jong-soo rhyee et al- anisotropic magnetization and charge density wave in a na0.78coo2 single...

8/3/2019 Jong-Soo Rhyee et al- Anisotropic Magnetization and Charge Density Wave in a Na0.78CoO2 Single Crystal

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Journal of the Korean Physical Society, Vol. 52, No. 2, February 2008, pp. 391395

Anisotropic Magnetization and Charge Density Wave ina Na0.78CoO2 Single Crystal

Jong-Soo Rhyee, J. B. Peng and C. T. Lin

Max-Plank-Institute for Solid State Research, Heisenbergstrasse 1, Stuttgart, Germany D-70569

S. M. Lee

Advanced Materials Lab., Samsung Advanced Institute of Technology, Suwon 440-600

(Received 15 October 2007)

Single crystals ofNa0.78

CoO2

were grown using the floating zone method. The static magneticsusceptibility M/H(T) of Na0.78CoO2 showed significant anisotropic behavior for different crystalorientations of H (ab) and H (c). While (M/H)ab(T) for a magnetic field H = 1 T in anab-plane followed the Curie-Weiss law at high temperatures (T 100 K), (M/H)c(T) for H c-axis deviated from Curie-Weiss behavior, which may be understood by using phonon localizationfrom strong electron-phonon coupling. The impurity spin-1/2 effect, dressed by spin fluctuation,was significant at low temperatures (T 30 K) for both field orientations ofH (ab) and H (c).The electrical resistivity (T) of Na0.78CoO2 showed a clear metallic character down to 16 K, witha weak increase in the resistivity (T) at low temperatures (T 16 K). The gap-like behavior of(T) was insensitive to applied magnetic fields up to 7 T, which indicates a non-degenerate chargegap. The electrical conductivity (T) followed the density wave behavior with a small energy gap(0.64 meV) at low temperatures. We discussed the electrical resistivity (T) and the anisotropicM/H(T) behavior of Na0.78CoO2 in terms of the charge density wave and a strong electron-phononinteraction.

PACS numbers: 75.30.Gw, 75.50.Ee, 71.45.Lr, 75.30.Mb

Keywords: Magnetic anisotropy, Crystal growth, Electron-phonon interactions, Valence fluctuations

I. INTRODUCTION

Much attention has been given to the NaxCoO2 systembecause of its emergent unconventional physical proper-ties since the discovery of superconductivity at Tc 4.5K for hydrated compounds of NaxCoO2yH2O (x 0.35,y 1.3) and because of the significantly enhanced ther-mopower of Na0.85CoO2 [13]. NaxCoO2 is a layeredcompound in which the Na charge reservoir layer is in-terspaced between CoO2 layers. The Na deintercalationand hydration reinforce the two-dimensional characterof NaxCoO2 by expanding the charge reservoir layer [4,5]. The two-dimensional anisotropic properties are stillevident for non-hydrated NaxCoO2 series compounds interms of electronic and magnetic ground states. Fromthe polarized- and unpolarized-neutron inelastic scatter-ing measurements of Na0.75CoO2, the ferromagnetic spinfluctuation was observed within the CoO2 layers whereasthe antiferromagnetic correlation was seen perpendicularto the layers, which corresponds to A-type antiferromag-

Corresponding Author: [email protected];E-mail: [email protected]

netic ordering [6,7].The two-dimensional spin state of the NaxCoO2 sys-

tem (x 0.75), which neutron diffraction studies con-firm as following an A-type antiferromagnetic order, isnot trivial for the broad range of Na non-stoichiometryx. The magnetic spin of this system is strongly corre-lated with the competing orders of the charge, orbital,and lattice degrees of freedom. The spectral ellipsom-

etry measurement shows that the spin-charge couplingis strong in the Na0.82CoO2 compound, which meansa charge-induced spin-state transition of the Co3+ ions[8]. In addition, the A-type antiferromagnetic order ofNa0.82CoO2 was characterized by spin wave dispersionsin a neutron diffraction experiment [9]. The magneticground states and the anisotropic properties of NaxCoO2are very different with respect to the Na concentration xbecause of the spin state of Co in the NaxCoO2 systembeing strongly influenced by the Na concentration. Theparent compound of CoO2 is regarded as an orbitallynondegenerate spin-1/2 antiferromagnetic Mott insula-tor with Co4+ [10]. In stoichiometric NaCoO2, the Co

