First-principles study of infrared, Raman, piezoelectric and elastic properties of Mg-IV-N\textsubscript{2} (IV = Ge, Si, Sn)

Mg-IV-N\textsubscript{2} compounds with IV=Si, Ge, Sn are ultra-wide band gap semiconductors with various potential electronic and optoelectronic applications. They share the $\mathit{\text{Pna}}$2\textsubscript{1} space group crystal structure. Here we present Density Function Perturbation Theory (DFPT) calculations of the vibrational modes of these materials. We focus on the vibrational modes at the zone center to establish the relation between vibrational modes and their corresponding point-group symmetries, which determine the Raman and infrared spectra but also report the full Brillouin zone phonon dispersions and density of states. We also determine the piezoelectric tensor and the elastic compliance tensor.