arXiv:cond-mat/0403031v1 [cond-mat.supr-con] 1 Mar 2004
Unconventional superconductivity in Na0.35CoO2·1.3D2O and proximity to a
magnetically ordered phase
Y.J. Uemura,1P.L. Russo,1A.T. Savici,1C.R. Wiebe,1,2G.J. MacDougall,2
G.M. Luke,2M. Mochizuki,3Y. Yanase,3M. Ogata,3M.L. Foo,4and R.J. Cava4
1Physics Department, Columbia University, 538 West, 120th Street, New York, NY 10027, USA
2Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
3Physics Department, University of Tokyo, Hongo, Tokyo 113-0033, Japan
4Chemistry Department and Princeton Materials Institute,
Princeton University, Princeton, NJ 08544, USA
(Dated: February 2, 2008)
Muon spin relaxation (µSR) measurements on the new layered cobalt oxide superconductor
Na0.35CoO2·1.3H2O and its parent, non-superconducting compounds, have revealed unconventional
nature of superconductivity through: (1) a small superfluid energy which implies a surprisingly
high effective mass of the charge carriers, approximately 100 times the bare electron mass; (2) the
superconducting transition temperature Tc scaling with the superfluid energy following the correla-
tions found in high-Tc cuprate and some other two-dimensional superconductors; (3) an anisotropic
pairing without broken time-reversal symmetry; and (4) the proximity of a magnetically ordered
insulating phase at Na0.5CoO2 below TN = 53 K.
PACS numbers: 74.20.Rp, 74.70.-b, 76.75.+i
Muon spin relaxation (µSR) measurements have been
very effective in demonstrating unconventional super-
conductivity in high-Tc cuprate (HTSC) and organic
superconductors. The absolute value of the measured
penetration-depth λ established correlations between
ns/m∗(superconducting carrier density / effective mass)
and Tc[1-3] which, together with the pseudogap behav-
ior, suggest a formation of paired charge carriers occur-
ing possibly at a temperature significantly higher than
the condensation temperature Tc [3,4].
ture dependence of λ indicated d-wave pairing symmetry
and line nodes in the energy gap [5,6]. Zero-field µSR
studies revealed and elucidated static magnetic order in
parent/relevant compounds of HTSC .
To these superconductors based on strongly correlated
electrons, the recent discovery of superconductivity in
Na0.35CoO2 intercalated with 1.3 H2O  has added a
unique compound which has highly 2-dimensional (2-d)
conducting planes of cobalt oxide in a triangular lattice
structure with geometrical spin frustration. The origi-
nal idea of resonating valence bonds was developed for
this geometry , but no superconducting system in this
geometry has been known before the new cobalt oxide
compound. Although extensive studies have been started
[9-15], detailed characteristics of this system are yet to
be demonstrated by conclusive experimental data sets.
We performed muon spin relaxation (µSR) measure-
ments at TRIUMF in superconducting Na0.35CoO2 in-
tercalated with 1.3D2O per formula unit, as well as in
anhydrous NaxCoO2with the Na concentration x = 0.35,
0.5, and 0.64.The samples were prepared at Prince-
ton as described in earlier reports [14,15], and pressed
into disc-shaped pellets with diameters of 6 mm. Elec-
tron microscopy of the pressed pellet samples indicates
that the 2-d cobalt oxide planes of the hydrated samples
are essentially aligned. The susceptibility (χ) measure-
ments showed superconducting Tc= 4.2 K for the sample
with D2O. The superconducting sample and Na0.35CoO2,
sensitive to air exposure, were transported to TRIUMF
in sealed containers. Measurements were performed at
T≥25 mK using a dilution cryostat.
We first describe Zero-field (ZF) µSR  studies
of mangetic order in non-superconducting anhydrous
NaxCoO2. Recent resistivity and susceptibility studies
by Foo et al.  showed that the x = 0.64 system can
be chracterized as the “Curie-Weiss” metal, x = 0.35 as a
“paramagnetic” metal, while x = 0.5 exhibits a transition
from a high-temperature metal to low-temperature insu-
lator at T = 53 K. In Fig. 1(a), we show the ZF-µSR
time spectra of these systems. In the x = 0.5 system,
the spectra above T = 53 K show slow relaxation with-
out oscillation, i.e., a line shape expected for systems
with nuclear dipolar fields without static magnetic or-
der of Co moments. Below T = 53 K, a clear oscillation
sets in, together with a rather fast damping. Below T
= 20-25 K, we see two frequencies beating. Figure 1(b)
shows the temperature dependence of these frequencies.
