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Enhanced thermoelectricity Enhanced thermoelectricity in the correlated semiconductor FeSb 2 Peijie SUN Max Planck Institute for Chemical Physics of Solids Dresden, Germany Acknowledgement: N. Oeschler, F. Steglich (MPI, Dresden) S Johnsen B B Iversen (Aarhus Univ Denmark) S. Johnsen, B.B. Iversen (Aarhus Univ., Denmark) 1

O tline Outline • Introduction to FeSb 2 -- A probable new d - based correlated semiconductor • Findings of colossal thermoelectricity in FeSb 2 • New detailed measurements and analyses New detailed measurements and analyses (Thermopower, Nernst effect…) • Comparison to non-correlated RuSb • Comparison to non-correlated RuSb 2 • Summary 2

Crystal structure & Gap opening • Marcasite-type orthorhombic structure • Fe surrounded by deformed Sb octahedra. 3 J. B. Goodenough, J. Solid State Chem. 5 (1972) 144 Hulliger, Nature, 198 (1963) 1081; J. Solid State Chem. 5 (1972) 144

Thermodynamics similar to FeSi FeSb 2 FeSi Mandrus, PRB 1995 Thermally activated paramagnetism, (narrow gap and narrow band model applicable) FeSb FeSb 2 FeSb 2 E g ~ 350 K 4 Optical spectral weight recovers above 1eV Perucchi, Eur. Phys. J. B., 2006 Petrovic, PRB 72 (2005) 045103; Fan et al, J. Solid State Chem. 5 (1972) 136

Colossal S and PF in FeSb 2 Largest S in d based systems Largest S in d -based systems, largest PF so far known largest PF so far known Dimensionless figure of merit ZT = T S 2 σ / к • Origin of the huge S and PF ? Large power factor PF = S 2 σ Large power factor PF S σ • Reducing к while keeping high PF ? Reducing к while keeping high PF ? Small thermal conductivity к 5 A. Bentien et al, EPL 80 (2007)17008

Experimental FeSb 2 Samples preparation Vapor transport (FeSb 2 ), self-flux (RuSb 2 ) Vapor transport (FeSb 2 ), self flux (RuSb 2 ) Crystal characterization Powder x-ray, Laue diffraction Home-made cryostat (1.5K-RT, 0-7T) Thermopower, S = V x /| ∆ T | N Nernst coeffi., v = (L/W) · V y / B | ∆ T | t ffi (L/W) V / B | ∆ T | 6

Resistivity & Hall effect Resistivity & Hall effect 2 -3 10 10 10 10 -3 3 1 1 10 10 10 10 -4 10 0 10 -5 10 0 -5 10 10 10 10 3 /C) ) ρ (Ω cm ) ρ ( Ω -cm) RH| (m3/C) -1 10 -6 10 R H | (m -7 10 -2 10 -2 -7 10 10 10 10 ρ |R ρ |R -8 10 -3 10 -9 10 -4 -9 10 10 10 10 -10 -4 10 10 10 10 0.0 0.1 0.2 400 1 10 100 -1 (K -1 ) T T (K) D Double gap, E g = 52 K and 350 K ( ρ = ρ 0 exp ( E g /2 T )) bl E 52 K d 350 K ( ( E /2 T )) 7

One band model analysis One band model analysis Mobility (| R H |/ ρ ) 0 10 -1 10 2 /Vs) -2 10 m µ H (m -3 3 10 -4 10 -5 10 1 10 100 T (K) negligibly small mobility of a second sub-band � One band analysis possible 8

Thermopower & Nernst coefficient p Large power factor Large power factor 0 0 0 0 -2 700 -200 600 600 (mV/K) -4 4 ν ( µ V/KT) 500 2 ) ( µ W/cmK -6 400 -400 300 ν S -8 PF 200 FeSb2 100 -10 -600 N(T), B = 0.5 T 0 N(T), B = 2 T 0 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 -12 T (K) 1 10 100 T (K) • S ~ 10000 µV/K (10 K) >> Classical Upper limit of semiconductor E g /2 eT max ~ 1500 µV/K • v ~ 550 µV/KT (7.5 K), 20 µV/KT (50 K), reflecting double gap feature . 9