spin state is the low spin state of Co3+

(t6

2g) with S = 0.For the intermediate region of Na concentration (x < 1),

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a mixed valent system between Co3+ and Co4+ wouldbe revealed in the NaxCoO2 system. The Na concen-tration controls both the carrier concentration and themagnetic moment due to Co4+ ions. From the uncon-

ventional magnetic ground states of the A-type antifer-romagnetic order and the spin density wave behavior inNa0.75CoO2 and Na0.82CoO2, respectively, the uncon-ventional spin state and the anisotropic properties of themagnetic and the electronic transport for NaxCoO2(0.75 x 0.82) compounds are of particular interest.

Presented in this paper are the anisotropic magneticground states and the electrical transport properties ofa high-quality Na0.78CoO2 single crystals grown usingthe floating zone method. The crystals two-dimensionalcharacteristics are identified by using the density wavegap in the electrical resistivity (T) and the stronganisotropic behavior of the magnetization M/H(T) with

respect to different magnetic field directions of H(c)-axis and H(ab)-plane of the Na0.78CoO2 compounds.The magnetic susceptibilities under a magnetic fieldH along the c- and the ab-directions show logarithmi-cally divergent behaviors of (M/H)ab(T) at low tem-peratures (T 20 K) and non-Curie-Weiss behaviorsof (M/H)c(T) at high temperatures (T 100 K), re-spectively. The unconventional electronic and magneticproperties are interpreted in terms of charge density waveand strong electron-phonon coupling under a spin fluc-tuation background, respectively.

II. EXPERIMENTAL DETAILS

The single crystals of Na0.78CoO2 were obtained us-ing the traveling solvent optical floating zone method[11]. Because of the strong volatilization of Na duringthe feed rod synthesis and the crystal growth, an excessof Na was added with an initial molar ratio of Na : Co =0.85 : 1.0. A well-mixed powder of Na2CO3 and Co3O4was put in an alumina crucible, calcined and sintered at750 C and 850 C for a day, respectively. The sinteredpowder was reground and made into a 6 mm 150 mmcylindrical bar with a hydrostatic pressure of 80 kN for

1 min. The bar was sintered at 850 C for a day withflowing oxygen in a tube furnace. The sintered rod waspremelted at a high traveling rate of 27 mm/h for a pre-densification of the rod. The premelted rod and a smallpiece of the same body (20 mm) were used for the feedand the seed rod, respectively, for the crystal growth.The feed and the seed rods were rotated at 15 rpm inopposite directions for homogeneous melting. The crys-tal growth traveling rate was 2 mm/h under an oxygenenvironment (200 cc/min).

The grown large single crystal could be easily cleaveddue to the layered structure. The chemical concen-trations of the nominal compound Na0.85CoO2 werecarefully analyzed using energy dispersive X-ray spec-troscopy (EDX) and inductively coupled plasma-atomic

Fig. 1. X-ray diffraction pattern of the single-crystallinecompound Na0.78CoO2. The sharp (00l) peaks indicate wellaligned high quality single crystal.

emission spectroscopy (ICP-AES). The final chemicalformula was confirmed as Na0.78CoO2. The chemicaldistribution images generated by EDX confirmed thatthe chemical inhomogeneity of the Na ions was less than2 at.%. The X-ray diffraction patterns of the pulverizedsingle crystals confirmed that the crystals were singlephase with NaxCoO2 (P63/mmc phase). The latticeparameters of Na0.78CoO2 were c = 10.80 A and a =

2.83 A. The crystal orientation was determined usingthe X-ray diffraction measurements. Figure 1 shows thewell-aligned sharp (00l) peaks in the caxis, perpendic-ular to the crystal plane. The temperature-dependentDC-magnetization M(T, H) and the electrical resistiv-ity (T, H) were measured using a magnetic propertymeasurement system (MPMS) and a physical propertymeasurement system (PPMS, Quantum Design, USA)in the temperature range of 2 K T 300 K under theindicated magnetic fields.

