## 1 Introduction
[19] examined bipolar doping behavior and band gap anomalies in CuM\({}^{III}\)O\({}_{2}\) (M = Al, Ga, In) transparent conductive oxides, revealing a counterintuitive trend of increasing band gap with heavier group III cations. This trend-observed in CuAlO\({}_{2}\), CuGaO\({}_{2}\), and CuInO\({}_{2}\)-contrasts sharply with the behavior of traditional semiconductors, where increasing atomic number typically results in a decrease in band gap. Such anomalous electronic characteristics are believed to arise from unique interactions between Cu 3d and O 2p orbitals and the specific nature of the M\({}^{3+}\) cation, which influence both the valence band structure and hybridization effects. Understanding these unconventional trends is essential for the rational design of delafossite-based optoelectronic materials with targeted band gap and carrier transport properties. The magnetic characteristics of CFO have been the subject of extensive investigation through diverse theoretical and computational methodologies aimed at capturing its complex spin dynamics and multiferroic behavior. [PERSON] et al. [20] demonstrated that a Heisenberg spin model with weak magnetic anisotropy offers a more precise description of CFO's magnetic interactions compared to the traditionally used two-dimensional Ising model, which inadequately accounts for the system's non-collinear magnetic ground states. To model the rich and intricate magnetic phase diagrams observed in delafossite multiferroic antiferromagnets, [PERSON] et al. [21] employed a Landau phenomenological approach, incorporating higher-order spin interactions and symmetry-breaking terms. In parallel, [PERSON] et al. [22] utilized first-principles density functional theory (DFT) to in vestigate the microscopic origins of ferroelectricity in CFO, examining both collinear and noncollinear spin arrangements and highlighting the importance of spin-lattice coupling in stabilizing ferroelectric polarization. More recently, [PERSON] et al. [7] developed a magnetic cluster expansion framework that systematically includes all symmetry-allowed spin interactions in CFO, successfully reproducing the multiferroic properties of both pristine and Al-substituted systems through a generalized spin-current model. However, inelastic neutron scattering studies performed by [PERSON] et al. [23] on CFO doped with 3.5% Ga unveiled a distorted screw-type magnetic ground state, indicating the presence of a magnetoelectric coupling mechanism distinct from the conventional spin-current model, possibly involving more complex exchange striction or lattice-mediated effects. These observations emphasize the nuanced and multifaceted nature of spin-lattice entanglement in doped CFO systems. Furthermore, they point to the necessity of integrating multiple theoretical frameworks--ranging from atomistic models to continuum-level approaches--to fully capture the interplay of magnetic, electric, and structural degrees of freedom. The development of such comprehensive models not only advances fundamental understanding but also provides predictive capabilities essential for the tailored design of CFO-based multiferroic materials. Ultimately, elucidating these mechanisms opens the door to engineering materials with finely tuned magnetoelectric responses for integration into multifunctional spintronic and energy-conversion devices. In our prior work [24], we investigated the effects of ion substitution on the magnetic and electronic properties of CFO nanoparticles, specifically examining Mn, Sc, and Mg doping at the Fe site, as well as Li and Ca doping at the Cu site. In the present study, we focus on the impact of Al, Ga, and In doping at the Fe site on the multiferroic behavior and band gap characteristics of bulk CFO, employing the s-d exchange model in conjunction with [PERSON]'s function theory. This approach allows for a microscopic understanding of how different dopant ions influence the spin-charge coupling and electronic structure in the delafossite lattice.