Dependence of the specific heat of Na
x
CoO
2
· yH
2
O/D
2
O on sodium and water concentrations
R. Jin,
1,
* B. C. Sales,
1
S. Li,
2
and D. Mandrus
1,2
1
Condensed Matter Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
2
Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
Received 1 June 2005; published 26 August 2005
We report specific heat measurements down to 0.4 K on the layered oxide Na
x
CoO
2
· yH
2
O/D
2
O with 0
x 0.74 and y = 0 and 1.4. For the nonhydrated system y =0, the electronic specific heat coefficient
N
and
the Debye temperature
D
vary nonmonotonically with x, both displaying minima when x is close to 0.5. This
indicates a systematic change of the electronic and vibrational structures with Na content. For both hydrated
and deuterated systems x = 0.35 and y = 1.4, the specific heat reveals a sharp peak with C
p
45.5 mJ/mol K at T
c
mid
4.7 K and an anomaly at T
x
0.8 K. While the origin of the latter is not clear, the
former corresponds to the superconducting transition. With the application of magnetic fields up to 14 Tesla, T
c
decreases gradually but T
x
remains more or less unchanged. The implication of these results is discussed.
DOI: 10.1103/PhysRevB.72.060512 PACS numbers: 74.25.Bt, 74.20.Rp, 74.25.Jb, 74.90.+n
There is growing evidence that the strong electron-
electron correlation in layered Na
x
CoO
2
is responsible for
some of its anomalous physical properties such as its “colos-
sal” thermopower
1,2
and possibly superconductivity in its hy-
drated form.
3
Although it is a good metal with high electrical
conductivity for a wide Na-doping range except for x = 0.5,
both local-density approximation LDA calculations
4
and
experimental work
5
indicate that the itinerant bands of
Na
x
CoO
2
are very narrow with W U, where W is the band
width and U is the effective on-site Coulomb interaction.
This implies a high value of the density of states DOS at
the Fermi level. However, all specific heat data reported so
far reveal a weak or moderate enhancement of electronic
specific heat coefficient
N
for both hydrated and nonhy-
drated cases compared to the value from the LDA band
structure.
4,6–9
In these reports, the
N
value was obtained by
analyzing specific heat data above 2 K for x in the range of
0.3–0.8. It is possible that the extracted
N
value does not
represent that for T 0 K. On the other hand, recent calcu-
lations, using the LDA+ U method, suggest that the strength
and effect of Coulomb interactions are reduced with decreas-
ing x.
10
One would thus expect a variation of
N
with x.
On the experimental side, the electronic properties of hy-
drated and nonhydrated Na
x
CoO
2
have not been systemati-
cally studied as a function of composition. While the phase
diagram shown in Ref. 11 is constructed from electrical
transport and magnetic measurements for 1 / 3 x 3/4 and
water content y = 1.4, little is known about how the thermo-
dynamic properties vary with both x and y. Of particular
importance is the specific heat behavior in the superconduct-
ing state of the system, which can provide key information
about the superconducting pairing symmetry. In this paper,
we report the low-temperature specific heat of
Na
x
CoO
2
· yH
2
O/D
2
O with 0 x 0.74 and y =0 and 1.4.
Single crystals of Na
x
CoO
2
were used for specific heat
measurements. Starting with Na
0.74
CoO
2
single crystals
grown using a flux method,
12
crystals with smaller x were
obtained by chemical deintercalation as described in Ref. 6.
By controlling the deintercalation time, we obtain single
crystals with x 0.72 and 0.48, as determined from measure-
ments of the c-axis lattice parameter using the calibration
curve in Ref. 11. However, it is known that the above tech-
nique cannot extract all Na from Na
x
CoO
2
. In order to obtain
CoO
2
x =0 with the hexagonal structure, we extract all Li
from LiCoO
2
powders using NO
2
BF
4
as described in Ref.
13. Polycrystalline samples of Na
0.35
CoO
2
and superconduct-
ing Na
0.35
CoO
2
· 1.4H
2
O/D
2
O were prepared following a
procedure similar to that described in Ref. 14. Specific heat
measurements were carried out using a physical property
measurement system PPMS from Quantum Design.
In Fig. 1a, we present the temperature T dependence
of the specific heat C
p
for Na
x
CoO
2
with x 0.74, 0.72,
0.48, 0.35, 0. Note that C
p
varies monotonically with T be-
tween 0.4 and 10 K and the curve tends to move upward with
increasing x. For easy analysis, we replot the data as
C
p
/ T vs T
2
as shown in Fig. 1b. If the specific heat is due
to electrons and phonons only, it is expected that C
p
/ T will
be a linear function of T
2
at low T. While this is true for
CoO
2
x 0 between 0.4 and 10 K, C
p
/ T clearly deviates
from linearity below 2 K for samples with x 0. The low-
T upturn indicates that an additional contribution sets in that
increases with decreasing T. Similar behavior was reported
previously and was attributed to a Schottky effect.
7
Thus, for
FIG. 1. a Temperature dependence of the specific heat C
p
for
single crystalline Na
0.74
CoO
2
filled circles, Na
0.72
CoO
2
unfilled
circles, Na
0.48
CoO
2
crosses, polycrystalline Na
0.35
CoO
2
filled
diamonds, and CoO
2
unfilled diamonds between 0.4 and 10 K.
Shown in b is the replot of the data as C
p
/ T vs T
2
, and the solid
curves are the fits of experimental data to Eq. 1.
PHYSICAL REVIEW B 72, 060512R2005
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