Electrons on a triangular lattice in Na-doped Cobalt Oxide Yayu - - PowerPoint PPT Presentation

Hvar Sep 2005

Electrons on a triangular lattice in Na-doped Cobalt Oxide

Yayu Wang, Lu Li, N.P.O. Nyrissa Rogado, M.L. Foo, S. Watauchi, R. J. Cava. Princeton University

• 1. Frustration on triangular lattice
• 2. Thermopower in NaxCoO2
• 3. ARPES
• 4. Hall effect
• 5. Phase diagram

Thermopower

Ratio of currents JQ/J = Π (Peltier coeff) Usually measured as thermopower S

• S = Π / T = JQ/ JT

Heat current density JQ = S T J specimen

W

n p

I

Thermoelectric cooler

J JQ

Heat current density JQ accompanies charge current density J holes

Figure of merit for thermoelectrics

The ZT number

ZT = (S2/ρ)(T/κ)

S = thermopower ρ = resistivity κ = thermal conductivity ZT ~ 1 in Bi2Te3 (at 300 K)

Maximize ZT and minimize resistivity (physically conflicting demands) ΔTmax = ½ ZT2 Max temp. difference

Nax CoO2

Na ions (dopants) sandwiched btw layers of tilted CoO2 octahedra Co ions define a triangular lattice tilt Octahedra tilted to form a layer

building block

Na Co

Terasaki, Uchinokura 1997

S

Sommerfeld x = 0.71

Terasaki et al Phys. Rev. B (1997)

Large thermopower S of NaxCoO2

as grown

Na Co

Metallic resistivity but antiferromagnetic in spin response

(Curie-Weiss Metal)

• In-plane field H || - T
• Strong field suppression
• f Thermopower

T

• B

V

S Field dependence of S in NaxCoO2

Wang et al. Nature ‘03

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

Conclusion:

• 1. Spin entropy is the source

for enhanced thermopower

• 2. Key for new thermo-electric

materials -- Spin

S(H)/S(0) - 1

Wang et al. Nature ‘03

ARPES: Weak quasiparticle dispersion Single-particle hopping :

t < 0 and |t| ~ 10 meV (bandwidth < 100 meV) Momentum Kinetic energy (eV)

Small bandwidth à Low degeneracy T

• Z. Hasan et al. (PRL ‘04)

Fermi Surface of Na0.71CoO2 measured by ARPES

Large hole-like FS Hopping integral t ~ 10 meV Fermi velocity < 0.4 eV.A

Hasan et al. Absence of small pockets

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

• nly below 150K

NaxCoO2

Multiple electronic phases vs. Na content as grown

Foo et al. PRL ‘04

Insulating state

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

x = 0.50 (1/2):

• Two kinks at Tc1=88K and Tc2=53K in χ
• Resistivity shows insulating behavior below T=53K

An unexpected insulator at x = ½

a* b* a b 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)

Thermal Conductivity Hall coefficient

Foo et al., PRL ‘04

Foo et al., PRL ‘04

Systematic change vs x except at x = ½

Susceptibility Resistivity

NaxCoO2

Multiple electronic phases vs. Na content as grown

Foo et al. PRL ‘04 Spin

• rdere

d

Is the 1-band description adequate? Do eg and t2g bands cross as x 1 ? Is this limit a band insulator? At x = 1, all Co are 3+ Is system a band insulator?

ρ (mΩcm)

300 mΩcm 150 mΩcm X = 1 X = 0.82

staging phase separation for x > 0.75 For x 1, remaining holes segregate into layers! But bulk is insulating. Resistivity of NaxCoO2 in limit x 1 holes Resistivity profile same as x incr. to 1 aside from scale factor

S x = 0.71 x = 0.88

Sommerfeld

Further enhancement of thermopower

ZT

NaxCoO2 (x = 0.88)

In doping interval 0.75< x < 1.0 1. Staging phase segegation of holes endemic 2. A band insulator in the limit x = 1.0 3. Thermopower is very large in this range (5 times value in x = 0.71 at 100 K) 4. Resistivity remains low 5. ZT value exceeds that of Bi2Te3 at 100 K. 6. Exploit staging/segregation to optimize ZT?

T-linear Hall coefficient

Yayu Wang, 03

RH conv. metal

High-frequency RH* in tJ model (B.S. Shastry ‘93, ‘03)

σH ~ i(βt)3 exp(iα) σ ~ (βt)2

R*H ~ σH/Hσ2 ~ (βt) -1 Hopping Hall current in triangular lattice (Holstein, ‘61)

σH ~ t12 t23 t 31 ~ i t3 exp(iα)

Why is RH T-linear? βt << 1 (β = 1/T) T-linear? Peierls phase α = 2π φ/φ0 φ t12 1 3 2 t13

Hopping on Kagome lattice (Maekawa)

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 S than at 0.7, ZT value at 100 K is encouraging

En d