Local orbital occupation and energy levels of Co in ${\text{Na}}_x{\text{CoO}}_2$: A soft x-ray absorption study

We present a combined experimental and theoretical investigation on the orbital occupation and local symmetry of Co in ${\text{Na}}_x{\text{CoO}}_2$. We have carried out polarization dependent $\text{Co}-L_{2,3}$ soft x-ray absorption spectroscopy measurements. By comparing the spectra with the results of configuration-interaction cluster calculations which include the full-atomic multiplet theory, we have found that the local symmetry for the Co ions are well-described by the $D_{3d}$ point group with intermixing between the cubic $t_{2g}^{\pm }$ and $e_g^{\pm }$ orbitals. We have determined that the $t_{2g}$ holes in both the ${\text{Na}}_{0.75}{\text{CoO}}_2$ and ${\text{Na}}_{0.5}{\text{CoO}}_2$ compositions reside mainly in the $a_{1g}$ orbital. The spectroscopically deduced ${\text{Co}}^{4+}/{\text{Co}}^{3+}$ ratio agrees well with the nominal Na concentration. We discuss the surprising observation that the single-site cluster approach is still adequate to reproduce the spectra despite the mixed valent character of the Co ions in this compound.

Figure 1

(Color online) Schematic one-electron energy level diagram for a ${\text{Co}}^{3+}3d^6$ ion: (a) in $O_h$ symmetry with low-spin configuration; (b) $D_{3d}$ symmetry, low spin; (c) $D_{3d}$, intermediate spin; (d) $D_{3d}$, high spin. For a ${\text{Co}}^{4+}3d^5$ ion, one spin down electron is removed from each diagram.

Figure 2

Experimental geometry with polarization of the light in the horizontal plane. $\theta$ is the angle between the electric field vector $\vec{E}$ and the $\mathbf{c}$-axis surface normal, and $\alpha$ the tilt between the Poynting vector and the surface normal.

Figure 3

(Color online) Experimental isotropic $\text{Co}{L}_{2,3}$ XAS spectra of (a) ${\text{Na}}_{0.5}{\text{CoO}}_2$, (b) ${\text{Na}}_{0.75}{\text{CoO}}_2$, (c) ${\text{LaCoO}}_3$ $\left({\text{Co}}^{3+}\right)$ in the low-spin phase, and (d) ${\text{BaCoO}}_3\left({\text{Co}}^{4+}\right)$. Composite spectra of $\left({\text{a}}^{\prime }\right)$ 50% ${\text{LaCoO}}_3$ plus 50% ${\text{BaCoO}}_3$ and $\left({\text{b}}^{\prime }\right)$ 0.75% ${\text{LaCoO}}_3$ plus 25% ${\text{BaCoO}}_3$.

Figure 4

(Color online) Polarization dependent $\text{Co}{L}_{2,3}$ XAS spectra of ${\text{Na}}_{0.5}{\text{CoO}}_2$ and ${\text{Na}}_{0.75}{\text{CoO}}_2$. (a) and (e) are the experimental spectra; (b)–d) and (f)–(h) are the corresponding theoretical spectra together with their respective ${\text{Co}}^{3+}$ and ${\text{Co}}^{4+}$ contributions.

Figure 5

(Color online) Calculated polarization dependent $\text{Co}{L}_{2,3}$ XAS spectra of ${\text{Co}}^{3+}$ (left) and ${\text{Co}}^{4+}$(right) as a function of the bare trigonal crystal field splitting $D_{trig}^0$ (top panel a) and as a function of the mixing parameter $V_{mix}$ in $D_{3d}$ symmetry. See text for definitions of $D_{trig}^0$ and $V_{mix}$.

Figure 6

(Color online) Panel (a): Intensity difference between the $\mathbf{E}\perp \mathbf{c}$ and $\mathbf{E}\parallel \mathbf{c}$ alignments for peak ${\text{A}}^{″}$ in the calculated ${\text{Co}}^{4+}$ spectra as a function of $D_{trig}^{eff}$. Panel (b): idem for peak ${\text{B}}^{″}$ of the ${\text{Co}}^{4+}$ and peak ${\text{B}}^{\prime }$ of the ${\text{Co}}^{3+}$ as a function of $V_{mix}$.