III. RESULTS AND DISCUSSION

Figure 2 shows the temperature-dependent magneticsusceptibility (M/H)ab(T) under a magnetic field ofH =1 T for the in-plane direction of the Na0.78CoO2 crystalwithin a temperature range of 2 K T 300 K. Themagnetic susceptibility (M/H)ab increases with decreas-ing temperature, following the broad peak near T = 30K. At low temperatures (T 20 K), (M/H)ab signifi-cantly increases with decreasing temperature. The in-verse magnetic susceptibility (H/M)ab(T) is shown inthe upper right inset of Figure 2. It follows the Curie-Weiss law (T) = C/(T) at high temperatures (T100 K). From the Curie-Weiss fitting in this temperatureregion (100 K T 300 K), the effective magnetic mo-


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Fig. 2. Temperature-dependent static magnetic suscep-tibility (M/H)ab(T) of Na0.78CoO2 under a magnetic fieldof H = 1 T parallel to the ab-direction in the temperaturerange of 2 K T 300 K. The upper right inset shows theinverse magnetic susceptibility (H/M)ab(T) of Na0.78CoO2.The Curie-Weiss behavior fitted the data well in the high-temperature region (T 100 K). The lower left inset shows asemi-log plot of the magnetic susceptibility (M/H)ab versusthe inverse temperature 1/T in the temperature range of 2K T 7.5 K. The logarithmic divergent behavior at lowtemperatures indicates an impurity spin-1/2 effect dressed bythe spin fluctuation: = 0 + ln(T

/T)/T.

ment and the Weiss temperature are estimated as eff =0.69 B and p = 3.98 K, respectively. The small neg-ative Weiss temperature p refers to a weak antiferro-magnetic interaction in the basal plane. If we assume thelow-spin state of Co ion, the effective magnetic momentsof Co4+ (3d5, S = 1/2) and Co3+ (3d6, S = 0) are 1.732B and zero B , respectively. Under the assumptionof Co low-spin states, the magnetic susceptibility comesfrom Co4+ ions with a partial fraction of 40 at.%. Thepartial fraction of the Co4+ ion indicates mixed valentstates of Co3+ and Co4+ ions.

The Co3+ ion, however, might have undergone a spinstate transition from low spin (LS, S = 0) to interme-diate spin (IS, S = 1) in the NaxCoO2 system. Fromthe optical conductivity measurements of Na0.82CoO2,the charge excitation pseudo-gap was observed [8]. Thepseudo-gap can be understood by using the spin statetransition from low spin to intermediate spin of Co3+

ions. Bernhard et al., from their muon spin rotation(SR) experiment, argued that a low-spin Co4+ (S =1/2) is surrounded by six intermediate-spin Co3+ (S =1) ions in NaxCoO2 [12]. The spin state transition iswidely observed in layered cobaltates, as for example, inperovskite cobaltates R1xAxCoO3 (R: rare earth and A:alkaline-earth elements) [13]. In this system, the Co3+

spin state varies via a spin-state transition from a low

spin (LS, t62g, S = 0) to an intermediate spin (IS, t52ge

1g,

S = 1) or a high spin (HS, t42ge2g, S = 2) with respect

to temperature. The coexistence of the spin-state transi-tion from the low (S = 0) to the intermediate spin states(S = 1) of the Co3+ ions and the mixed valence betweenthe Co3+ and Co4+ ions can easily invoke a spin fluc-tuation behavior. Actually, CoO2 intrinsically developsspin fluctuation at low temperatures, as confirmed bythe 59Co NMR study [14]. In the NaxCoO2 system, thespin fluctuation in the CoO2 layer is widely observed fora broad range of Na non-stoichiometries via the neutronscattering and NMR measurements [6,7,15].

