Crossover from itinerant to localized states in the thermoelectric oxide [Ca_2CoO_3]_{0.62}[CoO_2]
CCrossover from itinerant to localized states in the thermoelectric oxide [Ca CoO ] . [CoO ] H. Sakabayashi and R. Okazaki
Department of Physics, Faculty of Science and Technology, Tokyo University of Science, Noda 278-8510, Japan
The layered cobaltite [Ca CoO ] . [CoO ], often expressed as the approximate formula Ca Co O , is apromising candidate for e ffi cient oxide thermoelectrics but an origin of its unusual thermoelectric transportis still in debate. Here we investigate in-plane anisotropy of the transport properties in a broad temperaturerange to examine the detailed conduction mechanism. The in-plane anisotropy between a and b axes is clearlyobserved both in the resistivity and the thermopower, which is qualitatively understood with a simple bandstructure of the triangular lattice of Co ions derived from the angle-resolved photoemission spectroscopy ex-periments. On the other hand, at high temperatures, the anisotropy becomes smaller and the resistivity showsa temperature-independent behavior, both of which indicate a hopping conduction of localized carriers. Thusthe present observations reveal a crossover from low-temperature itinerant to high-temperature localized states,signifying both characters for the enhanced thermopower. I. INTRODUCTION
The layered cobaltites provide fascinating platform for ex-ploring functional properties of oxides both in fundamentaland applicational viewpoints [1]. Since the discovery of largethermopower in the metallic Na x CoO [2], this class of ma-terials has been recognized as potential oxide thermoelectricsthat possesses a high-temperature stability in air [3–5]. Thecrystal structure of this family is composed of two subsys-tems of an insulating layer and CdI -type CoO conductionlayer alternately stacked along the c axis. As for the origin ofthe large thermopower coexisting with the metallic conductiv-ity, Koshibae et al. have suggested a localized model in whicha hopping conduction of correlated d electrons with spin andorbital degeneracies involves large entropy flow [6]. This pic-ture is supported by magnetic field dependence of the ther-mopower [7] and is also discussed in semiconducting cobaltoxides [8]. On the other hand, Kuroki et al. have proposedan itinerant model based on “pudding-mold” band structure,in which the di ff erence in velocities of electrons and holes iscrucial [9]. Indeed, such a peculiar band shape is observedby angle-resolved photoemission spectroscopy (ARPES) ex-periments [10–14] and a large value of thermopower is calcu-lated accordingly [15, 16], remaining the detailed conductionmechanism in this system controversial.The misfit oxide [Ca CoO ] . [CoO ] [17–19] is a suitablecompound to shed light on above fundamental issue, becauseit straddles a border between localized and itinerant states ofCo 3 d electrons, from which interesting emergent phenomenaappear in correlated electron systems [20]. As shown in Figs.1(a) and 1(b), this material has a rocksalt-type Ca CoO blockas an insulating layer and its b -axis lattice parameter b is dif-ferent from that of CoO layer b , leading to a misfit structurewith incommensurate ratio of b / b (cid:39) .
62 while this sys-tem is often referred as the approximate formula Ca Co O .The metallic transport properties, along with a spin-density-wave (SDW) formation at T SDW (cid:39)
30 K [22–24], indicate anitinerant nature, although the magnetic structure revealed byrecent neutron experiments is quite unconventional [25]. Onthe other hand, compared with that of Na x CoO , this com-pound has moderately high resistivity [26], which is close tothe Io ff e-Regel limit [18]. Negative magnetothermopower is also found in [Ca CoO ] . [CoO ] [27]. In addition, largethermopower of Q (cid:39) µ V / K near room temperature is wellexplained in the extended Heikes formula based on the local-ized hopping picture of correlated electrons [28], which pre-vails not only in the conduction layer but also the rocksalt oneas suggested by recent spectroscopic studies [29]. These ex-perimental facts imply a complicated coexistence of itinerantand localized nature in this compound.In this study, we argue the itinerancy and localization ofconduction electrons in [Ca CoO ] . [CoO ] by means of in-plane transport anisotropy measurements between a - and b -axis directions. This is less investigated so far compared tothe strong anisotropy between in-plane and out-of-plane di-rections [18, 30] but is essential for thorough understandingof the underlying conduction mechanism. We find a con-siderable temperature dependence of the in-plane anisotropyboth in resistivity and thermopower. Below room temperature,the in-plane anisotropy is relatively large and qualitatively ex-plained by the anisotropy of the electronic velocities near theFermi energy estimated from the results of ARPES experi-ments [31]. This is also consistent with the results of recent (a) (b) b CoO layerCa CoO layer b b a b c ab b FIG. 1. Schematic view of the crystal structure of layered[Ca CoO ] . [CoO ] projected from (a) a axis and (b) c axis drawnby VESTA [21]. While the a -axis lattice parameter a is common, the b -axis lattice parameter of the rocksalt layer b is di ff erent from thatof CoO layer b , resulting in a misfit structure with incommensu-rate ratio of b / b (cid:39) .
