Structural,electronic, magnetic and vibrational properties of half-Heusler NaZrZ (Z = P,As, Sb) compounds

The structural, electronic, magnetic and vibrational properties of NaZrP, NaZrAs and NaZrSb half-Heusler alloys have been investigated on the basis of density functional theory and generalized gradient approximation. There are three types of structures for these compounds where type a is the most stable one. It is found that all of these materials are half-metallic ferromagnets with a magnetic moment of $2{\mu }_{\mathrm{B}}$. The half-metallic gaps are estimated to be 0.16, 0.35 and 0.55 eV for Z = P, As and Sb, respectively. The hybridization between s and $t_{2g}$ orbitals of Zr with s and p orbitals of Z leads to half-metallic ferromagnetism in these compounds. The effect of strain on the half-metallic property is also investigated, and we notice that the half-metallicity is conserved up to the lattice compressions of 54.43%, 48.29% and 47.55% for NaZrP, NaZrAs and NaZrSb, respectively. The dynamical stability of these compounds is confirmed using dispersion curves. The Curie temperatures are also estimated to be 501.29 K, 855.49 K and 1348.88 K for NaZrP, NaZrAs and NaZrSb, respectively. Therefore, it seems that NaZrZ (Z = P, As, Sb) could be suitable materials for spin-injector applications.