UIC! Serdar Öğüt. Department of Physics, University of Illinois at Chicago. Supported by DOE, NSF, Argonne, and NERSC. Materials Modeling Group

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1 Structural, Electronic, and Transport Properties of Thermoelectric Ca 3 Co 4 O 9 : Insights from First Principles Computations and Electron Microscopy Serdar Öğüt Department of Physics, University of Illinois at Chicago Supported by DOE, NSF, Argonne, and NERSC

2 Outline Ø Introduction Ø Misfit-Layered Cobalt Oxides Ø DFT Modeling of Ca 3 Co 4 O 9 (CCO) with Fibonacci approximants Ø Characterization of Ca 3 Co 4 O 9 in the STEM Ø Summary Ø Future Prospects q Structural and Electronic Properties q Size versus Electron Correlations q Phonons and Thermal Properties A. Rebola (UIC à Cornell) q Z-contract Imaging and EELS q Increased S and High-Spin Co 4+ in 40 nm CCO films q Supporting Evidence from DFT R. F Klie (UIC)

3 Introduction: Thermoelectric Materials Thermo-electric materials offer direct conversion of waste/excess heat into electrical power. Thermopower is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across a material. Seebeck coefficient: S = ΔV ΔT = 8π 4 3 k 2 " B 3eh m* T 1 % $ ' # 3n & 2 3 Figure of Merit: ZT = 2 S T ρκ Achieving low thermal conductivity, high electrical conductivity, and a large effective mass is often difficult in bulk materials.

4 Introduction: Thermoelectric Materials Problems with conventional TE materials: Bi 2 Te 3 /Bi 2 Se 3 Unstable at high temperature and O-rich environments (most materials are limited to 200 K 700 K) Toxic Expensive/rare constituent elements Low efficiency at desired temperatures (i.e. T<200K or T>1000K) Phonon glass/electron crystal or material with different subsystems needed for good TE properties. M. Dresselhaus et al, Adv. Mat. 19 (2007) Some important materials: Bi 2 Te 3 : S= -287 µv/k, ZT~1 Bi 2 Te 3 /Sb 2 Te 3 superlattice: ZT>2 at 300K PbTe/PbSeTe quantum dots: ZT>1.5 UO 2 : S=750 µv/k Ca 3 Co 4 O 9 : S= 135 µv/k, ZT~1 at 1000K

5 Incommensurately layered Cobalt Oxides NaCoO 2 (CaOH) 1.14 CoO 2 Ca 3 Co 4 O 9 (Ca 2 CoO 3 )(CoO 2 ) 1.62 (Bi 0.87 SrO 2 ) 2 (CoO 2 ) 1.82 Shizuya et al, J. Solid State Chem. 180, 249 (2007) Layered cobalt oxides are intrinsically nano-structured materials

6 Misfit-Layered Ca 3 Co 4 O 9 (CCO) Two subsystems, different behaviors: Ø CoO 2 (Hex): hole conducting, electron-crystal behavior. Ø Ca 2 CoO 3 (RS): distorted, mostly insulating, phonon-glass behavior O2 O1 CoO 2 a = 4.83 Å c = Å β = c Ca2 O2 Ca1 O3 O1 CaO CoO β a b CoO 2 RS ( b RS = Å) and CoO 2 (b CoO2 = Å) are incommensurate along b. b RS b

7 Rational Approximants The composition ratio for (Ca 2 CoO 3 )(CoO 2 ) 1.62, is very close to the golden mean τ = (1+ 5) / 2 = which is the limit of the sequence of the ratios of consecutive Fibonacci numbers F(n+1)/F(n) = 2/1, 3/2, 5/3, 8/5,13/8, To model the incommensurate structure of CCO we construct a series of rational approximants with composition (Ca 2 CoO 3 ) 2F(n) (CoO 2 ) 2F(n+1) and investigate how various properties evolve as a function of the size. Spin-polarized full structural relaxation (Quantum Espresso & VASP) up to 13/8 approximant (174 atoms in the unit cell). DFT (LDA, PBE) and DFT+U computations