62. The Co ions in CoO (green) and rocksalt(blue) layers are shown in di ff erent colors for clarity. a r X i v : . [ c ond - m a t . s t r- e l ] F e b (a) (b) a * b * ab (c) (d)1 mm0.5 mm0.5 mm ab FIG. 2. (a) Photograph of a single crystal of [Ca CoO ] . [CoO ]and (b) Laue pattern. (c) Photographs of samples for the resistivitymeasurements. Two samples with the rectangular shape of ∼ × . were obtained by cutting one single crystal. (d) SEM imageof [Ca CoO ] . [CoO ] for the sample thickness measurement. band calculation [32], indicating the itinerant nature in thissystem. Near T SDW (cid:39)
30 K, the in-plane anisotropy drasti-cally varies possibly due to a reconstruction of the Fermi sur-face. Above room temperature, in contrast, we find that thein-plane anisotropy is close to unity as temperature increases,which is captured as a localized picture. The present resultsunveil the temperature-induced crossover from itinerant to lo-calized states in [Ca CoO ] . [CoO ]. II. EXPERIMENTS
Single crystals of [Ca CoO ] . [CoO ] were grown by aflux method [33]. Powders of CaCO (99.9%) and Co O (99.9%) were mixed in a stoichiometric ratio and calcined twotimes in air at 1173 K for 20 h with intermediate grindings.Then KCl (99.999%) and K CO (99.999%) powders mixedwith a molar ratio of 1 : 4 was added with the calcined powderas a flux. The concentration of [Ca CoO ] . [CoO ] was setto be 1.5% in molar ratio. The mixture was put in an aluminacrucible and heated up to 1123 K in air with a heating rate of200 K / h. After keeping 1123 K for 1 h, it was slowly cooleddown with a rate of 1 K / h, and at 1023 K, the power of thefurnace was switched o ff . As-grown samples were rinsed indistilled water to remove the flux and then annealed in air at573 K for 3 h.The typical dimension of obtained single crystals is (cid:39) × × .
