Session X1: Cobaltates

Charge Disproportionation and Spin Ordering in Na$_x$CoO$_2$

Observation of strong correlation effects in Na$_x$CoO$_2$ for $x>$0.70 several years ago was followed by observation of superconductivity up to 5 K for $x\approx$0.3 when the material was hydrated, and then by charge disproportionation, spin ordering, and insulating behavior at $x=$0.5. The similarities with HTS cuprates are less compelling than the differences, and the first question for theorists is how to understand and describe the electronic system and how it varies with doping. Here we will focus on a description of correlation effects within the correlated band (LDA+U) approach, and compare closely with observed behavior to begin to quantify the strength and character of correlation effects. The $x$=0 and $x$=0.5 systems will be given particular atention. At $x$=0.5, disproportionation and gap opening is followed in detail through a first order charge disproportionation transition 2Co$^{3.5+} \rightarrow$ Co$^{3+}$+Co$^{4+}$ as the correlation strength (U/W) is increased. Comparing with data in the $x\approx 0.3$ regime suggests the system has moved into the multiband regime where the effective Coulomb repulsion becomes $U_{eff} = U/\sqrt{3}$ and strongly lessens correlation effects.   

ARPES studies on NaxCoO2

We report systematic angle-resolved photoemission studies on Na$_{x}$CoO$_{2}$ single crystals for a wide range of Na concentrations. We observe a large Fermi surface centered at the $\Gamma $ point, which satisfies Luttinger theorem. However, the small Fermi surface pockets predicted by band theory near the K points are not observed. Instead, ``sinking islands'' with the binding energy of 100 -- 200 meV are observed. In addition, we observe a strong ``kink'' in the band dispersion at $\sim $ 70 meV binding energy, with weak dependence on momentum, doping, and temperature, suggesting a strong coupling between electrons and a collective mode, possibly an oxygen phonon mode.   

The infrared conductivity of Na$_x$CoO$_2$: evidence of gapped states

We present infrared ab-plane conductivity data for the layered cobaltate Na$_x$CoO$_2$ for $x=0.25, 0.30, 0.50$, and $0.75$. The Drude weight increases monotonically with hole doping, $1-x$. At the lowest hole doping level 0.75 the system resembles the normal state of underdoped cuprate superconductors with a scattering rate that varies linearly with frequency and temperature and there is an onset of scattering by a bosonic mode at 600 cm$^{-1}$. The hole doping level of $x=$0.30 sample shows a metallic behavior and a bosonic mode with a similar onset frequency as $x=$0.75. Doping to both $x=0.50$ and 0.25 causes a gap to develop in the optical conductivity at low temperatures and the material becomes an insulator. The spectral weight lost in the gap region is shifted to a prominent peak. We propose that the two gapped states of $x$=0.50 and 0.25 are pinned charge ordered states.   

Charge ordering and magneto-polarons in Na$_x$CoO$_2$

Using spectral ellipsometry, we measured the dielectric function of a Na$_x$CoO$_2$ single crystals. In particular, we investigated samples with x$>$0.75 that exhibit bulk AF with T$_{N}$=20K. We identify two prominent transitions in the optical response as a function of temperature. The first one at 260-280 K involves marked changes of the electronic and lattice responses that are indicative of charge ordering. Besides the formation of a very narrow Drude-peak we observe a strong collective mode and the formation of a pseudogap with a large energy scale of about 0.5 eV. The second transition occurs at T$_N$, it also involves a surprisingly large energy scale of about 0.4 eV and gives clear evidence for a strong spin-charge coupling. The data are discussed in terms of charge ordering and formation of magneto-polarons due to a charge-induced spin-state transition of adjacent Co$^{+3}$ ions. \\ C.Bernhard et al., PRL 93, 167003 (2004)   

Spin fluctuations in Na$_{x}$CoO$_{2}$ from neutron inelastic scattering

The recent discovery of superconductivity in water-intercalated Na$_{x}$CoO$_{2}$ has been greeted with great excitement and has raised speculation about another possible route to high-$T_c$ superconductivity. What is exciting is that both the magnetic transition metal (Co) and the geometry of the layers (triangular) are different from other transition-metal oxide superconductors (e.g. cuprates and ruthenates), so it is likely that a new mechanism of superconductivity is applicable. Given what we know about superconductivity in other unconventional oxide superconductors it is also probably that magnetic fluctuations play a role in the formation of superconductivity. I will report neutron scattering measurements of the magnetic dynamics for the non-superconducting precursor material Na$_{x} $CoO$_{2}$ ($x=0.75$). The data reveal ferromagnetic correlations within the cobalt-layers and antiferromagnetic correlations perpendicular to the layers. Surprisingly, despite the two-dimensional structure of the material the magnetic correlations are found to be three-dimensional, with the inter- layer exhange about a factor two larger than the intra-layer exchange. I will discuss the results in relation to current theories of the electronic structure.