Effects of crystal structure on Co-$L_{2,3}$ x-ray absorption near-edge structure and electron-energy-loss near-edge structure of trivalent cobalt oxides

$\text{Co-}{L}_{2,3}$ x-ray-absorption near-edge structures (XANES) and electron-energy-loss near-edge structures (ELNES) are calculated from first principles, taking into account the configuration interactions among molecular orbitals for model clusters obtained using fully-relativistic one-electron calculations. The spectra for ${\text{LaCoO}}_3$ at low temperature and for ${\text{LiCoO}}_2$, both of which have low-spin ${\text{Co}}^{3+}$ ions in similar local environments, are well reproduced. To elucidate the cause of the spectral shape, the effects of the crystal structure and coordination distance are investigated using idealized crystal structures of layered rock salt, perovskite, rock salt, and spinel. The calculated spectra for these crystals with the same coordination distance are found to show clear differences despite identical $3d$ electronic configurations and local environments of the first ligand shell. The crystal structure dependence can be explained by the difference in the Madelung potential acting on the $3d$ orbitals. The results of the calculations for various coordination distances indicate that not only the crystal field splitting parameter, namely, $10Dq$, but also the coordination distance is a key factor in determining the spectral shape. This is attributed to the change in the spatial distribution of the $3d$ orbitals.

Figure 1

(Color online) Theoretical Co $L_{2,3}$-edge XANES for ${\text{LaCoO}}_3$ and ${\text{LiCoO}}_2$ compared with experimental spectra. The initial spin state of calculated spectra is fixed to low-spin state. The experimental spectra are taken from Refs. 20, 21.

Figure 2

(Color online) (Bottom) Theoretical $\text{Co-}{L}_{2,3}$ XANES for ${\text{Co}}^{3+}$ with low-spin state in idealized perovskite (PE) and idealized layered rock salt (LRS). (Second bottom) The corresponding oscillator strength for multielectron eigenstates. (Top and second top) The composition of final configurations for ${\left(2p\right)}^5{\left(t_{2g}\right)}^6{\left(e_g\right)}^1$ and ${\left(2p\right)}^5{\left(t_{2g}\right)}^5{\left(e_g\right)}^2$.

Figure 3

(Color online) (a) Crystal structures of layered rock salt (LRS), perovskite (PE), rock salt (RS), and spinel (SP). [(b), (c)] Madelung potential around the ${\text{CoO}}_6^{9-}$ cluster for each structure on the (100) plane. (d) The same potential on the (110) plane.

Figure 4

Difference between the Madelung potential acting on $e_g$ and $t_{2g}$ orbitals as a function of the reduction/enhancement factor, $Q$. $Q=1$ corresponds to the potential generated using formal charges.

Figure 5

Relationship between the difference between the Madelung potential acting on $e_g$ and $t_{2g}$ orbitals and the magnitude of $10Dq$ at the ground state. The Co-O bond length in the ${\text{CoO}}_6^{9-}$ cluster is fixed at $1.92\text{Å}$. The reduction/enhancement factor of the Madelung potential, $Q$, is set at 0, 0.25, 0.5, 0.75, 1, 1.25, and 1.5. Filled marks denote the values with $Q=1$.

Figure 6

(Color online) Theoretical $\text{Co-}{L}_{2,3}$ XANES with low-spin initial spin state with varying the reduction/enhancement factor of the Madelung potential, $Q$. $Q$ is set at 0, 0.25, 0.5, 0.75, 1, 1.25, and 1.5. The third spectrum from the top (highlighted by red) corresponds to the case with $Q=1$.

Figure 7

Energy and height of subpeak b relative to those of main-peak a as a function of $\Delta E^{\text{MP}}$. The Co-O bond length in the ${\text{CoO}}_6^{9-}$ cluster was fixed at $1.92\text{Å}$. Values with $Q=0$, 0.25, 0.5, 0.75, 1, 1.25, and 1.5 are included. Filled marks denote the values with $Q=1$.

Figure 8

(Color online) Relative intensity between peaks b and a as a function of $10Dq$. Values with the Co-O bond length $R=1.82$, 1.92, and $2.02\text{Å}$, and $Q=0$, 0.25, 0.5, 0.75, 1, 1.25, and 1.5 are included. Filled marks denote the values with $Q=1$. The straight lines (solid, dashed, or dotted) connect the results with $Q=1$. The dotted curves enclose the results with the same $R$.

Figure 9

(Color online) Theoretical $\text{Co-}{L}_{2,3}$ XANES for isolated clusters in ${\text{O}}_h$ symmetry with varying Co-O bond lengths, $R$.

Figure 10

(Color online) (a) Difference in partial charge distributions of the $e_g$ orbitals between PE and LRS with $R=1.92\text{Å}$, $\Delta \rho ={\rho }_{\text{LRS}}\text{−}{\rho }_{\text{PE}}$. (b) Averaged radial distance of $e_g$ orbitals, ${⟨r⟩}_{e_g}$, calculated for different Madelung potential and $R$, as a function of $10Dq$. $Q$ is set at 0, 0.25, 0.5, 0.75, 1, 1.25, and 1.5. Filled marks denote the values with $Q=1$. The straight lines connect the results with $Q=1$ and the dotted curves enclose the results with the same $R$.