The broad shoulder of (M/H)ab near T 30 K andthe sharp increase in its magnetic susceptibility at lowtemperatures (T 20 K) may have originated from thespin fluctuation of the Co ions between Co3+ (LS andIS) and Co4+ in the Na0.78CoO2 compound. At low tem-peratures (T 20 K), the (M/H)ab(T) logarithmicallydiverges. The lower left inset of Figure 2 shows a semi-log plot of the magnetic susceptibility (M/H)ab versusthe inverse temperature 1/T in the temperature range of2 K T 7.5 K. This shows a logarithmic behavior ofthe reciprocal temperature as ln(1/T). The strongCurie divergence at low temperatures is commonly ob-served in the two-channel Kondo model [16]. Clarke etal. argued that the sublattice symmetric impurity spincoupled with an antiferromangetic background is equiv-alent to the two-channel Kondo effect [17]. In the case ofthe spin-1/2 impurity, the spins form a collective motionof spinons through spin pairing, which results in a degen-erate ground state. If the impurity spin-1/2 is dressed bya spin fluctuation under a background antiferromagneticstate, the susceptibility diverges logarithmically: =0 + ln(T

/T)/T, where T is the characteristic tem-perature (T T) defined by T Jexp(Const.J/g)for weak coupling g J (g: coupling strength, J: trans-fer integral). The fitting parameters 0 = 2.5 10

4

emu/moleOe and T = 10,451.02 K = 0.9 eV are de-rived from = 0 + ln(T

/T)T.The magnetic susceptibility (M/H)c(T) under a mag-

netic field H = 1 T along the c-direction is quite differ-ent from (M/H)ab(T), as shown in Figure 3. It does notfollow the Curie-Weiss law at high temperatures. The(M/H)c(T) decreases with decreasing temperature downto 40 K, with a subsequent significant increase in sus-ceptibility for 10 K T 30 K. The antiferromagneticordering is observed near TN = 8 K, which is reasonabledue to the antiferromagnetic interaction, as confirmed bythe Weiss temperature p = 3.98 K from the Curie-Weiss fitting in the ab-direction. In an intermediate-temperature region, 60 K T 180 K, a logarithmictemperature behavior of the susceptibility is observed viathe expression = 0 + q ln(r + T), where 0, q and rare free parameters of 0 = 0.21 10

3 emu/moleOe,q = 0.12 103 emu/KmoleOe, and r = 2.41 K. Thelogarithmic temperature-dependent behavior of the sus-ceptibility is from the localized phonon based on the


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Fig. 3. Temperature-dependent static magnetic suscepti-bility (M/H)c(T) of Na0.78CoO2 under a magnetic field ofH= 1 T parallel to the c-direction in the temperature rangeof 2 K T 300 K. The inset shows an expanded plot in thetemperature range of 60 K T 180 K. The fitted line isbased on the localized phonon model, which is described by = p+q ln(r+T), due to a strong electron-phonon coupling.

strong electron-phonon coupling [18,19]. Strong electron-phonon coupling is observed in compounds of the higherNa concentrations. The optical conductivity measure-

ment for Na0.85CoO2 shows a phonon mode, stronglycoupled with lattice vibration, for a broad range of tem-peratures [8]. The anomalous phonon mode may havecome from a pinned collective phase mode of the chargedensity wave and from the polaronic band [20]. Becauseof the strong electron-phonon interaction, polaronic hop-ping is revealed in the marked blue shift of the opticalconductivity in Na0.85CoO2. The significant increase in(M/H)c(T) with decreasing temperature (10 K T 30 K) can be understood via an impurity spin fluctuationbehavior, as in the case of (M/H)ab(T) at low tempera-tures.

The charge density wave or polaronic hopping trans-

port can be found in the electrical transport proper-ties of Na0.78CoO2. The electrical resistivity (T) ofNa0.78CoO2 is presented in Figure 4. It shows a typicalmetallic character from room temperature down to 16 K.At low temperatures (T 15 K), (T) slightly increaseswith decreasing temperature. In this temperature range,there is no indication of a phase transition. The energy-gap property of (T) can be expressed by an exponen-tial temperature behavior of the electrical conductivity(T) = 1/. The lower right inset of Figure 4 shows theelectrical conductivity versus the inverse temperature1/T. It follows the exponential behavior of (T) givenby the equation (T) = 0+A exp(/kBT), where theresidual conductivity 0, the prefactor A and the energygap are 0 = 23.75 (m-cm)

