# Thermopower Enhancement from Engineering the Na0.7CoO2 Interacting Fermiology via Fe Doping

Authors: Raphael Richter; Denitsa Shopova; Wenjie Xie; Anke Weidenkaff; Frank Lechermann
Journal: Advances in Condensed Matter Physics
 (2018)

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## Abstract

The sodium cobaltate systemNaxCoO2 is a prominent representant of strongly correlated materials with promising thermoelectric response. In a combined theoretical and experimental study we show that, by doping the Co site of the compound at x=0.7 with iron, a further increase of the Seebeck coefficient is achieved. The Fe defects give rise to effective hole doping in the high-thermopower region of larger sodium content x. Originally filled hole pockets in the angular-resolved spectral function of the material shift to low energy when introducing Fe, leading to a multisheet interacting Fermi surface. Because of the higher sensitivity of correlated materials to doping, introducing adequate substitutional defects is thus a promising route to manipulate their thermopower.


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## Body

## 1. Introduction

Selected compounds subject to strong electronic correlations display a remarkable thermoelectric response. Layered cobaltates composed of stacked triangular CoO2 sheets are of particular interest because of their large doping range. High-thermopower above 75 μV/K has originally been detected in the NaxCoO2 system at larger sodium doping x~0.7 [1–4]. Even higher Seebeck coefficients and increased figure of merit have been measured for misfit cobaltates (see, e.g., [5] for a recent review). Due to the simpler crystal structure, the small-unit-cell sodium-compound system remains of key interest in view of the essential electronic structure effects underlying the pronounced thermoelectric response.The high-thermopower region is associated with clear signatures of strong electronic correlations. Charge disproportionation [6, 7], change of Pauli-like magnetic susceptibility to Curie-Weiss-like behavior [8], and eventual onset of in-plane ferromagnetic (FM) order [7, 9–15] at x=0.75 are observed. Moreover the region displays unique low-energy excitations [16].Several theoretical works addressed the thermoelectricity ofNaxCoO2 [17–23], ranging from applications of Heikes formula, Boltzmann-equation approaches, and Kubo-formula-oriented modeling. Correlation effects described beyond conventional density functional theory (DFT) indeed increase the thermopower. Depending on x, the oxidation state of cobalt nominally reads Co(4-x)+(3d5+x). A strong cubic crystal field establishes a Co (t2g,eg) low-spin state, and x controls the filling of the localized t2g manifold. The additional trigonal crystal field splits t2g into a1g and eg′ levels. But the measured Fermi surface (FS) shows only a single distinct hole-like a1g-dominated sheet centered around the Γ point [24, 25]. Hole pockets of mainly eg′ kind are suppressed by correlation effects [26, 27].In this work we show that there is the possibility of engineering the interacting electronic structure ofNaxCoO2 in view of an extra increase of the thermoelectric response. Substitutional doping of the Co site with Fe is for x~0.7 effective in shifting the eg′ hole pockets to the Fermi level εF. The hole doping with iron also enforces the correlation strength. But different from the small-x region where the thermopower is found to be rather weak, for Na0.7Co1-yFeyO2 the Seebeck coefficient is further enhanced. This finding paves the road for future design of thermoelectric transport in correlated materials.


## 2. Theoretical Approach

An advanced charge self-consistent DFT + dynamical mean-field theory (DMFT) scheme [28] is utilized. The method is based on an efficient combination of the mixed-basis pseudopotential framework [29] with continuous-time quantum Monte-Carlo in the hybridization-expansion representation [30–33] for the DMFT impurity problem. The correlated subspace consists of projected [34, 35] Co/Fe 3d(t2g) orbitals; that is, a threefold many-body treatment holds in the single-site DMFT part. The generic multiorbital Coulomb interaction is chosen in Slater-Kanamori parametrization with Hubbard U = 5 eV and Hund's exchange JH = 0.7 eV. A double-counting correction of the fully localized form [36] is used. We construct Na as well as Co pseudopotentials with fractional nuclear charge to cope with the doping scenario in a virtual-crystal approximation (VCA). Based on a primitive hexagonal cell for one formula unit NaxCoO2, the fractional-charged Na is in the so-called “Na2” position, that is, aside from the transition-metal position below (see Figure 1). No bilayer splitting is included. The calculations are readily extendable to more complex unit cells and geometries; however the present approach suits the purpose of rendering general qualitative statements.Figure 1
(Color online) Sketch of a Fe-dopedNaxCoO2 structure. Note that the virtual-crystal approximation is employed in the actual calculations.For the investigation of transport, the Kubo formalism based on the correlation functions,(1)Kn=∑k∫dωβnω-μn-∂fμ∂ω×TrvkAk,ωvkAk,ω,is used in the DMFT context [22, 27, 37, 38]. Here β=1/T is the inverse temperature, vk denotes the Fermi velocity calculated from the charge self-consistent Bloch bands, and fμ marks the Fermi-Dirac distribution. To extract the k-resolved one-particle spectral function Ak,ω=-π-1ImG(k,ω) from the Green's function G, an analytical continuation of the electronic self-energy in Matsubara space ωn is performed via the Padé approximation. For more details we refer to [27]. This framework allows us to compute the thermopower through S=-kB/|e|K1/K0, and the resistivity as ρ=1/K0, both beyond the constant-relaxation-time approximation.


