Multigap absorption in $\mathrm{CaCu}{}_3\mathrm{Ti}{}_4\mathrm{O}{}_{12}$ and the prediction capability of ab initio methods

We report the electronic properties of the quadruple perovskite $\mathrm{CaCu}{}_3\mathrm{Ti}{}_4\mathrm{O}{}_{12}$ as obtained via several density-functional based methods and propose a new interpretation of optical experiments to the effect that four distinct transitions (centered around 0.7, 1.5, 2.5, and 3.5 eV) contribute to the spectrum. The comparison with experiment is satisfactory, especially after we account for the effects of spin disorder, which does not close the fundamental gap but suppresses the transition intensity. We find that some of the methods we employ tend to overestimate considerably the gaps for standard values of the respective adjustable parameters.

Figure 1

Crystal structure of CCTO.

Figure 2

LDA vs VPSIC bands of CCTO. Arrows indicate schematically the four transitions discussed in the text.

Figure 3

DOS of CCTO from VPSIC in the near-gap region, projected on orbitals of the Cu and O atoms of a plaquette in the $xy$ plane (see Fig. 1).

Figure 4

Magnetization density in CCTO seen along the $z$ axis. All three kinds of Cu-O plaquettes are visible. The Cu onto which the DOS in Fig. 3 is projected is the one at bottom center, with the $xy$-orbital-shaped density.

Figure 5

GGA bands for the CCTO cell with noncollinear spins mimicking the disordered PM.

Figure 6

Extinction coefficient for PM and AF CCTO calculated with VPSIC. Compare with Fig. 7 (inset) of [10].

Figure 7

Tauc relation for CCTO (exponent for indirect forbidden transitions) calculated with VPSIC. Compare with Fig. 8.

Figure 8

Experimental Tauc relation [9] for CCTO, to be compared with Fig. 7. Lines are possible fits for indirect forbidden transitions whose intercepts with the frequency axis identify the minimum gap. Figure by courtesy of P. Lunkenheimer.

Figure 9

Dynamical conductivity for CCTO calculated with VPSIC. Compare with Fig. 7 of [8].

Figure 10

Energy-loss function of AF and PM CCTO. Inset: Main plasmon in the AF.

Figure 11

$\mathrm{GGA}+U$ transitions (see text and the scheme in Fig. 2) vs $U-J$ for Cu.

Figure 12

HSE transitions (see text and the scheme in Fig. 2) vs $\alpha$, with $\mu$ fixed at $0.2\AA {}^{-1}$.

Figure 13

HSE transitions (see text and the scheme in Fig. 2) vs $1/\mu$, with $\alpha$ fixed at 0.25.