1, A = 26.31 (m-cm)1

Fig. 4. Temperature-dependent electrical resistivity (T)of Na0.78CoO2 from 2 K to 300 K in which an electric currentis driven along the ab-plane. The upper left inset shows anexpanded plot of the electrical resistivity (T, H) under var-ious magnetic fields, as indicated, at low temperatures (2 K T 20 K). The lower right inset shows the conductivity versus the inverse temperature 1/T at low temperatures (2 K T 10 K). The exponential thermal excitation behaviorfitted the data well in this temperature region.

and = 7.46 K = 0.64 meV, respectively. The energy

gap is very small and is insensitive to the applied mag-netic field, as shown in the upper left inset of Figure 4.Up to an applied magnetic field H = 7 T, the (T) doesnot change. This indicates that the energy gap is nota spin gap but a charge gap. If the energy levels nearthe band gap edge are degenerated, the energy gap de-creases under a magnetic field due to Zeeman splitting.Lowering the local symmetry breaks the degeneracy. Thelocalized positive charge of the Co4+ ion and the neigh-boring oxygen can easily lower the local symmetry of theCo3+ ion. The field-insensitive behavior of (T) refers toa non-degenerated charge gap caused by local symmetrybreaking.

The non-degenerated charge gap can be understoodfrom the charge density wave gap by considering theuniversal two-dimensional transport properties of theNaxCoO2 system. As mentioned previously, the strongphonon mode of Na0.85CoO2 from the optical conductiv-ity can be characterized by either polaronic transport ora collective phase mode of the charge density wave. Thecharge density wave develops a single-particle energy gapnear the Fermi level. In the charge density wave state,the electrical conductivity follows an exponential tem-perature behavior at low temperatures, as shown in thelower right inset of Figure 4. However, no charge den-sity wave phase transition is observed in the tempera-ture range of 2 K T 300 K. If the three-dimensionallong-range order and the second-order phase transition


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Anisotropic Magnetization and Charge Density Wave in Jong-Soo Rhyee et al. -395-

of the charge density wave is considered, the weak cou-pling BCS (Bardeen-Cooper-Schrieffer) theory predictsthe relationship between the charge density wave gap and the transition temperature T3D as 2/kBT3D =

3.25 [21]. From this assumption, the T3D should be near4.2 K. As we mentioned previously, however, the intrin-sic nature of the NaxCoO2 system is two dimensional.Therefore, the charge density wave transition may beobserved at temperatures lower than 2 K. Another thingis that the second-order phase transition with a small en-ergy gap cannot be detected via the electrical resistivity.In this case, a hidden second-order phase transition canbe found in a specific heat measurement at temperatureslower than 2 K.

IV. CONCLUSION

In summary, a high-quality single-crystalline com-pound of Na0.78CoO2 was successfully synthesized usingthe traveling solvent floating zone method. The magne-tization measurement showed a highly anisotropic be-havior with different field orientations of H(ab) andH(c). The (M/H)ab(T) with H = 1 T along the (ab)-direction followed the Curie-Weiss law at high tempera-tures (T 100 K). The broad shoulder near 30 K andthe subsequent significant increase of (M/H)ab(T) withdecreasing temperature (T 20 K) may imply a spinfluctuation and an impurity 1/2-spin effect dressed by a

spin fluctuation, respectively. The non-Curie-Weiss be-havior for (M/H)c(T) along the magnetic field in the(c)-direction may be understood by using the localizedphonon mode from the strong electron-phonon coupling.A two-dimensional nature was observed via electrical re-sistivity measurements and the anisotropic behavior ofthe magnetic susceptibility. In the electrical resistivity(T) at low temperatures (T 16 K), a small gap-likeincrease of (T) was revealed. The field-insensitive be-havior of (T, H) for various magnetic fields up to 7 Tmay come from a non-degenerate small charge densitywave gap = 0.64 meV, which is evidence for the two-dimensional nature of the Na0.78CoO2 compound.

ACKNOWLEDGMENTS

The authors acknowledge G. Gotz and Christof Buschfor their technical assistance.

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