## 3. Materials Preparation, Characterization, and Measurement

The powders ofNa0.71Co1-yFeyO2 (y = 0, 0.05, 0.10, and 0.15) are prepared by the Pechini method. Stoichiometric amounts of the chemicals, sodium acetate (NaC2H3O2, 99.0%), Iron (III) nitrate nonahydrate (Sigma-Aldrich, purity 98%), cobalt acetate tetrahydrate ((CH3COO)2Co·4H2O, 98.0%), and citric acid (C6H8O7, 99%, CA), are each dissolved in deionized distilled water. The calculated amount of citric acid and ingredient acetates is mandated at a molar ratio of 1.5 : 1. The precursor solution is heated in an oil bath at 65°C while stirring continuously until a uniform viscous gel (2-3 h) forms. Subsequently, ethylene glycol (HOCH2CH2OH, EG, ρ=1.11 g/cm3) is added as a gelling agent in a molar ratio of 3 : 1 to the amount of citric acid. The gel is dried at 120°C for 4 hours and then heated in air to 300°C for 10 hours. The resulting powder is calcinated in air at 850°C for 20 hours. Densification was done in two steps: cold pressing in air (20 kN, 20 min) followed by isostatic pressing (800 kN, 1 min). Finally, the pellets are sintered for 24 hours at 900°C in air.The samples’ phase structure is identified by the Bruker D8-Advance diffractometer in Debye-Scherrer geometry with (220) Ge monochromator (Mo-Kα1, X-ray wavelength of 0.70930 Å). Seebeck coefficient and resistivity are measured simultaneously with a ZEM-3 (M10) ULVAC system, supplied with Pt electrodes, in the range T=30∘–350∘C and 950 mBar oxygen pressure. The uncertainties for both transport properties amount to ±7%.XRD patterns are plotted in Figure2. For Fe substitution > 10% an impurity phase occurs. Thus the experimental study of phase-pure Fe-doped samples is here limited to y≤0.1. Note that an Fe doping of Na0.63CoO2 with y≤0.03 has been reported by Zhou et al. [39], but without thermoelectric characterization.Figure 2
(Color online) XRD pattern of theNa0.71Co1-yFeyO2 (y = 0, 0.05, 0.10 and 0.15) powder samples. Black line: reference data obtained from the ICSD database.


## 4. Correlated Electronic Structure

TheNa0.7CoO2 electronic structure with multiorbital DMFT self-energy effects has been discussed in [27]. Electronic correlations are effective in renormalizing the low-energy t2g band manifold, introducing broadening due to finite lifetime effects and shifting the occupied eg pockets further away from the Fermi level (see top of Figure 3(a)). The single-sheet hole-like FS stems from an a1g dominated band.Figure 3
(Color online) DFT+DMFT electronic structure forNa0.7Co1-yFeyO2. (a) Spectral function for different y. Left: k-integrated A=∑kA(k,ω) and right: k-resolved along high-symmetry lines in the Brillouin zone. (b) y-dependent FS.
(a) (b)Replacing a fractiony of cobalt by iron introduces hole doping of the same concentration. The actual transition-metal t2g filling then reads n(t2g)=5+x-y≡5+x~. We here employ two rather large theoretical Fe doping cases of y=0.25,0.50 to illustrate the principle effect. Because of the averaged VCA treatment, we underestimate its realistic impact and thus the lower experimental doping cases yield comparable effective physics. Figure 3 exhibits the changes of the spectral function due to hole doping y. The eg′ pockets shift towards εF, develop a low-energy quasiparticle (QP) resonance, and participate already for y=0.25 in the FS. Since the partial bandwidth of the eg′ derived states is reduced compared to the a1g one due to smaller hopping, the pocket QP resonance is rather sharp. Additionally the overall renormalization is enhanced with y and an upper Hubbard band sets in for y=0.50. This strengthening of electronic correlations is not surprising since the Fe doping effectively drives Na0.7CoO2 again further away from the band-insulating (x=1) limit. However, importantly, note that systems at a sole Na doping level x1 and at effective doping level x~1=x2-y=!x1 arenot electronically identical. Let us assume lowering of the electron doping starting from x=0.7 where hole pockets are shifted below εF. Then it was shown in [27] that for x=0.3 the eg′ pockets are still suppressed at the Fermi level. But here for x~=0.7-0.25=0.45 these pockets already cross εF. Thus Fe doping strengthens the multiorbital transport character compared to pure Na doping.


