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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 [3].

To these superconductors based on strongly correlated

electrons, the recent discovery of superconductivity in

Na0.35CoO2 intercalated with 1.3 H2O [7] 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 [8], 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

The tempera-

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 [16] studies

of mangetic order in non-superconducting anhydrous

NaxCoO2. Recent resistivity and susceptibility studies

by Foo et al. [15] 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

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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 [17] [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 [18]. 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

the cuprates.

Intercalation of H2O or D2O into the NaxCoO2yields

superconducting systems in a rather narrow range of

x [14]. 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[19].

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 [16]. 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 [10],

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

formation [5].

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 [5] 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 [13] 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. [11] 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 [9] and µSR [10] 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

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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 [15] and high Hc2 values in poly-

crystalline superconducting specimens [21].

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 [22]

and numerical works [23], 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 [1] agree well with the value obtained using a

single crystal specimen with comparable Tcin a more ac-

curate line-shape analysis [5]. 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) [24], and organic

2-d superconductors based on (BEDT-TTF) salts [6]. 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 [4] proposed

a picture in which Tcis determined by phase fluctuations

in the argument essentially identical to the Kosterlitz-

Thouless (KT) theory [25]. 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. [11]. The heavy mass can

be expected for strongly correlated carriers in a trian-

gular lattice [12]. The high effective mass is consistent

with the electronic specific heat C/T ∼ 12 [mJ/mole K2]

of the superconducting cobalt oxide [26] just above Tc.

This value can be compared to ∼ 2 [mJ/mole K2] of

YBa2Cu3O7[27]. 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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(a)

(b)

T(K)

0

4

8

16

12

FIG. 1:

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 [15].

(a) Muon spin relaxation time spectra observed in

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FIG. 2:

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) [5].

sc= σ2

exp− σ2

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.