8 Rational Approximants (Ca 2 CoO 3 ) 4 (CoO 2 ) 6 (Ca 2 CoO 3 ) 16 (CoO 2 ) 26 b = 8.58 Å b = 36 Å 3/2 13/8 X 1 CoO 2 c O2 Ca2 O2 Ca1 O2 O1 X 4 CaO CoO β O1 a = 4.83 Å c = Å β = a b CoO 2 b RS b X 3 X 2 5/3 8/5 b = Å b = Å (Ca 2 CoO 3 ) 6 (CoO 2 ) 10 (Ca 2 CoO 3 ) 10 (CoO 2 ) 16

9 Earlier Studies (Exp. vs Theory) Experiment (PE) Takeuchi et al., PRB 69 (2004) IKO TANI Theory (DFT) atoms; the corhe Co muffin-tin Asahi et al., PRB 66 (2002) 3, and those in netic orderings. tic state ( E in X E DOS Intensity (Arb. (arb. Units) units) β a b CoO 2 b RS FIG. 4. Co 2p-3d on-resonant spectra of Ca 3 Co 4 O 9 CCO and b c O2 Ca2 O2 Ca1 O2 O1 O1 Rock Salt subsystem PHYSICAL REVIEW B 66, Na 0.6 CoO 2 after subtracting the background intensity. The spectrum of the -NCO was shifted by 240 mev towards higher binding energy, and its intensity was normalized such that the integrated intensity becomes 60% of that of the CCO. By considering NCO s spectrum as that of the CoO 2 layer in the CCO and subtracting it from that of CCO, we obtained a spectrum representing the rocksalt layer in the CCO. Binding Energy Energy (ev) sharp peak at 2.4 ev, a slightly broad one centered at 6.4 ev, and a broad hump extending up to 12 ev. The symmetry about the cobalt atom in the rocksalt layer gives rise to the CoO 2 CaO FIG. 5. a O CCO, CoO Bi 2 Sr 2 Co 2 The leading edge energy, while that the vicinity of E F are vertically shift tal dashed lines in sity persists at E slope at E F that w measurement see Though its leadin intensity at E F in others. This show sistivity of CCO a suggest that the 1 ev is domina layer. It is, there of the spectrum

10 Theory vs. Experiment How to reconcile experimental findings with theoretical predictions? q Two possibilities Ø Size effect: In previous study, only the lowest-order approximant (3/2) was considered. How does the electronic structure depend on the order of the Fibonacci approximant? Ø Correlation effects: In many cases the mean-field approach of DFT fails to provide a good description of highly localized d orbitals. Previous study did not include any strong correlation effects (even in an approximate way).

11 Size Effect: Higher order approximants 5/3 Approximant PDOS/(State/eV/Spin/Co) Spin Up 2.5 d in CoO d in RS E E f (ev) Spin Down d in CoO 2 d in RS c O2 O1 Ca2 O2 Ca1 O3 O E E f (ev) β CoO 2 CaO CoO Similar results for higher order approximants. a b CoO 2 b Good agreement with previous DFT calculations, except for the contribution at E F coming from CoO 2 spin down. Major contribution to electrical conductivity from the RS substructure, in disagreement with PE experiments. b RS

12 PDOS/(State/eV/Spin/Co) d in CoO 2 d in RS Adding Correlations: DFT+U LDA + U, U eff = 4 ev Spin Up 5/3 Approximant E E f (ev) d in CoO 2 d in RS Spin Down E E f (ev) Finite contribution at E F from the CoO 2 subsystem Almost negligible contribution from RS subsystem. Better agreement with photoemission experiments. Results insensitive to the value of U