01 mm as shown in Fig. 2(a). The crystal orientation wasdetermined by the Laue method. Although the spot intensityis weak in such thin samples, three-fold symmetry from CoO layer and four-fold symmetry from the rocksalt layer are re-solved in the Laue pattern shown in Fig. 2(b). To discuss theanisotropy precisely, we cut one single crystal into two sam- !" &’ !" ! " ( ) * + ) , $’’ & ! " ( + ) , $’’ ’ ! " ( . , $’’ (6,(7,(+, FIG. 3. Temperature variations of (a) resistivity ρ i ( i = a , b ), (b)conductivity σ i = ρ − i , and (c) thermopower Q i measured along the a - (red) and b -axis (blue) directions in [Ca CoO ] . [CoO ]. ples with the same rectangular shape of (cid:39) × . forthe transport measurements along the a and b axes as shownin Fig. 2(c). This method enables us to compare the trans-port properties of the samples with the same oxygen contents.Note that the resistivity anisotropy was also checked by uti-lizing the Montgomery method near room temperature [34],although it may produce a fairly large systematic error bar[35]. The sample thickness of (cid:39) µ m was determined bythe scanning electron microscopy (SEM) as shown in Fig.2(d). The resistivity and the thermopower were simultane-ously measured by using a conventional four-probe methodand a steady-state method, respectively. The thermoelectricvoltage from the wire leads was carefully subtracted. We useda Gi ff ord-McMahon refrigerator below room temperature andan electrical furnace for high-temperature measurement. III. RESULTS AND DISCUSSIONA. Temperature variations of resistivity and thermopower
Figures 3 summarize the temperature variations of the in-plane transport properties in [Ca CoO ] . [CoO ]. Hereafterwe use an abbreviated form like ρ a ( = ρ aa ) for the resistivitymeasured along the a -axis direction. Overall behaviors arewell reproduced compared with the earlier reports in whichthe transport coe ffi cients are measured with no distinctionamong the in-plane directions [18]. In addition, the ther-mopower measured along the b axis Q b is larger than thatalong the a axis Q a , consistent with recent theoretical cal-culation [32]. At low temperature below ∼
100 K, the re-sistivity shows an insulating behavior while the thermopowerseems to be metallic, which are discussed in terms of carrierlocalization [36], pseudogap opening [37], or quantum criti-cality [38]. Near room temperature, the thermopower showsa temperature-independent behavior with a relatively largevalue of Q (cid:39) µ V / K, quantitatively explained by the ex-tended Heikes formula of Q = − k B e ln (cid:32) g g y − y (cid:33) , (1)where k B is the Boltzmann coe ffi cient, e the elementarycharge, g and g the spin and orbital degeneracies of Co + and Co + ions, respectively, and y the Co + (hole) concen-tration [6]. Enhancement of the thermopower above roomtemperature may be possibly attributed to a small spin-statechange near T (cid:39)
380 K [39], above which the degeneracyratio g / g may vary with temperature. At this temperature,a small anomaly has been observed in several quantities suchas the resistivity, magnetic susceptibility, heat capacity, andlattice constants [18, 22, 39]. On the other hand, the magni-tude of the resistive anomaly may be sample-dependent [40]and is not resolved in the present samples. Although thepresent measurements are limited below 600 K, the increaseof thermopower may continue up to 1000 K according to high-temperature transport experiments in this compound [41]. B. Localized state at high temperatures
We first discuss high-temperature transport. The inset ofFig. 4(a) shows the temperature dependence of the anisotropyof thermopower Q b / Q a . The anisotropy Q b / Q a decreaseswith increasing temperature and becomes close to unity near600 K. This behavior is well consistent with the localizedmodel, because the thermopower at high temperatures can beexpressed by using chemical potential µ as Q = − µ eT , (2)which leads to the Heikes formula of Eq. (1) [6], and thechemical potential in the numerator is a thermodynamic quan-tity, which does not give the anisotropic property. Note thatother parameters to produce the anisotropy such as velocity FIG. 4. Temperature variations of the transport anisotropy in (a)thermopower Q b / Q a and (b) electrical conductivity σ b /σ a belowroom temperature. The SDW transition temperature T SDW (cid:39)
30 Kand its onset T ONSDW (cid:39)
100 K are indicated by the dashed lines. Theinsets depict these anisotropies in the whole temperature range mea-sured in the present study. and relaxation time are cancelled out in Eq. (2). Therefore,the thermopower anisotropy, which should be unity within theHeikes formula, is an indicator for localized electronic state.Moreover, as shown in Fig. 3(a), the resistivity becomesless temperature-dependent in both directions at high tem-peratures. Such a behavior has also been observed in high-temperature transport study while the in-plane orientation isundetermined [41], and is described as the hopping conduc-tion at the Io ff e-Regel limit [42–44], at which the Fermi wave-length λ F ( = π/ k F ) ( k F being Fermi wavenumber) is compa-rable to the mean free path l of conduction electrons. Indeed,the dimensionless value of k F l estimated from k F l = π (cid:126) c e ρ , (3)where (cid:126) is the reduced Planck constant and c is the c -axislength [37], is calculated as k F l ∼ .
