X-ray spectroscopic study of the electronic structure of the high-dielectric-constant material $\mathrm{Ca}{\mathrm{Cu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$

The element-specific valence- and conduction-band densities of states for the high-dielectric-material $\mathrm{Ca}{\mathrm{Cu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$ have been measured using soft x-ray emission and absorption spectroscopies. Ti $L_{\alpha ,\beta }$, Cu $L_{\alpha ,\beta }$, and O $K$ soft x-ray emission spectra of $\mathrm{Ca}{\mathrm{Cu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$ were measured with monochromatic photon excitation on selected energies above the Ti and Cu $L_{2,3}$ and O $K$ absorption edges, respectively. X-ray absorption spectra were recorded at the same edges. The electronic structure was also calculated using density functional theory employing the full-potential linearized augmented plane-wave method. Excellent agreement is seen between the results of these calculations and the measured x-ray emission and absorption spectra. This agreement is particularly good at the O $K$ edge where the resonant behavior of the x-ray emission spectrum can be attributed directly to $\sigma$- and $\pi$-state emission from valence-band O $2p$ states when in resonance with ${\pi }^{*}$ and ${\sigma }^{*}$ conduction-band O $2p$ states. Resonant inelastic x-ray scattering is observed at the Ti $L_{2,3}$ absorption edge and is compared to previous studies of Ti containing perovskite compounds. The role of Cu $3d$ states in determining the band gap of this material is discussed.

Figure 1

(Color online) The conventional cubic cell showing the crystal structure of CCTO with (a) all atoms in the conventional cubic cell comprising two formula units, (b) displaying $1∕8$ of the cell showing the octahedral coordination of the Ti atom, (c) showing the local planar coordination of each O atom, and (d) showing the planar coordination of each Cu atom.

Figure 2

Total DOS (states/eV cell spin) for CCTO and site- and angular-momentum-projected PDOS (states/eV site spin) for Cu $d$, Ti $d$, and O $p$ states. Arrows indicate direction of spin while the vertical line indicates the valence-band maximum. The Ca $d$ PDOS is negligible except above an onset of $6.5\mathrm{eV}$ with a large peak just above that energy.

Figure 3

Ti $L$-edge XAS and SXE spectra from CCTO are shown in the upper part of the figure. The XAS spectrum on the right of the figure corresponds to absorption from the Ti $2p_{1∕2}$ and $2p_{3∕2}$ states. The SXE spectrum on the left was recorded with an excitation energy of $460.9\mathrm{eV}$ and corresponds to radiative transitions into holes on the Ti $2p_{3∕2}$ level. On the lower half of the figure a model SXE spectrum is shown at the left based upon the calculated valence-band Ti $3d$ and $4s$ PDOS. At the lower right is the Ti $3d$ conduction band PDOS. The calculated SXE spectrum and calculated conduction-band PDOS are both broadened by appropriate lifetime and instrumental effects. Spectra and calculations are vertically offset for clarity. Experimental and theoretical energy scales are aligned by reference to the $t_{2g}$ peak in the XAS spectrum.

Figure 4

(a): Series of Ti $L$-edge SXE spectra as a function of excitation energy. (b) The same series of Ti $L$-edge SXE spectra plotted as a function of loss energy. Inset: Ti $L$-edge XAS spectrum with markers indicating excitation energies used in this series of emission spectra. The uppermost emission spectrum in panel (a) was obtained with a photon energy of $480\mathrm{eV}$. The triangular markers in the emission spectra indicate the excitation energy used for each spectrum. The emission spectra are vertically offset for clarity with the interval being proportional to the difference in excitation energies between successive spectra. The vertical lines are a guide to the eye to indicate the location of PDOS features (a) or loss and RIXS features (b).

Figure 5

O $K$-edge XAS and SXE spectra from CCTO are shown in the upper panel. The XAS spectrum on the right of the figure corresponds to absorption from the O $1s$ state. The SXE spectrum on the left was recorded with an excitation energy of $551.2\mathrm{eV}$ and corresponds to radiative transitions into holes on the O $1s$ level. The lower panel shows the calculated O $K$ SXE and XAS on the left and right, respectively. The calculated spectra are derived from the O $2p$ PDOS and broadened by the core-hole lifetime and instrumental broadening. Experimental and theoretical energy scales are aligned by reference to the $t_{2g}$ peak in the XAS spectrum.

Figure 6

Series of O $K$-edge SXE spectra as a function of excitation energy. The photon energies used are indicated by the markers and vertical lines in the XAS spectrum included in the upper left. The topmost SXE spectrum is that shown in Fig. 2 with an excitation energy of $551.2\mathrm{eV}$. The SXE spectra are vertically offset for clarity. The lower panel shows the calculated O $2p$ SXE from $\pi$ and $\sigma$ states as well as the calculated XAS spectrum to ${\pi }^{*}$ and ${\sigma }^{*}$ states. Experimental and theoretical energy scales are aligned by reference to the $t_{2g}$ peak in the XAS spectrum.

Figure 7

Cu $L$-edge XAS and SXE spectra from CCTO. The XAS spectrum (solid) to the right of the figure corresponds to absorption from the Cu $2p_{1∕2}$ and $2p_{3∕2}$ states. The SXE spectrum (dots) to the left was recorded with an excitation energy of $965\mathrm{eV}$. The lower half of the figure shows the calculated Cu $L_{\alpha }$ SXE and XAS spectra based on the Cu $3d$ PDOS taking into account core-hole lifetime and instrumental broadening. The intensity of the calculated XAS spectrum is multiplied by 7 with respect to the calculated SXE spectrum for ease of comparison with the measured spectra.