High-throughput computational screening of Heusler compounds with phonon considerations for enhanced material discovery

High-throughput (HTP) $ab$ $initio$ calculations are performed on 27,865 Heusler compositions, covering a broad range of regular, inverse, and half-Heusler compounds in both cubic and tetragonal phases. In addition to conventional stability metrics, such as formation energy, Hull distance, and magnetic critical temperature $T_{\mathrm{c}}$, phonon stability is assessed by systematically conducting $ab$ $initio$ phonon calculations for over 8,000 compounds. The performance of $ab$ $initio$ stability criteria is systematically assessed against 189 experimentally synthesized compounds, and magnetic critical temperature calculations are validated using 59 experimental data points. As a result, we identify 631 stable compounds as promising candidates for further functional material exploration. Notably, 47 low-moment ferrimagnets are identified, with their spin polarization and anomalous Hall/Nernst conductivity calculated to provide insights into potential applications in spintronics and energy harvesting. Furthermore, our analyses reveal linear relationship between $T_{\mathrm{c}}$ and magnetization in 14 systems and correlations between stability and atomic properties such as atomic radius and ionization energy. The regular/inverse structures preference in $X_2YZ$ compound and tetragonal distortion are also investigated for a broad Heusler family.