Anomalous Quasiparticle Renormalization in ${\mathrm{Na}}_{0.73}{\mathrm{CoO}}_2$: Role of Interorbital Interactions and Magnetic Correlations

We report an angular resolved photoemission study of ${\mathrm{Na}}_x{\mathrm{CoO}}_2$ with $x\simeq 0.73$ where it is found that the renormalization of the quasiparticle (QP) dispersion changes dramatically upon a rotation from $\Gamma \mathrm{M}$ to $\Gamma \mathrm{K}$. The comparison of the experimental data to the calculated band structure reveals that the quasiparticle renormalization is most pronounced along the $\Gamma \mathrm{K}$ direction, while it is significantly weaker along the $\Gamma \mathrm{M}$ direction. We discuss the observed anisotropy in terms of multiorbital effects and point out the relevance of magnetic correlations for the band structure of ${\mathrm{Na}}_x{\mathrm{CoO}}_2$ with $x\simeq 0.75$.

Figure 1

Left: typical Fermi level crossing observed along a cut close to $\Gamma \mathrm{M}$ [$\psi =173°$ cf. Fig. 2b] Right: corresponding energy distribution curve (EDC) and momentum distribution curve (MDC) at $k=k_F$ and $E_B=0\mathrm{eV}$, respectively.

Figure 2

ARPES data for ${\mathrm{Na}}_{0.73}{\mathrm{CoO}}_2$ (excitation energy $h\nu =21.2\mathrm{eV}$). (a), (b) Momentum distribution maps of the photoelectron intensity integrated over a small energy interval ($E_B\pm 3\mathrm{meV}$) at $E_B=0\mathrm{eV}$ and 0.132 eV measured at $T=25\mathrm{K}$. The measured $k$ region is indicated by the black dotted line in (a). The other regions in $k$ space were obtained by rotating this data set by 120° and 240°. The broken white lines in (a) show the two-dimensional Brillouin zone. High-symmetry points $\Gamma$, K, and M are indicated in (a) and the definition of $\psi$ is given in (b). A fit to $k_F=k_F(\psi )$ is shown as a solid black line. (c) Comparison of the measured band structure and the LDA calculation by Singh (black lines) [17]. The crystal field split $e_g^{\prime }$ and $a_{1g}$ manifolds are indicated.

Figure 3

Cuts through the map data shown in Fig. 2a, 2b. The data are normalized to binding energies above 0.25 eV. Black symbols: QP dispersion determined by fitting MDCs at different $E_B$. Broken lines indicate the fitted linear dispersions (see text). The inset shows the ARPES (symbols) and LDA (lines) dispersions as a function of $k-k_F(\psi )$. LDA for $x=0.73$ in the rigid band approximation (cf. Fig. 4).

Figure 4

(a), (b) $v_F^{\mathrm{PES}}$ and $v_F^{\mathrm{LDA}}$ as a function of $\psi$. The experimental $v_F^{\mathrm{PES}}$ values at a given value of $\psi$ were obtained by averaging over two equivalent cuts (e.g., $\psi =150°$, 210°). The LDA calculations were performed in the rigid band approximation for the low temperature lattice structure using Wien2K. The same behavior was also found by LDA and LSDA calculations in the virtual crystal approximation (cf. Fig. 5). (c) Effective mass of the QP. (a)–(c) $h\nu =21.2\mathrm{eV}$. Solid curves are fits to a sinus function intended to serve as guides to the eye. (d) $\kappa =v_F^{\mathrm{LDA}}/v_F^{\mathrm{PES}}-1$ characterizing the QPR.

Figure 5

(a), (b) FS obtained for $x=0.75$ by LDA in the virtual crystal approximation (VCA), revealing a three-dimensional band structure. (c) FS for the AFM ground state obtained by LSDA in the VCA where the band structure retains its pronounced two dimensionality. The color scale in (a)–(c) indicates $v_F$. (d) Comparison of the measured and LSDA FS. The DFT calculations have been performed using the FPLO code [23].