Non-Fermi liquid behavior in the layered NaxCoO₂
The specific heat in the temperature region of 100 mK–360 K and in magnetic fields of 0 and 9 T, as well as the susceptibility from 2 to 360 K and in a magnetic field of 1 T have been measured in the layered NaxCoO₂ (x = 0.65, 0.70, and 0.75) oxides. Analysis of the data revealed non-Fermi liquid be...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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| Cite this: | Non-Fermi liquid behavior in the layered NaxCoO₂ / A. Zorkovská, J. Šebek, E. Šantavá, I. Bradaric, A. Feher // Физика низких температур. — 2007. — Т. 33, № 11. — С. 1243-1247. — Бібліогр.: 19 назв. — англ. |
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| citation_txt | Non-Fermi liquid behavior in the layered NaxCoO₂ / A. Zorkovská, J. Šebek, E. Šantavá, I. Bradaric, A. Feher // Физика низких температур. — 2007. — Т. 33, № 11. — С. 1243-1247. — Бібліогр.: 19 назв. — англ. |
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| description | The specific heat in the temperature region of 100 mK–360 K and in magnetic fields of 0 and 9 T, as well as the susceptibility from 2 to 360 K and in a magnetic field of 1 T have been measured in the layered NaxCoO₂ (x = 0.65, 0.70, and 0.75) oxides. Analysis of the data revealed non-Fermi liquid behavior. The character of the observed anomalies seems to be connected to the mesoscopic phase separation, underlining the impact of disorder on the low-lying excitations in cobaltates.
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Fizika Nizkikh Temperatur, 2007, v. 33, No. 11, p. 1243–1247
Non-Fermi liquid behavior in the layered NaxCoO2
A. Zorkovská1, J. �ebek2, E. �antavá2, I. Bradaric3, and A. Feher1
1Centre of Low Temperature Physics of the P. J. Šafárik University & the Slovak Academy of Science
9 Park Angelinum, Košice 04154, Slovakia
E-mail: anna.zorkovska@upjs.sk
2Institute of Physics AS CR, 2 Na Slovance, Prague 18221, Czech Republic
3The «Vinèa» Institute of Nuclear Sciences, P.O. Box 522, Belgrade 11001, Serbia
Received April 17, 2007, revised June 22, 2007
The specific heat in the temperature region of 100 mK–360 K and in magnetic fields of 0 and 9 T, as well
as the susceptibility from 2 to 360 K and in a magnetic field of 1 T have been measured in the layered
NaxCoO2 (x = 0.65, 0.70, and 0.75) oxides. Analysis of the data revealed non-Fermi liquid behavior. The
character of the observed anomalies seems to be connected to the mesoscopic phase separation, underlining
the impact of disorder on the low-lying excitations in cobaltates.
PACS: 71.27.+a Strongly correlated electron systems; heavy fermions;
73.43.Nq Quantum phase transitions;
74.20.Mn Nonconventional mechanisms.
Keywords: cobaltates, specific heat, non-Fermi liquid behavior, phase separation, magnetic susceptibility.
Introduction
The layered NaxCoO2 and its hydrated counterpart
represent a d-electron system, in which the interplay of
reduced dimensionality, magnetic frustration and electron
correlations drives the system towards new quantum
phases. Besides the multitude of open fundamental prob-
lems it also offers promising technological applications:
superconductivity [1] and the unique combination of high
thermo-power with low electrical resistivity [2].
Reminiscent of high-TC superconductors and manga-
nite materials, the NaxCoO2 system is extremely sensitive
to doping and preparation protocols. In fact, the diverse
properties are a consequence of the complexity arising
from the disorder inherent in this system. The NaxCoO2 is
considered a two-dimensional (2D) Mott insulator doped
with electrons via sodium, which serves as a charge reser-
voir between the CoO2 layers. The Co atoms are arranged
on a triangular lattice, and this configuration generates
the geometrical frustration of the antiferromagnetic inter-
actions in the system. Consequently, the issue of the mag-
netic ground states with respect to quantum effects and
spin frustration becomes appealing. As the extra electron
from sodium converts the originally magnetic Co4+ (3d5)
ions with spin S = 1/2 into nonmagnetic Co3+ (3d6) ones,
stronger magnetic features might be naively expected in
the low doping regime. However, the opposite is true.
