramagnetic (PM) metal" on the left (x < 
0.5) and a "Curie-Weiss (CW) metal" on the right (x > 
0.5).6)  In contrast, Yokoi et al. found that the boundary 
between the two metals is located approximately at x = 0.6.7)  
The reason for this discrepancy is not known. Moreover, the 
origin of the change in metallic character has not yet been 
interpreted in a clear manner.  On the charge-ordered 
insulator at x = 0.5, it is known that the ordering of Na ions, 
which is already present at high temperature, triggers a 
magnetic as well as a metal-insulator transitions at low 
temperatures.6-8) 
The electronic states of NaxCoO2 near the Fermi level 
come from the Co d derived t2g state that splits into an a1g 
singlet and an e'g doublet.  These bands are filled 
progressively with x, because one Na+ ion donates one 
electron to the CoO2 layer.  According to band structure 
calculations,9-14) the a1g band always crosses the Fermi level, 
irrespective of band filling, which gives a large circular 
(cylindrical) Fermi surface (FS) around the Γ point in the 
Brillouin zone.  In addition, two important features on the 
FS are found in the local-density approximation 
calculations: one is a set of small hole pockets originating 
from the e'g band near the K points, which are expected to 
appear at low fillings such as x = 0.3.  The other is a small 
concentric electron FS around Γ coming from a dip in the 
band energy of the a1g state, which may appear at high 
fillings such as x = 0.7.  However, the absence of the latter 
was suggested for any doping levels by more sophisticated 
band structure calculations incorporating spin polarizations 
or the on-site Coulomb interaction U.11)  Experimentally, 
angle-resolved photoemission spectroscopy (ARPES) study 
on Na0.7CoO2 observed only a large circular FS around Γ 
and failed to detect the other FSs.15) Recently, Mochizuki 
and Ogata pointed out in their tight binding model that band 
dispersions and FS topology change sensitively with the 
thickness of the CoO2 layer:
16, 17)  the hole pockets near K 
would appear for a thinner CoO2 layer, while the small 
electron pocket around Γ would be present for a thicker 
CoO2 layer.  Thus, the current status is miles away from a 
complete understanding of the basic electronic structures of 
NaxCoO2. 
In this letter, we study systematically the transport and 
thermodynamic properties of NaxCoO2 using a series of 
polycrystalline samples.  The key point of the present study 
is a novel method used to prepare samples: most of samples 
studied so far were obtained by a soft-chemistry method at 
ambient temperature,3) which might cause an 
inhomogeneous distribution of Na ions or otherwise lead to 
Precise Control of Band Filling in NaxCoO2 
Daisuke YOSHIZUMI, Yuji MURAOKA**, Yoshihiko OKAMOTO, Yoko KIUCHI, 
Jun-Ichi YAMAURA, Masahito MOCHIZUKI1, ***, Masao OGATA2 and Zenji HIROI* 
Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581 
1RIKEN, Hirosawa, Wako, Saitama 351-0198 
2Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033 
Electronic properties of the sodium cobaltate NaxCoO2 are systematically studied through a precise 
control of band filling.  Resistivity, magnetic susceptibility and specific heat measurements are carried 
out on a series of high-quality polycrystalline samples prepared at 200°C with Na content in a wide 
range of 0.35 ≤ x ≤ 0.70.  It is found that dramatic changes in electronic properties take place at a critical 
Na concentration x* that lies between 0.58 and 0.59, which separates a Pauli paramagnetic and a Curie-
Weiss metals.  It is suggested that at x* the Fermi level touches the bottom of the a1g band at the Γ point, 
leading to a crucial change in the density of states across x* and the emergence of a small electron pocket 
around the Γ point for x > x*. 
KEYWORDS:  sodium cobaltate, resistivity, magnetic susceptibility, specific heat, Sommerfeld 
coefficient, Fermi surface, band filling 
*E-mail: hiroi@issp.u-tokyo.ac.jp 
**Present address: The Graduate School of Natural Science and Technology, Okayama University, 
1-1, Naka-3, Tsushima, Okayama 700-8530 
***Present address: Tokura Multiferroics Project, ERATO, Japan Science and Technology Agency (JST) 
a strong tendency for Na ordering at certain fractional 
compositions such as x = 0.5.  Particularly, the Na ordering 
strongly influences the electronic state of the (CoO2)
x- layer 
and may mask the intrinsic features.  We adopted 
alternatively a solid-state reaction at higher temperatures 
starting from two end members of Na0.35CoO2 and 
Na0.70CoO2 and succeeded in controlling x on a scale of 0.01.  