Thermal activation of S at low T 20 K 20 K 10 K 10 K 6 6 K 6.6 K 12 S ( T ) = k B /e · E g /2 T + C (1) mV/K ) ) 8 Thermal activation of S , in agreement with T -activated ρ |S| (m and R H in this T -range. g H 4 However, E g ~ 840 K g >> 52 K (from ρ and R H ) 0 0.15 0.1 0 0 0.05 0.05 1/T (1/K) 10

Electron-diffusion contributions in degenerate g and nondegenerate regimes Non-degenerate model (2) Degenerate model (3) 11

Electron-diffusion effect qualitatively interprets S 1 10 (a) (a) 15 x (3) 30 x (2) 0 K ) 10 S| (mV/ (3) (2) -1 1 |S 10 10 m *= m 0 -2 10 100 1 10 T (K) � A factor is needed to optimize the description quantitatively. Enhanced electron-diffusion contribution ? Enhanced electron diffusion contribution ? 12

Fermi energy gy FeSb 2 100 E F (K) 10 10 E 1 1 10 100 T (K) ( ) � The measuremental temperatures are not very different with E F 13

Results of a different batch 100000 FeSb 2 AAFa-batch 10000 ( µ V/K) 1000 |S| ( 100 S measured deg. model m*=0.1m 0 factor 25 non-deg. model m*=0.1m 0 factor 40 10 10 100 T (K) T (K) Assuming m * = 0.1 m 0 , the same discussion works. 14

Qualitatively interpreting Nernst signal Two origin of Nernst signal 4 10 (b) (b) Metal/degenerate semicond. M t l/d t i d 3 10 -- large ∂ τ / ∂ E S tan θ H /B /KT) 2 10 | ν | ( µ V/ 1 10 0 10 10 N (B=0.5T) N (B= 2T) -1 10 1 10 100 Intrinsic/compensated semicond. T (K) T (K) -- ambipolar effect (positive signal) bi l ff t ( iti i l) Huge Nernst signal for the first mechanism! Enhanced ∂ τ / ∂ E accompanying onset of the gaps probably account for the double peaks Delves, Rep. Prog. Phys. 1965 Wang, et al, PRB 2001 15

Thermal conductivity & mean free path 3 400 10 3/2 ∼ T 2 10 10 300 1 10 µ m) mK) l p , l e ( µ κ (W/m l P 0 200 10 -1 10 10 κ l e 100 -2 10 -3 3 0 10 10 100 4 T (K) � Extremely small electron mfp compared to that of phonon indicates large room for optimizing ZT g p g 16

Comparing FeSb 2 and RuSb 2 Comparing FeSb 2 and RuSb 2 6 4 ol) emu/mo FeSb 2 2 -4 e ( 10 0 RuSb 2 R Sb χ ( -2 -2 0 100 200 300 400 T (K) Magnetic susceptibility 17

Comparing FeSb 2 and RuSb 2 Comparing FeSb 2 and RuSb 2 2 10 10000 FeSb 2 FeSb 2 1000 1 10 K) m) |S| (mV/K F ( µ W/K2cm 100 RuSb 2 0 10 10 PF RuSb 2 -1 10 1 -2 10 10 300 1 10 100 0.1 0 10 20 30 40 50 60 T (K) T (K) Huge S and PF below 30 K in FeSb 2 relative to RuSb 2 , despite the similar n and even larger к of the latter 18

Similar case in 2D-SrTiO 3 ---- an enhanced S - log n slope ---- an enhanced S - log n slope When T = Const. S ( T ) ~ ± k /e · (ln n + C ) S ( T ) ~ ± k B /e · (ln n + C ) A five fold enhanced slope in 2D system, relevance to FeSb 2 ? Ohta et al, Nature material 2007 19

Summary Summary � Huge S and PF are observed in FeSb 2 , while low values in RuSb 2 . � Classical electron-diffusion model qualitatively describes the observed S . � An enhancing factor is needed for quantitative explanations. � Large mobility contributes to the large PF as well. 20