Singly occupied 4$f$ antiferromagnetic insulators: CePO$_4$ and CeVO$_4$

Rare-earth containing wide band gap oxides, which provide spin-photon interface and narrow linewidth optical emission, are getting significant attention as the most promising candidate materials in advancing quantum transduction and memories. Here, from $ab~initio$ calculations, we identify antiferromagnetic ground states in structurally preferred monoclinic CePO$_4$ and tetragonal CeVO$_4$ exhibiting localized occupied and unoccupied Ce $4f$ states with $4f-4f$ transition characteristics. Interestingly, in CePO$_4$, O $2p$ and P $3p$ states hybridize negligibly with Ce $4f$ states, while in CeVO$_4$, V $3d$ and O $2p$ states hybridize and appear as extended states in between the occupied and unoccupied Ce $4f$ states. Here, phonon calculations and analysis identify and differentiate Raman active phonon modes along with the spin phonon coupling of Ce in both CePO$_4$ and CeVO$_4$ that ultimately lead to different $4f$ ground state crystal field multiplets, which are critical to accurately describe electronic transitions for foundational quantum transduction and memories. Further, the identified $C_1$ site symmetry of Ce, lacking inversion symmetry in CePO$_4$, is relevant for quantum memories and $D_{2d}$ site symmetry of Ce exhibiting inversion symmetry in CeVO$_4$ is relevant for quantum transduction.