NMR experiments and electronic structure calculations in type-I BaAlGe clathrates

We describe ${}^{27}\text{A}\text{l}$ NMR experiments on ${\text{Ba}}_8{\text{Al}}_x{\text{Ge}}_{46-x}$ type-I clathrates coupled with ab initio computational studies. For $x=16$, calculated spectra determined by the ab initio results gave good agreement with the measurements, with best-fitting configurations also corresponding to the computed lowest-energy atomic arrangements. Analysis of the NMR results showed that a distribution of Knight shifts dominates the central portion of the line. Computational results demonstrate that this stems from the large variation of carrier density on different sites. Al-deficient samples with $x=12$ and 13 exhibited a split central NMR peak, signaling two main local environments for Al ions, which we connected to the presence of vacancies. Modeling of the wide-line spectrum for $x=12$ indicates a configuration with more Al on the $24k$ site than for $x=16$. The results indicate the importance of nonbonding hybrids adjacent to the vacancies in the electronic structure near $E_F$. We also address the static distortions from $Pm\overline{3}n$ symmetry in these structures.

Figure 1

(Color online) NMR central lines for ${\text{Ba}}_8{\text{Al}}_x{\text{Ge}}_{46-x}$, $x=12$, 13, and 16, at room temperature.

Figure 2

Full NMR lineshape for ${\text{Ba}}_8{\text{Al}}_{12}{\text{Ge}}_{34}$ from a spin-echo measurement at 4.2 K. Inset shows central line portion of the spectrum.

Figure 3

Spinning NMR measurement of ${\text{Ba}}_8{\text{Al}}_{12}{\text{Ge}}_{34}$ at room temperature, with 14 kHz rotor speed, and higher frequencies to the left. Inset: rotor speed dependence shows that broad background corresponds to lower-shift peak. Note reversal of paramagnetic shift axis orientation relative to other figures.

Figure 4

(Color online) Frequency dependence of $T_1$ for ${\text{Ba}}_8{\text{Al}}_{12}{\text{Ge}}_{34}$ compared to central line shape (lower curve). Solid curve with monatonic decay is $T_1$ calculated according to Korringa law, described in text.

Figure 5

(Color online) Frequency dependence of $T_1$ for ${\text{Ba}}_8{\text{Al}}_{16}{\text{Ge}}_{30}$ compared to central line shape (lower curve). Solid curve with monatonic decay is $T_1$ calculated according to Korringa law.

Figure 6

(Color online) $T_{1}T$ reciprocal product for ${\text{Al}}_{12}$ and ${\text{Al}}_{16}$ samples at peaks of the central lineshapes. Horizontal line indicates Korringa behavior. Inset: $K^2{T}_{1}T$ product measured at the same peak positions, with same symbols as main plot. Horizontal line: Korringa relation for bare ${}^{27}\text{A}\text{l}$ nucleus. Dashed lines are guides to the eye.

Figure 7

Simulated NMR spectra for several ${\text{Ba}}_8{\text{Al}}_{16}{\text{Ge}}_{30}$ configurations, together with spin-echo NMR spectrum measured at 4 K. Inset: expanded view of the central-transition region.

Figure 8

(Color online) Calculated electronic structures for Ba-Al-Ge clathrate configurations. (a) and (b): Band structures for ${\text{Ba}}_8{\text{Al}}_{16}{\text{Ge}}_{30}$, 3-1-12-0 and 3-4-9-2, respectively, notation as defined in text; (c), (d), and (e): Band structures for ${\text{Ba}}_8{\text{Al}}_{12}{\text{Ge}}_{34-y}{◻}_y$, ${◻}_0$ 4-8-0-0-0, ${◻}_1$ 4-8-0-0-0, and ${◻}_1$ 0-0-12-0-2 configurations, respectively. (f): Density of states for the latter, including partial densities for Al adjacent to a vacancy, $\text{Ge}\left(6c\right)$, $\text{Ba}\left(2d\right)$, and the total scaled by 1/10.

Figure 9

(Color online) Calculated NMR line shape from computed Knight shifts for 3-1-12-0 configuration, with carrier density $1.1\times {10}^{21}{\text{cm}}^{-3}$, compared to ${\text{Al}}_{16}$ room- temperature data (filled circles). Calculated $6c$ and $16i$ portions are as indicated; remainder due to $24k$ sites.

Figure 10

Simulated NMR lines for several configurations of ${\text{Ba}}_8{\text{Al}}_{12}{\text{Ge}}_{34-y}$ together with spin-echo NMR lineshape. Inset: expanded view of the central transition region, with calculated spectrum only for ${◻}_1$ 0-0-12-0-2 configuration with one vacancy shown.

Figure 11

(Color online) Calculated NMR line shape (solid curve) from computed Knight shifts for ${◻}_1$ 0-0-12-0-2 configuration, compared to ${\text{Al}}_{12}$ room-temperature data (filled circles).