Strong frustration interferes with the magnetic ordering,
and the magnetic phases were observed only for doping
levels of x � 0.7 [3,4]. The low-doped systems show con-
ventional metallic character with Pauli-like paramagnet-
ism and only light electron mass renormalization [5] (the
linear specific heat coefficient � ~ 12–16 mJ/(mol�K2));
however, when hydrated it becomes superconducting [1].
On the other hand, the higher-doped systems exhibit curi-
ous Curie–Weiss like metallic behavior and substantial
electron mass enhancement [6] (� ~ 25–30 mJ/mol�K2)
typical for strongly correlated electron systems. Even
though there are several hints of unconventional metallic
behavior with non-Fermi liquid features such as anoma-
lous resistivity and spin-lattice relaxation behavior [7,8],
the mass-enhanced Fermi liquid ground state is consid-
ered [9]. In this article the fundamental issue of the nature
of the magnetic fluctuations and their influence on the
electronic behavior at low temperature in the sodium
doped cobalt oxides is addressed.
Experimental
The NaxCoO2 polycrystalline samples with nominal
Na content of x = 0.65, 0.70, and 0.75 (hereafter denoted
© A. Zorkovsk�, J. �ebek, E. �antava, I. Bradaric, and A. Feher, 2007
as Na65, Na70, and Na75, respectively), the doping re-
gime where a magnetic order is about to form, were pre-
pared by the rapid heat-up method [10]. X-ray powder
diffraction confirmed the samples to be a single phase of
hexagonal �-NaxCoO2 with lattice parameter a around
2.827 � for all samples, while c = 10.939, 10.907, and
10.892 � for x = 0.65, 0.70, and 0.75, respectively. Spe-
cific heat measurements from 2.5 to 360 K have been per-
formed in magnetic fields of zero and 9 T using the con-
ventional Quantum Design PPMS-9 device. This
instrument was also used for the susceptibility measure-
ments performed at 1 T and over the same range of tem-
perature. The specific heat from 100 mK to 3 K was mea-
sured by the dual slope method, using a 3He–4He
refrigerator, TLE-200 Oxford Instruments.
Results and discussion
The susceptibility results are consistent with the find-
ing of other authors [3,4] and the temperature behavior
was similar for all three samples. Generally speaking the
response is characterized by an increase on cooling (re-
sembling local moment behavior), a steep increase below
10 K (reminiscent of heavy fermions and Kondo sys-
tems), and a small kink around 26–28 K (possibly the
manifestation of short-range magnetic ordering).
The specific heat data can be seen on Fig. 1. Focusing
on the low temperature region, we found a pronounced
upturn of the C/T data below 10 K (note the correspon-
dence with the susceptibility behavior), sensitive to the
magnetic field. This usually indicates emerging low-level
excitations. The fact that they can be progressively sup-
pressed by the magnetic field points to magnetic character
of these excitations. For closer inspection of this feature
we investigated the specific heat at lower temperatures.
As it might have been expected, the low-temperature be-
havior of the specific heat for all the samples showed
divergence from the Fermi liquid predictions (Fig. 2,a). In
this temperature region the electronic contribution C = � T is
dominant and the Sommerfeld coefficcient � for Fermi liq-
uids should be independent of T when approaching T = 0.
For more detailed analysis of the observed anomalies
we considered two NFL scenarios: (i) the spin fluctuation
theory for a 2D antiferromagnet [11] predicts a logarith-
mic divergence of C/T and � ~ –lnT; and (ii) the Griffiths
phase scenario [12] predicts the T –1+� law for C/T and �
with the same parameter �. The comparison of the analy-
ses of C and � (Figs. 2 and 3) suggests that for the Na65
and Na70 samples the prediction for Griffiths phase sce-
nario provides better description of the experimental
data. However, for the Na75 sample it should be noted,
that the data can be described by both dependences quite
reasonably.
It should be stressed that the values of � obtained from
the analysis of specific heat and susceptibility below 10 K
agree especially for the Na65 and Na70 samples ex-
tremely well. We found a substantial coincidence be-
tween the upper temperature limit for the validity of
power law behavior of the susceptibility and between the
results of several resonance studies implying some
change in electronic states around this temperature. More
specifically, Mössbauer studies on Fe enriched samples
have implied slow spin relaxation phenomena just below
10 K [13]; further, anomalous low-temperature behavior
of the spin-lattice relaxation time T1 has been observed by
23Na nuclear magnetic resonance measurements in
Na0.7CoO2 [8]. Interestingly, 1/T1 was found to follow a
Tn relation below 10 K with n = 0.73. These notions are
consistent with the existence of Griffiths phases, charac-
terized by typically slow dynamics. The parameter � is a
non-universal exponent, tunable by the disorder strength.