13 Partial DOS (DFT+U) Spin Up Spin Down d xy d xy CoO 2 subsystem PDOS (Arb. Units) units) d yz d 3z 2 r 2 d xz d x 2 y 2 d yz d 3z 2 r 2 d xz d x 2 y 2 RS subsystem PDOS (Arb. units) PDOS (Arb. Units) Spin Up d xy E E (ev) d yz d 3z 2 r 2 d xz d x 2 y 2 d xy Spin Down E E (ev) d yz d 3z 2 r 2 d xz d x 2 y E E f (ev) E E f (ev)

14 Size Evolution (Higher Approximants) Spin Up Spin Down 3/2 3/2 CoO 2 PDOS/(Arb. units) 5/3 8/5 13/8 5/3 8/5 13/8 RS PDOS/(Arb. units) Spin Up /2 5/3 8/5 13/8 Spin Down E E (ev) 3/2 5/3 8/5 13/ E E f (ev) E E f (ev) Small contribution to the RS PDOS coming from e g orbitals for the 3/2, 8/5, 13/8 approximants, composed of combinations of X 1, X 2 and/or X 4 clusters. 5/3 is composed of X 3 clusters, fully occupied/unoccupied e g orbitals.

15 3/2 Clustering along b 13/8 X 1 X 4 X 3 X 2 b 5/3 8/5 n unit X Ca 2 CoO 3 clusters (n = 1 4) occurring along the b direction. Related to the incommensurate nature of the CoO 2 and RS subsystems, and depends critically on how the system can minimize the total energy globally within the constraints imposed by the ratio of the Fibonacci numbers.

16 Thermal Properties Recalling that: ZT = σ S 2 κ T The thermal conductivity is determined by two contributions: κ = κ ph +κ holes From Wiedemann-Franz Law: κ holes = L 0 Tσ In CCO: σ ~ 0.1 (mω cm) -1 κ holes ~ 0.1 mw/cmk (at 100K) κ ~ 30 mw/cmk most contributions are due to phonons.

17 Phonons in CCO Calculations for the 3/2 (Ca 2 CoO 3 ) 4 (CoO 2 ) 6 and 5/3 (Ca 2 CoO 3 ) 6 (CoO 2 ) 10 Cell optimizations and force constants: VASP, PBE + U, (Co, U eff = 4eV). 3/2 approximant (b opt = 8.81 Å) 2x1x1 supercell, 84 atoms. 5/3 approximant (b opt = Å) 2x1x1 supercell, 132 atoms. Phonon Calculations: Systems are too big to apply DFPT. Finite differences method (Phonopy).

18 Phonons in CCO Total DOS (Arb. Units) /2 approximant 5/3 approximant Co, Ca, O Frequency (THz) 3/2 5/3 z O Frequency, THz /3 approximant Γ X Α Γ Ε D y

19 Phonons in CCO: Low frequency Low Frequency Modes: Contributions from all the atoms (Ca, Co, O).

20 Phonons in CCO: High frequency High Frequency Modes: Mostly due to O atoms.

21 Heat Capacity Heat capacity at constant volume: ! ω(q, s) $ c v = k B # & " k B T % q,s 2 exp( ω(q, s) / k B T ) [ exp( ω(q, s) / k B T ) 1] 2 Experiment: Wu et al. JPCM 24 (2012) C V ( J/mgK) Experiment 400 3/2 approximant 5/3 approximant Temperature (K) Reasonably good agreement with experimental data for both approximants.

22 Thermal Conductivity Boltzmann Transport Equation within the relaxation time approximation: k αβ = v αλ (q)v βλ (q)τ λ (q) dn (ω ) B λq dt λq For each approximant, velocities are obtained from the full dispersion. τ λ (q) is assumed to be constant, Typical values for τ 1ps τ λ (q) = τ Also computed projected thermal conductivity : e µ,i 2 k αβ,µ = e µ,i vαλ (q)v λβ (q)τ λ (q) dn (ω ) B λq dt i λq where refers to the i th Cartesian component of phonon eigenvector corresponding to atom μ.