The amplitude of the damping signal indicate that all
the muons feel a strong static magnetic field below T =
53 K. The static magnetic order sets in at the onset of a
metal-insulator transition, and the establishment of the
second frequency takes place at T = 20 K, which roughly
corresponds to the “kink” temperature in the resistivity
shown in the inset. Although a conclusive picture re-
quires neutron scattering studies, it seems that one of two
interpenetrating Co spin networks acquires a long-range
order below T = 53 K, followed by the other network es-
tablishing long-range order below 20 K. The spatial spin
correlation should be antiferromagnetic (AF), since sus-
ceptibility shows no divergence at T = 53 K [evidence
against ferromagnetism], and the damping of the T = 25
mK data is significantly slower than that of the Bessel
function expected for the incommensurate spin-density-
wave (ISDW) states  [evidence against ISDW].
We also confirmed the absence of static magnetic order
in anhydrous NaxCoO2with x = 0.35 and 0.64, down to
T = 25-35 mK, as shown in Fig. 1(a). Static antiferro-
magnetic order was reported for x = 0.75 - 0.9 by earlier
µSR studies . Together, the present data establish
a rather complicated evolution of the magnetic ground
states from paramagetic (PM) (x = 0.35) to AF (0.5) to
PM (0.64) to AF (0.75) to ISDW (0.9), with increasing
x. The ∼ 2 MHz frequency in the x = 0.5 system is close
to ∼ 3 MHz in x = 0.75, suggesting that the ordered
moment sizes in these systems are of comparable mag-
nitudes. The existence of an insulating magnetic state
in the vicinity of superconductivity resembles the case in
Intercalation of H2O or D2O into the NaxCoO2yields
superconducting systems in a rather narrow range of
x . ZF-µSR is a powerful tool to detect a static
magnetic field due to the particular superconducting
pairing states associated with Time-Reversal-Symmetry-
Breaking (TRSB), as shown in the case of Sr2RuO4.
We observed Gaussian damping of the muon asymmetry
in ZF-µSR of Na0.35CoO2·1.3D2O. This damping is due
to nuclear dipolar fields, and the Gaussian shape comes
from the initial decay of the Kubo-Toyabe function for
nuclear dipolar broadening . Since the recoveryof this
function was missing in our observable time range (up to
8 µs), we fitted this damping with the simple Gaussian
function exp(−σ2t2/2). As shown in Fig. 2(a), the relax-
ation rate σ in ZF is independent of temperature between
T = 6 K and T = 25 mK. The arrows with “TRSB” in-
dicate the expected changes of σ for the TRSB fields
having random directions and Gaussian distribution of
width (RMS second moment) 1 G and 2 G, respectively,
added quadratically to the nuclear dipolar fields. Our
results rule out the existence of a TRSB field above the
1 G level. This is consistent with an earlier report ,
yet we extended the temperature range from 2 K to 25
mK. On a triangular lattice, d-wave pairing has coexisit-
ing real and imaginary parts, resulting in a TRSB field.
The present data sets a rather severe constraint to the
d-wave pairing cases.