It indicates how «close» the system is to the normal Fermi
liquid state, characterized by � = 1. Phenomenology shows
that its typical values lie in the range 0.7–1 for heavy
fermion compounds, whereas doped semiconductors have
a more singular response with � in the range 0.3–0.4 [14].
With respect to the obtained values the cobaltates rank to
the former group. It might be speculated that in the higher
doped «magnetic» side of the phase diagram spin fluctua-
tions, while at lower doping disorder effects play the domi-
nant role in electronic behavior.
Let us discuss briefly the possible microscopic back-
ground of the observed behavior in this system. Griffiths
phases are common in the proximity to magnetic phase
transitions of percolating character [15]. Nevertheless,
they can occur in the absence of any form of magnetic or-
dering as well, as in the disordered Kondo-lattice case
(electronic Griffiths phases) [16]. To produce an anoma-
1244 Fizika Nizkikh Temperatur, 2007, v. 33, No. 11
A. Zorkovsk�, J. �ebek, E. �antava, I. Bradaric, and A. Feher
0 5 10 15 20 25
0
0.03
0.06
0.09
0 60 120 180 240 300
25
50
75
100
Na65 B = 0
Na65 B = 9
Na70 B = 0
Na70 B = 9
Na75 B = 0
T K,
T K
C
,J
/(
m
ol
·K
)
ex
p
C
/T
, J
/(
m
ol
·K
2)
Fig. 1. Specific heat experimental data for the Na65 sample.
Inset: The C/T data for all three samples, measured in mag-
netic field of 0 T (full symbols) and 9 T (hollow symbols). The
Na70 and Na75 data are shifted for clarity down by 0.015 and
0.03 J/mol�K2, respectively.
Non-Fermi liquid behavior in the layered NaxCoO2
Fizika Nizkikh Temperatur, 2007, v. 33, No. 11 1245
5 10 15 20
0.002
0.003
0.004
0.1 1
0.1
0.01
T, K T, K
a Na65
Na70
Na75
b
C
, J
/(
m
ol
·K
)
Fig. 2. Log-log plots of specific heat C (a) and magnetic susceptibility � (b) vs temperature. Solid lines represent the fits to power
law dependences C/T and � ~ T–1+�.
0.1 1.0
0.015
0.030
0.045
0.060
0.075
5 10 15
0.0015
0.0020
0.0025
0.0030
0.0035
T, K T, K
a b
Na65
Na70
Na75
C
/T
,J
/(
m
ol
·K
)2
20
Fig. 3. Semilog plots of specific heat over temperature C/T (a) and magnetic susceptibility � (b) vs temperature. Dotted lines repre-
sent the best fits to the logarithmic dependences C/T and � ~ lnT. For comparison the power law fits are also shown, represented by
solid lines.
lous power-law divergence, only an assembly of
fluctuators, whose energy scales are distributed in a
power-law fashion, are needed, and these fluctuators can
be magnetic clusters as well as Kondo spins. The
NaxCoO2 system of concentrations under study is at the
verge of magnetic ordering: only short-range magnetic
order (finite magnetic clusters or in the correlated direc-
tion even infinite magnetic layers) is present below
~ 80 K [17]. However, we should keep in mind that the
precursors of the magnetic clusters with wide size-distri-
bution, i.e. the mesoscopic regions consisting of Co4+
ions, are formed at much higher temperatures, around
250 K, this process is governed by charge ordering
[18,19]. According to the Griffiths scenario these clusters
are able to tunnel at low enough temperatures between the
two different configurations with reversed sign of stag-
gered magnetization. The scenario of quantum tunnelling
seems to be consistent also with the temperature evolu-
tion of the magnetic entropy (Fig. 4), obtained from the
specific heat data after subtraction of both the lattice and
electronic contributions [17]. One can observe a weaker
temperature dependence of this entropy below 10–12 K
(Fig. 4 inset). The entropy decrease becomes slower be-
cause of additional degrees of freedom, which slow down
the entropy removal upon cooling. Simple entropy con-
siderations [14] allow to estimate roughly the average
cluster size N in this region. The entropy of a cluster
being a two-level system is kBln2, the total entropy
S = nkBln2, if n is the number of clusters. In the case of a
mole of spins, S is a molar entropy and:
S/NA = nkBln2/NA = kBln2/N
Thus N ~ Rln2/S, leading to N ~ 1600 in our system. Tak-
ing into account two-dimensionality, this number repre-
sents approximately 40�40 spins in the clusters, that is re-
ally a mesoscopic scale. Realizing that the cluster size is
probably not significantly affected by temperature after
completion of charge ordering, this can be the upper esti-
mate of the cluster size in addition to the lower estimate of
6 lattice steps as proposed in [19].
