Core-hole effect on dipolar and quadrupolar transitions of $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ and $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ at Ti $K$ edge

Experimental pre-edge fine structures in the x-ray absorption spectra of $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ and $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ at Ti $K$ edge are successfully reproduced within the framework of first-principles one-electron theory using the full-potential augmented plane wave plus local orbitals method. The importance of the following two points has been demonstrated: (1) proper inclusion of a Ti $1s$ core-hole using a large supercell, and (2) consideration of both dipolar and quadrupolar transitions. The core-hole effect is found to be more significant for quadrupolar transitions that form the first two peaks of the pre-edge structure, i.e., $p1$ to $p2$. They correspond to $t_{2g}$ and $e_g$ bands of the core-holed Ti. The other two peaks, $p3$ and $p4$, are found to be entirely due to the dipolar transition.

Figure 1

Comparison of Ti $K$-edge NEXAFS spectra of $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ between (a) experiment and calculations (b) without core-hole effect by unit-cell, and (c) with core-hole effect by supercell. The calculated spectra are the sum of dipolar and quaprupolar contributions. Note that the energies of calculated spectra are (b) the relative energy to the highest occupied band and (c) the calculated transition energy, respectively.

Figure 2

Same view for $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ as Fig. 1.

Figure 3

View of pre-edge region for $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$. Thin dashed and solid lines are for dipolar (d) and quaprupolar (q) contributions, and thick solid line is the sum of these two.

Figure 4

Same view for $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ as Fig. 3.

Figure 5

(Top) Projected partial density of states $\left(p\text{−}\mathrm{PDOS}\right)$ of the core-holed Ti in $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$. (bottom) $p\text{−}\mathrm{PDOS}$ of Ti at the ground state. From left to right, $3d$, $4s$, and $4p$ components. $3d$ components are divided into $t_{2g}$ (dashed) and $e_g$ (solid) symmetries. Energies are relative ones to the highest occupied band.

Figure 6

Same view for $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ as Fig. 5. Note that $e_g$ and $t_{2g}$ components are approximately denoted by the sums of $d_{x2}$, $d_{y2}$, and $d_{z2}$, and $d_{xy}$, $d_{yz}$, and $d_{xz}$ in Ti $3d$, respectively, assuming a pseudocubic structure.