Electrons on a triangular lattice in Na-doped Cobalt Oxide

1. Electrons on a triangular lattice in Na-doped Cobalt Oxide Yayu Wang, Maw Lin Foo, Lu Li, Nyrissa Rogado, S. Watauchi, R. J. Cava, N.P.O. Princeton University • Frustration on triangular lattice • Large thermopower in NaxCoO2 • ARPES • Hall effect • Phase diagram Supported by NSF, ONR

2. Geometrical Frustration on triangular lattice H = -J Si Sj Antiferromagnetic Ising model ? (i,j) Impossible to have AF alignment on all 3 bonds Ground state is disordered and highly degenerate Resonating valence bond model(s) 1971, 1987 Spin Ice in pyrochlores 1998 Frustrated magnetic states in spinels 1999

3. Co Na Nax CoO2 Terasaki, Uchinokura 1997 building block tilt Octahedra tilted to form a layer Na ions (dopants) sandwiched btw layers of tilted CoO2 octahedra Co ions define a triangular lattice

4. Co Na as grown

5. Terasaki et al., PRB 1997 Resistivity of NaxCoO2 (x ~ 0.71) Wang et al. Nature ‘03

6. c ~ 1/ T Curie susceptibility c kT Pauli DOS 0 T energy AF spins • In Antiferromagnets • = C/(T + q) q = T (Neel temp) 1/c free spins N 0 T Susceptibility of insulators vs metals Susceptibility c= dM/dH In metals, c small and indept of T

7. Co3+ Co4+ Susceptibility c has Curie-Weiss form • AF Neel temperature • TN ~ 60-100 K • Magnitude of c implies • Co4+ ions spin S = ½ • Co3+ is diamagnetic (S = 0),

8. Metallic resistivity but antiferromagnetic in spin response (Curie-Weiss Metal)

9. Thermopower and Peltier coef. holes J E JQ Heat current densityJQ accompanies charge current densityJ Ratio of currentsJQ/J = P (Peltier coeff) S = P / T = JQ/ JT

10. S Large thermopower S of NaxCoO2 Terasaki et al Phys. Rev. B (1997) x = 0.71 • Large thermopower • ~10 times Sommerfeld value at 300 K Sommerfeld

11. Semiconductor JQ = n v D S = (kB/e)(D/kBT) D Thermopower • Classical gas • J = nev • JQ = n kBT v • Peltier coef. • = JQ/J = kBT/e Seebeck coef. S = P / T = kB/e kBT e Natural unit of S kB/e = 86 mV/K m

12. e(k) m Fermi level E dk = c-k Thermopower of conventional metals “Excitation picture” hole particle Fermi Gas in E field Charge currents add mass currents cancel Heat currents cancel S = JQ/JT strongly suppressed hole excitations vacancies TF ~ 50,000 K S ~ (kB/e) (T/TF) ~ 86 x 10-2mV/K particle excitations S virtually indepndnt of H E

13. - T V B S • In-plane field H || - T • Strong field suppression • of Thermopower Field dependence of S in NaxCoO2 Wang et al. Nature ‘03

14. Spin contribution to thermopower (Chaikin Beni, 1976) JQ J J = nev Spin entropy per carrier = kBlog 2 JQ = nv kBT log 2 S = JQ/JT = (kB/e) log 2 ~ 60 mV/K Not signif. in conv. metals

15. S(H)/S(0) - 1 S(H,T) curve is a function of H/T only

16. S(H)/S(0) - 1 Conclusion: 1. Spin entropy is the source for enhanced thermopower 2. Key for new thermo-electric materials -- Spin Wang et al. Nature ‘03

17. In NaxCoO2, hole density nh = 1-x Co 3d states

18. Superconductivity NaxCoO2 Multiple electronic phases vs. Na content

19. Water intercalated superconductor Takada et al.,Nature(2003). • pairing symmetry: • s, p or d-wave? • Why is water essential? • What is pairing mechanism: • e-ph or e-e or magnetic? NaxCoO2·yH2O, x ~ 0.35, y ~ 1.30 Superconductor with Tc ~ 4.5K

21. RH conv. metal T-linear Hall coefficient Yayu Wang, 03

22. 2 sH ~ t12 t23 t 31 ~ i t3 exp(ia) t12 t13 f 1 3 Why is RHT-linear? Hopping Hall current in triangular lattice (Holstein, ‘61) Peierls phase a = 2pf/f0 High-frequency RH* in tJ model (B.S. Shastry ‘93, ‘03) • sH ~ i(bt)3 exp(ia) s ~ (bt)2 R*H ~ sH/Hs2 ~ (bt) -1 bt << 1 (b = 1/T) T-linear M2S-RIO conf. Rio de Janeiro, May 28th 2003 (N.P. Ong)

23. ARPES: Weak quasiparticle dispersion Z. Hasan et al. (PRL ‘04) Small bandwidth  Low degeneracy T Single-particle hopping : t < 0 and |t| ~ 10 meV (bandwidth < 100 meV) Momentum Kinetic energy (eV)

24. Fermi Surface of Na0.71CoO2 measured by ARPES Hasan et al. Large hole-like FS Hopping integral t ~ 10 meV Fermi velocity < 0.4 eV.A