µSR data in transverse external fields (TF) reflect field
broadening due to the flux vortex lattice in type-II su-
perconductors, from which one can derive the magnetic
field penetration depth λ [3,5]. We performed TF-µSR
measurements in superconducting samples intercalated
with D2O [Fig. 2 (a)(b)], with the external field TF =
200 G applied perpendicular to the aligned CoO planes.
Figure 2(b) shows the muon spin relaxation rate, fitted
to the Gaussian damping exp(−σ2t2/2), with σnindicat-
ing the average relaxation rate in the normal state. If
the observed change in TF=200 G were due to a mech-
anism sensitive to ZF-µSR, we would have observed a
change of the ZF relaxation rate to the level indicated
by the “TF” arrow in Fig. 2(a). Thus, we proceed our
discussion by assuming that the increase of σ in TF in
Fig. 2(b) is solely due to the in-plane penetration depth
λab. By quadratically subtracting σnfrom the observed
relaxation rate σexp, we obtained the relaxation rate σsc
due to superconductivity as shown in Fig. 3. In separate
measurements (not shown), we found essentially no de-
pendence of σscon TF in the range between 100 G and 2
kG, which assures no involvement of 2-d pancake vortex
In Fig. 3, we compared the temperature dependence
of σsc(T) ∝ λ−2of Na0.35CoO2·1.3D2O with various
models, in a fit of 16 data points with σ(T = 0) as
a free parameter.The observed results clearly dis-
agree with curves of the two-fluid model (normalized chi
square NCS=3.51) and s-wave BCS weak-coupling model
(NCS=1.75, Durbin-Watson value of a normalized resid-
ual error correlations DW=1.11). Comparison with the
scaled µSR results from YBCO  yields NCS=1.39 and
DW=1.59, showing a rather poor agreement yet in a sta-
tistically acceptable range. For a 5% confidence level, a
model with NCS>1.666 or DW<1.1 or DW>2.9 should
be rejected, 1.1<DW<1.37 or 2.63<DW<2.9 is inconclu-
sive, while 1.37<DW<2.63 is comfortably acceptable.
For the cobalt oxide superconductors, several authors
proposed f-wave models [13,20], which have a particular
matching with the symmetry of triangular lattice. In Fig.
3, we also show a theoretical curve for an f-wave pairing,
obtained by using a tight-binding fit of the LDA band
calculation  and by assuming a separable effective in-
teraction supporting a simple f-wave order parameter. In
the present system, there is a large Fermi surface around
the Γ point as well as six small hole-pockets near the
K points. The line in Fig. 3 represents a case where
nodes of f-wave symmetry exist only on the large Fermi
surface and not on the six hole-pockets, while the order
parameter on each Fermi surface has the same maximum
value. This f-wave model gives a good agreement with
the observed data with NCS=1.19 and DW=2.34.
These results rule out a fully isotropic energy gap. Be-
fore concluding a particular pairing symmetry, however,
one has to test various other models with/without the
possible effect of impurities. In ref.  the authors dis-
cussed anisotropy of the energy gap based on TF-µSR
data with a few temperature points below Tc. Our find-
ing of an anisotripic energy gap is consistent with earlier
reports of a power-law T-dependence of the NMR relax-
ation rate 1/T1as well as with the T-independent Knight
shift of NMR  and µSR  below Tc.
The penetration depth λ is related to the supercon-
ducting carrier density nsdivided by the effective mass
m∗as σ(T) ∝ λ−2∝ [4πnse2/m∗c2][1/(1 + ξ/l)], where
ξ is the coherence length and l denotes the mean free
path. At this moment, it is difficult to prove the clean
limit situation ξ << l for the cobalt oxide superconduc-
tor, due to the lack of high-quality superconducting sin-
gle crystals necessary to estimate the in-plane values of
ξ and l. In the following, we proceed the discussion of
the superfluid energy scale ns/m∗by assuming the clean-
limit, in view of an excellent conductivity in anhydrous
Na0.31CoO2 crystals  and high Hc2 values in poly-
crystalline superconducting specimens .
Derivation of the absolute values of λ and ns/m∗is
subject to modeling of flux vortex lattice line shapes, ob-
served functional forms of field distribution, and angular
averaging in the polycrystal samples. Based on the re-
sults of µSR measurements on c-axis aligned YBCO 
and numerical works , we have adopted the conver-
sion factor for polycrystal to aligned samples σaligned∼
1.4σpolyto account for the effect of applying the TF per-
pendicular to the conducting planes of highly 2-d super-
conductors. For σ to λ conversion λ = A/√σ, we have
adopted a factor A = 2,700 [˚ A(µs)1/2] for the Gaussian
width σ. With these conversion factors, the values of
λabof polycrystalline samples of underdoped YBCO with
Tc∼ 60 K  agree well with the value obtained using a
single crystal specimen with comparable Tcin a more ac-
curate line-shape analysis . The above factor A gives
λ = 7,200˚ A for the in-plane penetration depth of the
cobalt oxide system at T → 0.
For highly 2-d superconductors, it is also interesting
to study correlations between Tcand the 2-d superfluid
density ns2d/m∗which can be obtained by multplying
σaligned with the average distance cint of conducting
planes. Figure 4 shows such a comparison, including the
cuprates [3,22], alkali-doped (Hf/Zr)NCl with/without
intercalation of THF (tetrhydrofuran) , and organic
2-d superconductors based on (BEDT-TTF) salts . All
the data points are taken using single crystal or aligned
samples with TF perpendicular to the conducting planes,
while “cuprate” lines represent polycrystal results [1,3]
after the factor 1.4 correction. We find that Tc of all
these 2-d superconductors could have a common relation-
ship to the 2-d superfluid density ns2d/m∗, which can be
converted into corresponding 2-dimensional Fermi energy
as given in the lower horizontal axis.