Conclusion
To summarize, our specific heat and magnetic suscep-
tibility analysis at low temperatures on polycrystalline
NaxCoO2 oxides with x = 0.65, 0.7, and 0.75 gives evi-
dence of anomalous metallic behavior of non-Fermi liq-
uid character. Closer inspection reveals low-lying elec-
tronic quantum states resembling Griffiths phases. The
underlaying microscopic mechanism is likely of magnetic
character, related to the mesoscopic phase separation, i.e.
the coexistence of partially ordered magnetic regions
with Fermi liquid electrons.
Acknowledgement
This paper is dedicated to the late Prof. A.I. Zviagin in
grateful recollection by one of the authors (A. Feher) of
years of fruitful and gratifying collaboration.
Financially has been supported by the Grant Agency
VEGA, grant No. 1/3027/06, by the Science and Techno-
logy Assistance Agency under contracts No. 20-005204
and by the Highly Frustrated Magnetism ESF Network. I.
Bradaric was supported by the Serbian Ministry of Sci-
ence, Technology and Development, Grant No. 1899. Ma-
terial support of U. S. Steel DZ Energetika is gratefully
acknowledged.
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Non-Fermi liquid behavior in the layered NaxCoO2
Fizika Nizkikh Temperatur, 2007, v. 33, No. 11 1247
|
| id | nasplib_isofts_kiev_ua-123456789-7716 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-11-24T09:51:41Z |
| publishDate | 2007 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Zorkovská, A. Šebek, J. Šantavá, E. Bradaric, I. Feher, A. 2010-04-08T12:17:53Z 2010-04-08T12:17:53Z 2007 Non-Fermi liquid behavior in the layered NaxCoO₂ / A. Zorkovská, J. Šebek, E. Šantavá, I. Bradaric, A. Feher // Физика низких температур. — 2007. — Т. 33, № 11. — С. 1243-1247. — Бібліогр.: 19 назв. — англ. 0132-6414 PACS: 71.27.+a; 73.43.Nq; 74.20.Mn https://nasplib.isofts.kiev.ua/handle/123456789/7716 The specific heat in the temperature region of 100 mK–360 K and in magnetic fields of 0 and 9 T, as well as the susceptibility from 2 to 360 K and in a magnetic field of 1 T have been measured in the layered NaxCoO₂ (x = 0.65, 0.70, and 0.75) oxides. Analysis of the data revealed non-Fermi liquid behavior. The character of the observed anomalies seems to be connected to the mesoscopic phase separation, underlining the impact of disorder on the low-lying excitations in cobaltates. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Non-Fermi liquid behavior in the layered NaxCoO₂ Article published earlier |
| spellingShingle | Non-Fermi liquid behavior in the layered NaxCoO₂ Zorkovská, A. Šebek, J. Šantavá, E. Bradaric, I. Feher, A. |
| title | Non-Fermi liquid behavior in the layered NaxCoO₂ |
| title_full | Non-Fermi liquid behavior in the layered NaxCoO₂ |
| title_fullStr | Non-Fermi liquid behavior in the layered NaxCoO₂ |
| title_full_unstemmed | Non-Fermi liquid behavior in the layered NaxCoO₂ |
| title_short | Non-Fermi liquid behavior in the layered NaxCoO₂ |
| title_sort | non-fermi liquid behavior in the layered naxcoo₂ |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/7716 |
| work_keys_str_mv | AT zorkovskaa nonfermiliquidbehaviorinthelayerednaxcoo2 AT sebekj nonfermiliquidbehaviorinthelayerednaxcoo2 AT santavae nonfermiliquidbehaviorinthelayerednaxcoo2 AT bradarici nonfermiliquidbehaviorinthelayerednaxcoo2 AT fehera nonfermiliquidbehaviorinthelayerednaxcoo2 |