23 Thermal Conductivity 3/2 approximant 5/3 approximant κ (mw/kcm) τ=2ps b axis a axis τ=2ps a axis b axis 10 c axis 10 c axis Temperature (K) b axis a axis Temperature (K) Similar results along a and c for both approximants Differences for κ along the incommensurate direction b (Different clustering). 5/3 approximant: Qualitatively good agreement with experiment (different saturation temperatures).

24 Characterization of Ca 3 Co 4 O 9 in the STEM: A Combined Z-contrast Imaging, EELS, and DFT Study R.F. Klie, Q. Qiao, T. Paulauskas, A. Gulec, A. Rebola, S. Ogut, M. Prange, J. Idrobo, and S. Pantelides, Phys. Rev. Lett. 108, (2012)

25 The Key to STEM Incident Probe Annular Detector Z- contrast Image Spectrometer CCD- EELS Detector

26 Z-contrast image in conventional STEM Ca 3 Co 4 O 9 [010] Z-Contrast Imaging Z-contrast image in aberrationcorrected TEAM Ca 3 Co 4 O 9 [010] 0.5 nm CoO 2 CaO CoO CaO CoO 2

27 Seebeck Coefficient in Layered Cobaltites In materials with strong electron-electron interactions, e.g transition-metal oxides, the Seebeck coefficient can be described using the Heikes form: kb x S = ln β β = g e 1 x o g s : the orbital/spin degeneracy, x fraction of mobile charges. Koshibae et al, PRB (2000) Ca 3 Co 4 O 9 Cobalt valence and spin state control the TE properties of Ca 3 Co 4 O 9

28 Ca 3 Co 4 O 9 Thin Films Thin films grown on SrTiO 3, LaAlO 3, LSAT and Al 2 O 3 support. In-plane Seebeck coefficient at 300 K. c-lattice parameter for all thin film samples around nm Bulk Ca 3 Co 4 O 9 lattice parameter: nm High quality textured Ca 3 Co 4 O 9 films were grown, but films appear unstrained. (Q. Qiao, A. Gulec, T. Paulauskas, S. Kolesnik, B. Dabrowski, B.M. Ozdemir, C. Boyraz, D. Mazumdar, A. Gupta, R.F. Klie, J. Phys. Cond. Mat., 23(30), (2011))

29 Ca 3 Co 4 O 9 Thin Films on SrTiO 3 Z-contrast image of 40 nm thick Ca 3 Co 4 O 9 Seebeck coefficient Co 3 Co 4 O 9 2 n m SrTiO 3 Unusually high Seebeck coefficient appears to be related to presence of stacking faults and twin boundaries. R.F. Klie, Q. Qiao, T. Paulauskas, A. Gulec, A. Rebola, S. Ogut, M.P. Prange, J.C. Idrobo, and S.T. Pantelides, Phys. Rev. Lett. 108(19), (2012)

30 Ca 3 Co 4 O 9 Thin Films on SrTiO 3 Undoped 40 nm Ca 3 Co 4 O 9 film EELS of O K-edge R.F. Klie et al., Phys. Rev. Lett. 108, (2012) O K-edge pre-peak is significantly higher in stacking fault, indicating a change in Co spin state. (Co L-edge remains unchanged)

31 Ca 3 Co 4 O 9 Thin Films on SrTiO 3 Undoped DFT Calculations 40 nm 3 Co 4 O 9 film EELS of O K-edge Stacking faults stabilize Co 4+ ion in higher spin state.

32 Summary Ø The incommensurate thermoelectric Ca 3 Co 4 O 9 can be modeled with relatively low-order rational approximants within the framework of DFT+U. Ø Good agreement with experiment with respect to structural, electronic, magnetic, and thermal properties. Ø Electron correlations are important in accounting for PE experiments. Size of the rational approximant plays a relatively minor role. Ø Ultrathin (40 nm) CCO epitaxial film grown on SrTiO 3 shows a high concentration of stacking faults which stabilize the Co 4+ -ion with increased spin state. Ø This change in the spin state results in a significant increase in the in-plane Seebeck coefficient of CCO (180 µv/k) at room temperature.