First Principles Study of Electronic and Vibrational Properties of BaHfN$_{2}$*

The transition metal nitride BaHfN$_{2}$, which consists of weakly bonded neutral slabs of closed shell ions, has structural and chemical similarities to other layered nitrides which have impressive superconducting T$_{c}$'s when electron doped: A$_{x}$HfNCl, A$_{x}$ZrNCl, A$_{x}$TiNCl, with T$_{c}$= 26, 15.5 and 16 K, respectively for appropriate donor (A) concentrations x. These similarities suggest that BaHfN$_{2}$ may exhibit relatively high T$_{c}$ upon doping, with effects of structure and the role of specific transition metal ions yet to be understood. We carried out electronic structure calculations for stoichiometric BaHfN$_{2}$ and found a direct band gap of about 0.8 eV within Density Functional Theory, using the local density approximation. Doped electrons are expected to occupy the lowest conduction band, which has primarily Hf 5d$_{xy}$ character (similar to $\alpha $-TiNCl which has the lowest conduction band primarily composed of Ti 3d$_{xy})$. We also find that the two N sites, N1 in the Hf layer and N2 in the Ba layer, have very different Born effective charges (BEC). The deviations from the formal (-3) charge are opposite for the two sites. Comparison to the BEC's of the other compounds, and to the LO-TO splitting, will be discussed.