Moreover, since the high-temperature reaction favoured 
disordering of Na ions, more intrinsic properties of the 
(CoO2)
x- layer have been clarified.   
We prepared a series of polycrystalline samples of 
NaxCoO2 by a solid-state reaction of Na0.35CoO2 and 
Na0.70CoO2.  First, powders of Na0.70CoO2 were synthesized 
by a reaction of stoichiometric amounts of Na2CO3 and 
Co3O4 in air at 860°C.  Sodium deintercalation was then 
carried out in a 1.0 M Br2 solution in acetnitrile to obtain 
powders of Na0.35CoO2.  The Na content was determined by 
the inductively coupled plasma-atomic emission 
spectroscopy (ICP) method.  A dozen of samples with 
intermediate compositions were prepared by reacting the 
two powders of Na0.35CoO2 and Na0.70CoO2 in an 
appropriate ratio in a sealed quartz tube at 200°C for 24 
hours, followed by slow cooling to room temperature.  The 
Na content of the products was also examined by the ICP 
analysis.  The phase purity was confirmed by means of 
powder x-ray diffraction.  More detail on the sample 
preparation and characterization will be reported 
elsewhere.18)  Resistivity and specific heat were measured in 
a Quantum Design PPMS system, and magnetic 
susceptibility measurements were performed in a Quantum 
Design MPMS system. 
Figure 1 shows the systematic variation of resistivity ρ 
with x.  For clarity, each set of data is divided by the value 
at 250 K.  The ρ of x = 0.50 exhibits a smooth, 
semiconductor-like increase at low temperature with no 
anomalies for a metal-insulator transition, in contrast to the 
previous report where a soft-chemically prepared sample of 
x = 0.50 exhibits a sharp rise in ρ below 53 K.6, 7)  We 
examined our sample by electron diffraction and found that 
a superstructure coming from Na ordering was almost 
absent.18)  We think that this semiconducting behavior is due 
to a partial ordering of Na ions, because even at room 
temperature the Na ions tend to align.18)  As x increases 
from 0.50, such a semiconducting increase in ρ is 
progressively suppressed, and finally a metallic T 
dependence appears above 0.55.  Nevertheless, a small 
upturn is observed below 20 K, as shown in the inset to Fig. 
1, which may be ascribed to weak localization due to a 
random electrostatic potential from disordered Na 
distributions. 
Compared with the T dependence in ρ for x ≤ 0.58, which 
is always concave-downward, those of x ≥ 0.59 are 
apparently dissimilar; almost T linear for x = 0.59 and 
concave-upward for x = 0.66 and 0.70.  The last one shows a 
steep decrease below 30 K, which is similar as reported 
previously for x = 0.75.6)  Therefore, the  T dependence of 
ρ changes significantly across x = 0.58 ~ 0.59. 
Another related change is found in the evolution of 
magnetic susceptibility χ, as shown in Fig. 2.  The χ for x ≤ 
0.58 shown in the left panel is relatively small in magnitude 
and weakly T dependent, while, in distinct contrast, the χ for 
x ≥ 0.59 is large in magnitude and shows a characteristic 
CW divergence that is progressively enhanced with 
increasing x.  Hence, a substantial change in magnetism 
must occur across a critical Na concentration x* between 
0.58 and 0.59, accurately corresponding to the above results 
from resistivity. 
Looking in more detail, the χ of x = 0.35 decreases 
gradually with decreasing T from 300 K, exhibits a 
minimum at 120 K and then shows a CW divergence at low 
Fig. 1.  Evolution of the temperature dependence of 
resistivity ρ normalized to the value at 250 K for 0.50 ≤ 
x ≤ 0.58 (left) and 0.59 ≤ x ≤ 0.70 (right). 
Fig. 2.  Magnetic susceptibility χ measured on heating in a 
magnetic field of 10 kOe for  0.35 ≤ x ≤ 0.58 (left) and 
0.59 ≤ x ≤ 0.70 (right).  Note the difference in the 
vertical scale. 
temperature.  This low-temperature CW component may be 
due to a minor portion of spins that come from defects or 
impurities and are noninteracting with majority spins. The 
positive slope above 120 K suggests the existence of a peak 
in χ at a higher temperature.  In fact, the 0.50 and 0.52 
samples seem to show a broad maximum near 300 K.  
