Electronic structure of the ternary Zintl-phase compounds ${\mathrm{Zr}}_3{\mathrm{Ni}}_3{\mathrm{Sb}}_4$, ${\mathrm{Hf}}_3{\mathrm{Ni}}_3{\mathrm{Sb}}_4$, and ${\mathrm{Zr}}_3{\mathrm{Pt}}_3{\mathrm{Sb}}_4$ and their similarity to half-Heusler compounds such as $\mathrm{ZrNiSn}$

The Zintl-phase compounds ${\mathrm{Zr}}_3{\mathrm{Ni}}_3{\mathrm{Sb}}_4$, ${\mathrm{Hf}}_3{\mathrm{Ni}}_3{\mathrm{Sb}}_4$, and ${\mathrm{Zr}}_3{\mathrm{Pt}}_3{\mathrm{Sb}}_4$, are the first compounds discovered in this crystal structure not to contain Y or an $f$-electron atom. We have attempted to understand their electronic structure by comparison to the more extensively studied half-Heusler compounds such as $\mathrm{ZrNiSn}$. While the half-Heusler compounds have more ionic bonding in its stuffed-$\mathrm{NaCl}$ crystal structure compared to the covalent Zintl network, several similarities were found between the calculated electronic structures. These similarities include the nature of the bonding, the formation of the ternary compound by adding Ni (or Pt) atoms into the octahedrally coordinated pockets of a known binary compound, and the gap formation due to Ni (or Pt) $d\text{−}\mathrm{Zr}$ $d$ hybridization.

Figure 1

Half-Heusler crystal structure of $\mathrm{YNiSb}$ where Ni atoms are inserted into a $\mathrm{YSb}$ $\mathrm{NaCl}$-type lattice.

Figure 2

Crystal structure of ${\mathrm{Th}}_3{\mathrm{Co}}_3{\mathrm{Sb}}_4$. The ${\mathrm{Th}}_3{\mathrm{Sb}}_4$ network is shown by the heavy lines with the Co atoms lying within the voids left by this network.

Figure 3

Electronic structures of (a) ${\mathrm{Zr}}_3{\mathrm{Ni}}_3{\mathrm{Sb}}_4$, (b) ${\mathrm{Hf}}_3{\mathrm{Ni}}_3{\mathrm{Sb}}_4$, and (c) ${\mathrm{Zr}}_3{\mathrm{Pt}}_3{\mathrm{Sb}}_4$.

Figure 4

The (a) $\mathrm{Sn}p$ and (b) $\mathrm{Zr}d$ orbital characters of $\mathrm{NaCl}\mathrm{ZrSn}$, the parent compound of the half-Heusler $\mathrm{ZrNiSn}$. The size of the circles associated with the “fatband” representation corresponds to the orbital character of the band.

Figure 5

The (a) $\mathrm{Sb}p$ and (b) $\mathrm{Zr}d$ orbital characters of ${\mathrm{Zr}}_3{\mathrm{Sb}}_4$. The size of the circles corresponds to the amount of the orbital character in the band. Note the similarity between the band characters in ${\mathrm{Zr}}_3{\mathrm{Sb}}_4$ and $\mathrm{ZrSn}$ (Fig. 4) with the $\mathrm{Zr}d$ above and $\mathrm{Sb}p$ below $E_F$ forming a semimetal.

Figure 6

The (a) $\mathrm{Zr}d$, (b) $\mathrm{Sb}p$, and (c) $\mathrm{Ni}d$ orbital characters of ${\mathrm{Zr}}_3{\mathrm{Ni}}_3{\mathrm{Sb}}_4$. Again, the size of the circles corresponds to the amount of orbital character. The orbital character for $\mathrm{Zr}d$ and $\mathrm{Sb}p$ is almost the same as in ${\mathrm{Zr}}_3{\mathrm{Sb}}_4$ (Fig. 5), but the $\mathrm{Ni}d$ states hybridize with the $\mathrm{Zr}d$ to open a band gap.