Based on correlations between Tc and the superfluid
density in the cuprates, Emery and Kivelson  proposed
a picture in which Tcis determined by phase fluctuations
in the argument essentially identical to the Kosterlitz-
Thouless (KT) theory . In KT transitions, Tcand the
superfluid density at the transition temperature TKTare
related with a universal system-independent relationship,
which is shown by the TKT line in Fig. 4. In Fig. 4,
most of the points lie at about a factor 2-3 away in the
horizontal axis from the TKTline, which implies that the
superfluid density undergoes about a 2-3 times reduction
from the T = 0 value to the value near Tcwhere phase
fluctuations may destroy 3-d superconductivity. In the
cuprates, this reduction could be related to excitations
of nodal quasi particles, or classical thermal fluctuations,
or some elementary excitations. Further studies for the
origin of the T-dependence of σ(T) could provide a key
to understanding the correlations shown in Fig. 4.
If we assume the charge carrier density to be equal
to the Na concentration, we obtain the in-plane effec-
tive mass of the cobalt-oxide superconductor to be about
100 times the bare electron mass me. A similar esti-
mate for m∗was given in ref. . The heavy mass can
be expected for strongly correlated carriers in a trian-
gular lattice . The high effective mass is consistent
with the electronic specific heat C/T ∼ 12 [mJ/mole K2]
of the superconducting cobalt oxide  just above Tc.
This value can be compared to ∼ 2 [mJ/mole K2] of
YBa2Cu3O7. After normalizing the values to a unit
sheet area of conducting planes, C/T for the cobalt oxide
becomes about 25 times larger than that for YBCO. In
the non-interacting 2-d Fermi gas, C/T is proportional
to m∗but independent of carrier density. Thus, within
this approximation, we expect m∗of cobalt oxide to be
25 times that of the cuprates.
In conclusion, we have shown that the cobalt oxide
superconductors have an anisotropic energy gap and a
heavy effective mass m∗∼ 100me, without a TRSB field
(limit given as 1 G). We established the existence of an
antiferromagnetic insulating compound in the vicinity of
the superconducting cobalt-oxide system without mag-
netic order, which suggests the possible involvement of
magnetism in the superconducting mechanism.
The work at Columbia has been supported by the
NSF DMR-0102752 and CHE-0117752 (Nanoscale Sci-
ence and Engineering Initiative), at Princeton by NSF
DMR-0213706 (MRSEC) and by the DOE DE-FG02-98-
ER45706, and at McMaster by NSERC and the CIAR
(Quantum Materials Program). We acknowledge F.D.
Callaghan and J.E. Sonier for technical assistance.
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zero field in anhydrous NaxCoO2 with x = 0.50, 0.35 and
0.64. (b) The muon spin precession frequency observed in the
x = 0.5 system, shown with the resistivity in the inset .
(a) Muon spin relaxation time spectra observed in
ducting specimen of Na0.35CoO2·1.3D2O, which has Tc(χ) =
4.2 K from susceptibility χ. (a) shows results in zero field,
while (b) in TF = 200 G applied perpendicular to the con-
ducting planes. See text for the arrows in (a) and σn in (b).
Muon spin relaxation rate observed in a supercon-
FIG. 3: Muon spin relaxation rate σsc(T) due to supercon-
ductivity in Na0.35CoO2·1.3D2O, with TF = 200 G applied
perpendicular to the aligned conducting planes, obtained by
quadratic subtranction of σ2
σn are shown in Fig. 2(b). The results are compared with
fits to several models and the scaled plot of µSR results on
YBa2Cu3O6.95 (YBCO) .
n, where σexp and
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FIG. 4: A comparison of highly 2-d superconductors in a plot
of Tc versus σsc(T = 0), multiplied by the average interlayer
distance cint of the conducting planes. Data points are from
aligned pellet or single-crystal specimens [6,22,24], while the
dotted lines are from ceramic specimens of YBCO [1-3] after
a factor 1.4 correction. For σ × cint ∝ ns2d/m∗, we show the
corresponding Fermi temperature TF2dof the 2-d electron gas.