54 for the a - and 0 . b -axis directions. Although there is an unavoidable er-ror bar mainly due to the sample thickness, these values areclose to unity, indicating the hopping conduction. Thus, thesetransport coe ffi cients indicate the localized nature at high tem-peratures. ! " ! " % & ’ ! " "% $ % $ & + % , - . ’ ’ ( ) %/’ !* $ % $ & " % , - . ’ ! " %1’ FIG. 5. (a) Constant-energy surfaces near the Fermi energy cal-culated by using the tight-binding model [Eq. (4)]. (b) Dispersionrelations along Γ → K ( a ∗ direction, red) and Γ → M ( b ∗ direction,blue). C. Itinerant state at low temperatures
We then focus on low-temperature transport anisotropy be-low room temperature. The main panels of Figs. 4(a) and4(b) show the temperature variations of the anisotropies ofthermopower Q b / Q a and electrical conductivity σ b /σ a belowroom temperature, respectively. In temperature range of 40 K (cid:46) T (cid:46)
300 K, both Q b / Q a and σ b /σ a increase with loweringtemperature. Note that similar behaviors in thermopower andconductivity are also observed in the related layered cobali-tite (Bi,Pb) Sr Co O y [45], implying a universal anisotropicproperty in the CoO -based materials as is discussed below.To clarify the origin of the anisotropic transport at low tem-peratures, we discuss the electronic band structure measuredby ARPES at T =
40 K [31]. Note that the band structureis also proposed theoretically but there is a di ffi culty origi-nating from the misfit structure of this system, in which anapproximate formula is required for calculations [32, 46–49].In fact, the calculated thermopower strongly depends on thecalculation methods [32, 49]. Thus, the present results mayo ff er an experimental clue for the challenging issue to theo-retically obtain the transport properties precisely in correlatedelectron systems with an incommensurate structure like thismaterial. Now the band structure experimentally obtained in[Ca CoO ] . [CoO ] is well fitted by a tight-binding disper-sion relation for the hexagonal lattice with primitive vectors (cid:126) a h and (cid:126) b h as [50] ε ( k ) = ε − t cos( k a a h ) + √ k b a h cos (cid:32) k a a h (cid:33) − t (cid:48) (cid:110) cos(2 k a a h ) + (cid:16) √ k b a h (cid:17) cos ( k a a h ) (cid:111) , (4)where ε = − . a h = .
82 Å thelattice constant. In this model, the conducting CoO layeris considered only, and modeled as a hexagonal lattice. t = − . t (cid:48) = . (cid:126) a h and those with 2 (cid:126) a h .As is discussed in Ref. 31, tight-binding fit with t (cid:48)(cid:48) , which istransfer integral along (cid:126) a h + (cid:126) b h direction, leads to wrong resultprobably due to a one-dimensional σ -bond formation along (cid:126) a h direction. Figure 5(a) shows the calculated contour plot forthe constant-energy surfaces, in which a Fermi surface with ahexagonal shape is confirmed as seen in ARPES experiments[31]. Note that k a and k b directions correspond to ∼ a and b directions in real space, respectively [51].Figure 5(b) shows the dispersion relations along the Γ → Kand Γ → M directions. The flat region in the top of these dis-persions indicates a pudding mold energy band, in which thethermopower is approximately determined by the di ff erencein the velocities of electrons and holes as [9] Q i = k B e (cid:80) ( v i , h − v i , e ) (cid:80) ( v i , h + v i , e ) , (5)where v i , e and v i , h are the velocities of electrons and hole forthe i direction ( i = a , b ), respectively. Figure 6(a) presentsthe carrier velocity calculated as v a = / (cid:126) ( ∂ε/∂ k a ) | k b = and v b = / (cid:126) ( ∂ε/∂ k b ) | k a = as a function of energy near the Fermienergy. Although the summation in Eq. (5) is taken over allthe k states within the thermal energy k B T , for simplicity weonly consider these v a and v b , which largely contribute to thetransport coe ffi cients for each direction. In this approxima-tion, one obtains v i , e = v i ( ε > ε F ) and v i , h = v i ( ε < ε F ). !" ! ) ($ & ) * + , " -&$ -’$ -($ $ ($ ’$ &$" $ % *./" )&%’ (0$$01$02$0%$0’$0$ ( ! &$’$($$ )" $ )% *./")&%’
3" !"