25. Behavior of quasi-particles versus temperature ARPES Quasiparticles are coherent only below 150K Resistivity is T-linear below 100K

26. Insulating state as grown NaxCoO2 Multiple electronic phases vs. Na content Foo et al. PRL ‘04

27. Stronger oxidation agent Fine-tuning of Na content in NaxCoO2 single crystals Foo et al., condmat/0312174 (2003), PRL ‘04 • Reduce the Na content by a series of chemical de-intercalation • x = 0.75, as grown crystals of Floating zone or flux method • x = 0.68: NaClO3 in water • x = 0.50: I2 in Acetonitrile • x = 0.31: Br2 in Acetonitrile High-quality crystals with Na content 0.31 < x < 0.75

28. Calibration of the Na content vs. c-axis lattice parameter • Calibration procedure • treat powder and crystals • under same conditions • powder x-ray diffraction to • get c-axis lattice constant • ICP-AES to determine the • Na contents of powders • x vs. c-axis calibration curve • from the c-axis of crystal, • extract the Na content

29. x = 0.50 (1/2): • Two kinks at Tc1=88K and Tc2=53K in  • Resistivity shows insulating behavior below T=53K

30. An unexpected insulator at x = ½

31. b a b* a* Na Na vacancy Electron diffraction at 300K shows the superlattice formed by the Na ions, consistent with a zig-zag order Zendbergen et al., condmat/0403206 (2004)

32. Foo et al., PRL ‘04 Thermal Conductivity Hall coefficient

33. 0

35. as grown Spin ordered NaxCoO2 Multiple electronic phases vs. Na content Foo et al. PRL ‘04

36. Further enhancement of thermopower x = 0.71 x = 0.88 S Sommerfeld

37. P = S2s x ~ 0.85 x = 0.71

38. Unusual electronic behavior in NaxCoO2 • Strongly correlated s = ½ holes hopping on triangular lattice • Paramagnetic Metal (x ~ 1/3) • High conductivity, superconducting with H2O intercalatn. • Charge-ordered Insulator (x = ½) • Na ion ordering, hole ordering (stripes?), • giant thermal conductivity • Curie-Weiss metal (x ~ 2/3) • Curie-Weiss susceptibility, metallic cond., large thermopower • from spin entropy, T-linear Hall coef. • Spin Ordered Phase (x > ¾) • Even larger thermopower, field-induced metamagnetism

40. x= 0.31 (~ 1/3), parent compound of the SC •  is T-independent, not Curie-Weiss • M-H curves are linear at low T, no ferromagnetic order • Magnetic properties rather normal

41. x= 0.31 (~ 1/3): • Smaller high temperature thermopower • Smaller Hall coefficient, weaker T-dependent • larger hole concentration (~3x1022/cm3) and reduced correlation • Consistent with ARPES (MZ Hasan et al., and Hong Ding et al.)

42. x = 0.71 (~ 2/3) •  Curie-Weiss, AF interaction • is T-linear at low T • S large, ~90 V/K at 300K • RH strong T-linear • Curie-Weiss metal • Strong magnetic interaction • and electron correlation • x = 0.31 (~ 1/3) •  is T-independent, non • Curie-Weiss •  smaller, T 2 at low T • S small, ~34 V/K at 300K • RH weaker T-dependence • Paramagnetic (T 2) metal • More like conventional metal

43. Sodium ion ordering versus x Lynn, Cava et al.

44. S have giant negative values below Tc1 The number of holes are strongly reduced, the residual charge carriers seem to be electron like

45. RH becomes negative and the amplitude is 100 times larger • charge density reduces by ~ 100 times • particle-hole symmetry at low T

46. hole electron hole electron x = 1/3 x = 2/3 hole electron 3 a  3 a 3 a  3 a   hole electron x = 1/2  Possible charge ordering in NaxCoO2

47. 1/4 < x < 1/3 dome shape SC 3/4 < x < 1 Magnetic ordering? 0 < x < 1/4 No results, Doped Mott Insulator? Schaak et al., Nature (2003) CoO2: 1 electron per Co site, Mott insulator? NaCoO2: 1 pair of electron per Co site, band insulator. X = 1/2 Charge ordered insulator x ~ 2/3 Strong magnetic interaction and electron correlation x ~ 1/3 More like conventional metal Motohashi et al., PRB (2003) Sugiyama et al., condmat (2003) Bayrakci et al., condmat (2003) Maw-lin Foo et al., condmat (2003) To appear in PRL (2004)

48. Hall coefficient n2D ~ 4× 1022 /cm2 • Good conductor • r is T-linear below 100 K

49. 2 2 • x= 0.31 (~ 1/3), parent compound of the SC • Better metal,  is smaller that x = 0.71 • R ~ T2 below 30K,  ~ 10 cm at 4K • More like a conventional Fermi liquid

50. JQ specimen J p n Thermoelectric cooler Thermoelectric and Peltier effects holes J JQ Heat current densityJQ accompanies charge current densityJ Ratio of currentsJQ/J = P (Peltier coeff) S = P / T = JQ/ JT