Influence of cage distortions on the electronic structure and optical properties of ${\mathrm{Ba}}_6{\mathrm{Ge}}_{25}$

Measurements of the optical conductivity on ${\mathrm{Ba}}_6{\mathrm{Ge}}_{25}$ reveal a shift of optical spectral weights towards higher energies, as temperature is lowered below the structural phase transition. This behavior may be understood from the structural modifications revealed from the new structure refinements of x-ray diffraction data from high quality single crystals. Apart from Ba atoms, some Ge cage atoms are also shifted into distant split sites below the phase transition. In this way one covalent bond is broken between the corresponding Ge atoms and they become threefold bonded. Electronic band structure calculations for the low symmetry ordered model show that the bond breaking causes a shifting of three bands from the conduction to the valence region. This leads to a shifting of optical spectral weights towards higher energies, which is in agreement with the experimental data.

Figure 1

The environment of Ge(4-4) in the space group $R3$. Ge atoms are represented by small circles, while Ba’s are represented by gray spheres. The bi-pyramid around Ge(4-4) is formed by Ba(1-2), Ba(1-3), and Ba(3-1) in the basal plane, and Ba(2-4) and Ba(2-2) on the apices. The arrows denote the shifting of the Ge(4-4) and Ba(2-4) to their corresponding split sites. As Ge(4-4) is shifted to one of the split sites, the covalent bond $[\mathrm{Ge}\left(4\text{−}4\right)-\mathrm{Ge}\left(6\text{−}3\right)]$ is broken. The Ge atoms most affected by bond breaking are denoted by black spheres. The dashed lines denote the connections to Ba atoms which, apart from Ge atoms, contribute mostly to the partial DOS of the three shifted bands (see Fig. 3).

Figure 2

(Color online.) The electronic band structures for the HT (above) and LT (below) structural models. The three bands on the bottom of the conduction region in the HT model, denoted by bold (blue) lines, are shifted onto the top of the valence region in the LT model. The reduction of the DOS at the Fermi level, from $61{\mathrm{eV}}^{-1}$ per unit cell for the HT model to $39{\mathrm{eV}}^{-1}$ per unit cell for the LT model, may be seen in the right part of the figure.

Figure 3

The $l$-projected DOS around the region of three shifted bands: Ge $4p$ states and Ba $5d$ states are shown. The contributions from the three bands are shaded black and the rest gray. The contributions from the atoms in the cluster shown in Fig. 1 are presented. Left: Hypothetical structure, where only the Ge(4-4) atom is moved to one of the split sites, and all other atoms are left in their average symmetrical positions. The strongest contributions come from the atoms in the cluster. The large contribution from the Ba(2-4) is due to the fact that Ge(4-4) comes close to Ba(2-4), whose atomic sphere is large. Right: LT model. The only distinctively pronounced contributions come from Ge(6-3) and its neighbor Ge(5-5). The contributions from the other atoms in the cluster are diminished, in comparison with the structure from the left figure. This indicates a stronger hybridization with other states.

Figure 4

The optical conductivity of ${\mathrm{Ba}}_6{\mathrm{Ge}}_{25}$ above $(T=250\mathrm{K})$ and below $(T=170\mathrm{K})$ the structural phase transition. A shift of spectral weights towards higher energies occurs below the phase transition.

Figure 5

The theoretical calculation of the absorptive part of the optical conductivity, based on band structure calculations for the average symmetry HT model and the low symmetry LT model (below the phase transition temperature).