## 1 Introduction  
CuFeO\({}_{2}\) (CFO) belongs to the delafossite family of minerals, generally represented by the formula ABO\({}_{2}\). This structural class is distinguished by layers of linearly coordinated A-site cations interleaved with edge-sharing BO\({}_{6}\) octahedral networks [1, 2]. CFO finds utility in a range of energy-related applications, such as solar cells, photocathodes, photoelectrochemical water splitting, and as a cathode material for lithium-ion batteries. It is recognized as a prototypical type-II multiferroic compound, in which electric polarization arises from complex non-collinear spin arrangements. In CFO, ferroelectric polarization can be induced either through the application of an external magnetic field or by substituting the Fe site with dopant ions such as Al, Ga, Rh, Ni, Mn, or Co [3, 4, 5, 6, 7]. The effects of Ga and Sc doping on the dielectric polarization of CFO have been systematically investigated by [PERSON] et al. [8] and [PERSON] et al. [9], respectively. Their results indicated that the polarization increases with higher Ga content, while Sc doping suppresses the polarization. This doping sensitivity is thought to arise from the modulation of superexchange pathways and local structural distortions, which influence magnetic interactions and polar order. Recent experimental and computational studies suggest that dopant-induced modifications in bond geometry, especially Fe-O-Fe angles, play a pivotal role in tuning the magnetic frustration and spin-lattice coupling. Consequently, precise control over chemical substitution provides a viable strategy to tailor CFO's multiferroic response, offering new avenues for the development of advanced multifunctional devices in electronics, spintronics, and energy conversion technologies. In contrast to CFO, compounds such as CuCrO\({}_{2}\) and AgCrO\({}_{2}\) exhibit spin-induced ferroelectricity below their Neel temperature \(T_{N}\) without the need for an external magnetic field [10]. Investigations of the dielectric constant measured both parallel and perpendicular to the crystallographic \(c\)-axis in CFO reveal that magnetic phase transitions have a pronounced influence on its dielectric behavior [11]. [PERSON] et al. [12; 13] measured the temperature-dependent dielectric constant \(\epsilon_{[110]}\) in single crystals of Ga- and Al-doped CFO, observing significant anomalies associated with spin-lattice interactions. Complementary studies by [PERSON] et al. [14; 15] examined the dielectric response of CFO under uniaxial pressure, providing further evidence of strong spin-lattice coupling. The impact of Al doping on the stability of the ground-state spin configuration was investigated by [PERSON] et al. [16] using pulsed magnetic fields, with the results interpreted through a magnetic domain framework. These collective findings illustrate the intricate interplay between magnetic ordering, lattice distortions, and impurity effects in determining the multiferroic properties of CFO. Notably, pressure and chemical doping can shift the energetic balance among competing magnetic ground states, thereby enabling external control over ferroelectric polarization. Such understanding is essential for advancing the development of tunable multiferroic systems that respond predictably to external fields or mechanical strain, a key requirement for their integration into next-generation adaptive electronic and spintronic platforms. The delafossite compound CFO functions as a p-type oxide semiconductor, featuring a direct band gap of approximately 1.5 eV [17], which positions it as a strong candidate for solar energy harvesting, photocatalysis, and next-generation oxide-based electronic devices. In a comparative study, [PERSON] et al. [18] reported that CuAlO\({}_{2}\) exhibits a relatively narrower band gap than CFO, highlighting the tunability of optical and electronic properties within the delafossite family. Further experimental research conducted by [PERSON] et al.