We report the results of the full-potential linearized augmented plane wave (FP-LAPW) calculations on the structural, elastic, optoelectronic and magnetic properties of CdHo$_2$S$_4$ spinel. Both the generalized gradient approximation (GGA) and Trans-Blaha modified Becke-Johnson potential (TB-mBJ) are used to model the exchange-correlation effects. The computed lattice parameter, internal coordinate and bulk modulus are in good agreement with the existing experimentaldata. According to the calculated elastic moduli, CdHo$_2$S$_4$ is mechanically stable with a ductile nature and a noticeableelastic anisotropy. The ferromagnetic phase of CdHo2S4 is energetically favourable compared to non-magnetic one, with ahigh magnetic moment of about 8.15 $\mu$B. The calculated band structure demonstrates that the title compound is a direct bandgap semiconductor. The TB-mBJ yields a band gap of $\sim$1.86 and $\sim$2.17 eV for the minority and majority spins, respectively.The calculated optical spectra reveal a strong response in the energy range between the visible light and the extreme UVregions.

Owing to the fact of the AB$_2$O$_4$ spinel oxide’s chemical and thermal stability, and other intriguing properties make them suitable candidate materials for many applications, including chemical looping and catalytic reactions. To do our investigations, a short-range non-Coulomb potential theoretical model is used to calculate the zone-centre, elastic constants, infrared phonon mode frequencies, Raman phonon mode frequencies, velocities of the sound wave along the highly symmetric three crystallographic-axes and Debye temperature of the vanadium spinel oxides AV$_2$O$_4$ (A $=$ Mn, Fe and Zn). The preliminary results of our calculations show that the interaction inthe second neighbour (V–O) is much stronger than the interaction of the first neighbour (A–O). Moreover, from the analysis of the obtained results of elastic constants, the nature of the studied vanadium spinels are found to beductile.