Moreover, a broad peak is clearly observed at around 150 K 
for x = 0.56.  The peak is possibly further shifted to a lower 
T for x = 0.58 and becomes obscure.  This broad peak 
indicates the development of antiferromagnetic (AF) short-
range order on cooling.  Then, its systematic shift to lower 
temperatures implies that the characteristic energy of AF 
spin fluctuations or effective superexchange Jeff decreases 
with increasing x.  Since the density of spins (1-x) decreases 
as x increases, we expect that Jeff between nearest-neighbour 
spins also decreases, consistent with the observed behavior 
in χ.  For x ≥ 0.59, on the other hand, the Weiss temperature 
deduced from fitting the data to the CW law χ = C/(T - Θ) is 
always negative in sign (AF) and gradually increases from -
156 K (x = 0.59) to -99 K (x = 0.70).  This fact indicates that 
AF fluctuations are suppressed or additional ferromagnetic 
interactions are enhanced with increasing x. 
In order to demonstrate more explicitly the dramatic 
changes across x*, the ρ and χ data of x = 0.58 and 0.59 are 
compared in Fig. 3.  The ρ of 0.58 is proportional to T2 in a 
wide T range below 70 K, as shown in the inset, provided 
that the low-temperature upturn is ignored.  Such T2 
behavior is what one expects generally  for a strongly 
correlated electron system.  In contrast, the T dependence in 
ρ of 0.59 is rather unusual, showing an almost linear 
variation in a similarly wide T range below 80 K.  Hence, 
there must be a substantial difference in the scattering 
mechanism of carriers between the two samples. 
On the other hand, it is apparent from Fig. 3 that χ is 
enhanced enormously from 0.58 to 0.59.  Moreover, the T 
dependence above 50 K changes from linear to CW-like.  
This T linear behavior for 0.58 may be accidental as a few 
contributions of different origins coexist. The unusual T-
linear dependence in ρ for 0.59 must be related to the 
appearance of the CW component in χ: additional magnetic 
scattering can be the source. 
To evaluate the change in the T dependence of χ, the 
slope at 100 K is plotted in Fig. 4, following the previous 
analysis done by Yokoi et al.7)  The slope is close to zero or 
takes small negative values for x ≤ 0.58, while it decreases 
almost discontinuously to a relatively large negative value at 
0.59, followed by a further decrease with increasing x.   
Another experimental evidence to support the existence 
of a critical x value has been obtained from specific heat 
measurements.  The x dependence of the Sommerfeld 
coefficient γ determined from the intercept of the C/T versus 
T2 plot is shown in Fig. 4.  Obviously, there is a change in γ  
at x*: γ increases slightly with x for x ≤ 0.58 and suddenly 
rises at x* by 17 %, from 16.8 mJ K-2 mol-1 for 0.58 to 19.7 
mJ K-2 mol-1 for 0.59.  Then, it increases rapidly to be 
saturated at 31.5 mJ K-2 mol-1 for x = 0.70.  Note that the γ 
of 0.50 is finite because of the metallic nature of our sample 
in the absence of charge order.  Since γ is proportional to the 
density of states (DOS), we conclude that the DOS at the 
Fermi level suddenly increases above x*. 
All the above results indicate that the electronic structure 
of NaxCoO2 does not change smoothly with x, but there is a 
well-defined boundary at x*.  It is found that the critical 
concentration lies between 0.58 and 0.59, not at 0.5 as 
reported by Foo et al.,6) but close to 0.60 as reported by 
Fig. 4. x dependences of the slope in χ at 100 K (top) and 
the Sommerfeld coefficient γ (bottom).  Crosses in the 
bottom panel represent the data reported by Yokoi et 
al.7)  Dotted lines serve as guides to the eye. 
Fig. 3.  Comparisons of resistivity (left) and magnetic 
susceptibility (right) between x = 0.58 and 0.59.  Inset in 
the left panel shows a ρ - ρ0 versus T
2 plot for 0.58, 
where ρ0 is the residual resistivity and is 1.83 mΩ cm.  
Inset in the right panel shows the T dependence of 
inverse χ for 0.59. 
Yokoi et al.7)  The sharp boundary breaks the phase diagram 
into two regions: a Pauli paramagnetic metal with a 
relatively small DOS for x < x*and a CW metal with an 
enhanced DOS for x > x* (Fig. 5).  A main reason why we 
observed such sharp changes in properties at x* in the 
present study may be ascribed to the high quality of our 
samples prepared at high temperature as well as the reduced 
influence of the Na ordering. 
On the basis of these experimental lines of evidence, we 
are now ready to consider what is going on with x in 
NaxCoO2 in terms of band structures.  As x decides filling in 
the t2g band, it is reasonable to assume that the band 
structure changes at a certain filling in the rigid band picture.  