## 5. Theoretical Transport

In [27] the anisotropic thermopower of sodium cobaltate at x=0.70,0.75 has been revealed using the present DFT+DMFT-based multiorbital Kubo formalism. Here we compare in Figure 4(a) the results with and without Fe doping for Na0.7CoO2. Quantitatively, the in-plane Seebeck values without Fe doping match the experimental data by Kaurav et al. [3]. As a proof of principles, theory documents an enhancement of the in-plane thermoelectric transport compared to the Fe-free case. For once, it may be explained by the increase of transport-relevant electron-hole asymmetry due to the emerging eg′ pockets at εF. A Seebeck increase because of this effect was predicted early on by model studies [20], though its realization by Fe doping was not foreseen. In addition, the small negative c-axis thermopower in Fe-free Na0.7CoO2 eventually changes sign for larger y. This fosters the coherency of the net thermoelectric transport.Figure 4
(Color online) Thermopower and resistivity for different Fe dopingy. (a) Theoretical data from DFT + DMFT for y=0,0.25,0.50. Solid lines: in-plane and dashed lines: along c-axis. (b) Experimental data for y=0,0.05,0.10.
(a) (b)The resistivity also increases with Fe doping and the in-plane values match our experimental data (see below). A gain of scattering because of reinforced electron correlations and appearing interband processes is to be blamed. Though thec-axis resistivity largely exceeds the in-plane one, the transport anisotropy seems still underestimated compared to measurements by Wang et al. [40].


## 6. Experimental Transport

In direct comparison to the theoretical data, Figure4(b) displays the experimentally determined Seebeck coefficient. A clear observation can be extracted; namely, Fe doping gives rise to an increase of the experimental thermopower compared to the Fe-free case. But this enhancement is not of monotonic form with y and, as already remarked, the achievable phase-pure Fe content is experimentally limited to y=0.1. Still, experiment verifies qualitatively the theoretical prediction on a similar quantitative level in terms of relative thermopower growth. The nonmonotonic character might result from intricate real-space effects, for example, a modification of the Co/Fe local-moment landscape, which is beyond the VCA method that was employed in theory.The resistivity increase reported in Figure4(b) also verifies the theoretically obtained scattering enhancement. More pronounced correlation effects, the introduced interband scattering for finite y, and/or modified vibrational properties are at the origin of this behavior. Also here, a deeper theoretical analysis beyond VCA, with additional inclusion of the phonon degrees of freedom, is in order to single out the dominate scattering mechanism.


## 7. Conclusions

Theory and experiment agree in the enhancement of the sodium cobaltate thermopower iron doping. This agreement may serve as a proof of principles for further engineering protocols. Our calculations for Fe-dopedNa0.7CoO2 show that effective hole doping takes place. This shifts the originally occupied eg′-like pockets to the Fermi level. The increased electron-hole transport asymmetry sustains an enlarged Seebeck coefficient. Iron doping also increases electronic correlations by driving the system further away from the band-insulating regime. Yet the doping is different from a nominal identical hole doping via reducing Na content. This is not of complete surprise since first, the Na atom is here an electron donor compared to the Fe atom. Second, Na ions are positioned in between the CoO2 planes and their contribution to bonding and scattering is rather different from substitutional Fe within the planes.It would be interesting to further analyze the engineering possibilities of the cobaltate thermopower. Strobel et al. [41] already performed experimental studies for doping with Fe-isovalent Ru and also observed a nonmonotonic thermopower increase, yet with semiconducting properties. A recent theoretical study of Sb-doped NaxCoO2 predicted a decrease in thermopower [42]. Generally, correlated materials are much more sensitive to doping than weakly correlated systems because of induced transfer of spectral weight. Another aspect in this regard is the nanostructuring of thermoelectric compounds [43, 44]. Research on such structuring for the case of correlated materials, combined with a tailored chemical doping, in view of increasing the figure of merit is still at its infancy. The novel field of oxide heterostructures could serve as an ideal playground.



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*Source: 9725321-2018-04-23.xml*