FIG. 6. (a) Electronic velocity v i = / (cid:126) ( ∂ε/∂ k i ) as a function ofenergy measured from the Fermi energy for a (red) and b (blue) di-rections. The velocity v a ( v b ) is calculated for k b = k a = x i ≡ ( v i , h − v i , e ) / ( v i , h + v i , e ) for a (red) and b (blue) di-rections as a function of the energy measured from ε F in magnitude. Figure 6(b) depicts a velocity ratio x i ≡ ( v i , h − v i , e ) / ( v i , h + v i , e )for each direction as a function of the energy from the Fermienergy in magnitude. In the present energy range, which iscomparable to the thermal energy k B T , x b > x a holds, leadingto Q b > Q a . This is consistent with the present result shownin Fig. 3(c), indicating a validity of itinerant picture based onthe observed Fermi surface.We mention the anisotropy in the SDW phase below 30 K.This material shows the SDW transition at T SDW (cid:39)
30 K andits onset temperature is T ONSDW (cid:39)
100 K. As shown in Fig.4(a), although no prominent feature is found at T ONSDW , we ob-served a cusp near T SDW in the temperature dependence ofthe thermopower anisotropy. The cusp structure in the ther-mopower anisotropy indicates that the electronic structure isdrastically varied at T SDW , as is seen in the significant changein thermopower anisotropy at the SDW transition in Fe-basedsuperconductors [52]. On the other hand, the conductivityanisotropy σ b /σ a is monotonically increased as temperaturedecreases and shows no anomaly at T SDW as seen in Fig.4(b). This result implies that, although the anisotropy of thevelocities is crucial since v b > v a leads to σ b > σ a from σ i ∼ (cid:80) (cid:16) v i , h + v i , e (cid:17) τ , where τ is the relaxation time, the con-ductivity anisotropy may be governed by the relaxation time,which is cancelled out in the thermopower formula of Eq. (5). IV. SUMMARY
To summarize, we have measured the anisotropiesof the resistivity and the thermopower in the layered [Ca CoO ] . [CoO ] and found the considerable temperaturevariations. In high-temperature range, the anisotropy in thethermopower becomes close to unity, indicating a localizedpicture. On the other hand, low-temperature anisotropies arequalitatively explained in the itinerant band picture based onthe results from ARPES, and the change in the electronicstructure associated with the SDW transition is probed asa cusp behavior of the thermopower anisotropy. These re-sults show a crossover from low-temperature itinerant to high-temperature localized electronic states in this material. ACKNOWLEDGMENTS
The authors would like to thank S. Makino for an earlystage of the present study. We are grateful to S. Yosh-ioka for allowing us to use the scanning electron microscope(SEM). We thank H. Yaguchi for discussion and H. Uta-gawa, H. Hatada for experimental supports. This work wassupported by JSPS KAKENHI Grants No. 17H06136, No.JP18K03503, and No. JP18K13504. [1] F. Schipper, E. M. Erickson, C. Erk, J.-Y. Shin, F. F. Chesneau,and D. Aurbach, J. Electrochem. Soc. , A6220 (2017).[2] I. Terasaki, Y. Sasago, and K. Uchinokura, Phys. Rev. B ,R12685 (1997).[3] G. J. Snyder and E. S. Toberer, Nat. Mater. , 105 (2008).[4] K. Koumoto, Y. Wang, R. Zhang, A. Kosuga, and R. Funahashi,Annu. Rev. Mater. Res. , 363 (2010).[5] S. H´ebert, D. Berthebaud, R. Daou, Y. Br´eard, D. Pelloquin, E.Guilmeau, F. Gascoin, O. Lebedev, and A. Maignan, J. Phys.:Condens. Matter , 013001 (2016).[6] W. Koshibae, K. Tsutsui, and S. Maekawa, Phys. Rev. B ,6869 (2000).[7] Y. Wang, N. S. Rogado, R. J. Cava, and N. P. 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