According to band structure calculations,9-13) there is a dip 
around the Γ point in the a1g band, though it has not yet been 
detected experimentally.15)  Then, it is likely that at x* the 
Fermi level with energy E* touches the bottom of the a1g 
band exactly at the Γ point, as schematically depicted in Fig. 
5.  An approximate profile of DOS expected from the band 
structure is also illustrated in Fig. 5, which is constant below 
E* due to the two dimensionality and exhibits a 
discontinuous jump at E*, followed by a further increase 
above E*.  This profile of DOS is qualitatively in good 
agreement with the observed x dependence of γ shown in 
Fig. 4.  A minor difference between them may come from 
the actual three dimensionality of the band structure that 
splits the a1g band into two.
9, 12)  On the other hand, the top 
of the e'g band must be below the Fermi level even at the 
lowest filling, because no enhancement in γ is observed for 
0.35 ≤ x < x* in Fig. 4.  
Furthermore, one expects a distinct change in the 
topology of the FS at x*:  an additional small electron pocket 
should appear for x > x*.  Because of this small electron 
pocket, strong ferromagnetic correlations are expected for x 
> x*, which has been predicted theoretically10, 13, 19) and 
evidenced by neutron diffraction20, 21) and other 
experiments.22-24)  The observed change from a PM metal to 
a CW metal is obviously attributed to the emergence of this 
small electron FS. 
It seems difficult to estimate the accurate value of x* 
from band structure calculations, because the band structure 
is highly sensitivity to the crystal structure or the effect of 
electron correlations.9-14)  However, Korshunov et al. 
estimated x* (xm in their report) to be 0.56 based on a tight-
binding fit to an LAPW calculation, which is close to our 
value.13, 14)  They pointed out that taking account of electron 
correlations would push it up to 0.68,13, 14) which suggests 
that electron correlations may not be so important in 
NaxCoO2. 
Concerning superconductivity found in the hydrated 
compound, Sakurai et al. found that superconductivity  
appears at two specific Co valences of +3.48 and +3.40.4, 5) 
Interestingly, the latter corresponds to x = 0.60 in NaxCoO2, 
just above our x*.  Kuroki and his coworkers pointed out 
theoretically that the presence of the two concentric FSs 
around the Γ point leads to an enhanced spin fluctuation and 
thus gives rise to an extended s-wave superconductivity in 
the hydrated compound.25)  We think that superconductivity 
would show up at just above x* even in nonhydrated 
NaxCoO2, if the influence of disordered Na ions is 
appropriately taken away.  The other Co valence of +3.48 
corresponds to x = 0.52 in NaxCoO2, which is a simple PM 
metal.  However, a neutron diffraction experiment found 
that hydration squashes the CoO2 layer.
26)  It is theoretically 
predicted that this structural change with hydration pushes 
the e'g band above the Fermi level, leading to an 
enhancement in DOS and thus the occurrence of a spin-
triplet superconductivity.16, 17)  Therefore, the two 
superconducting states may be associated with the two 
corresponding FSs with enhanced DOS. 
In summary, we have studied the electronic properties of 
NaxCoO2 with varying x, using a series of high quality 
samples prepared at high temperature.  Dramatic changes in 
various quantities and thus in the electronic structure are 
found at a critical Na concentration x* between 0.58 and 
0.59.  This provides strong evidence of the presence of an 
electron pocket around the Γ point for high band fillings of x 
> x*.  The intrinsic phase diagram of the (CoO2)
x- layer is 
rather simple, as depicted in Fig. 5, in the absence of an 
electrostatic potential superimposed from the Na layers 
above and below. 
Fig. 5. Schematic representation of the band structure of 
NaxCoO2.  Band dispersions along the Γ-K line (left), an 
expected profile of density of states (middle) and an x-T 
phase diagram (right) are depicted.  The critical Na 
content x* in the phase diagram corresponds to a band 
filling with the Fermi energy equal to E*, as shown by a 
broken line, where the Fermi level touches the bottom of 
the a1g band at the Γ point.  Hexagons represent the 
Brillouin zone with the Γ point at the center and the K 
points at the corners. A small electron Fermi surface 
appears for the Fermi energy above E* in addition to a 
large Fermi surface around Γ.  In the phase diagram, a 
Curie-Weiss metal exists above x*, while a Pauli 
paramagnetic metal below x*.  A charge-ordered 
insulator reported at x = 0.5 is excluded in this phase 
diagram, because it is extrinsic, coming from the Na 
ordering. 
Acknowledgment 
We thank M. Ichihara for his help in electron microscopy 
observations. 
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