## 1 Introduction  
The fast-paced development of scientific and industrial innovations has led to an increased environmental discharge of wastewater and hazardous materials from industrial facilities [1, 2]. Particularly, dye wastewater poses significant treatment challenges due to its persistent chromaticity and complex chemical composition, resulting in elevated treatment costs. This necessitates the development of cost-effective treatment technologiesto address these challenges effectively [3; 4]. To address these challenges, researchers have proposed strategies encompassing physical, chemical, and semiconductor-based photocatalytic approaches. Semiconductor photocatalytic technology offers distinct advantages over physical and chemical methods, including simple fabrication and the absence of secondary pollutants during the reaction process [5; 6]. [PERSON] and [PERSON] initially suggested the concept of photocatalysis. Under illumination, the TiO\({}_{2}\) and Pt electrodes immersed in an aqueous medium induced photocatalytic water splitting, resulting in the successful generation of oxygen and hydrogen gases [7]. [PERSON] et al. demonstrated the photodegradation of polychlorinated biphenyls and haloalkanes using TiO\({}_{2}\) as a photocatalyst [8]. [PERSON] et al. investigated the use of TiO\({}_{2}\) for the removal of trichloroethylene [9]. The proven effectiveness of photocatalytic processes in pollutant degradation establishes this technology as a strategic focus area, with ongoing research being imperative to advance its real-world applicability [10]. Among various semiconductor-based photocatalysts, TiO\({}_{2}\) has emerged as the most extensively studied material, because of its unique combination of advantageous properties, including exceptional structural stability, non-harmfulness, cost-effectiveness, and remarkable photocatalytic activity [11; 12]. However, TiO\({}_{2}\) photocatalysis is fundamentally limited by three major technical challenges. The primary limitation stems from its high energy gap (3.2 eV), which restricts photoactivation to ultraviolet wavelengths (\(\uplambda<\) 387 nm) [13]. A secondary limitation involves the quick recombination of light-generated electron-hole pairs, resulting in a diminished quantum yield and consequently reduced photocatalytic efficiency [14]. Furthermore, practical applications are hindered by the technical difficulties associated with post-treatment separation and the recovery of TiO\({}_{2}\) particulate matter from aqueous systems [15]. Two predominant approaches for augmenting TiO\({}_{2}\) photocatalysis emerge: lattice modification through controlled dopant incorporation and interfacial engineering by constructing hybrid composites with complementary semiconductor materials. The strategic incorporation of doped metal ions into the TiO\({}_{2}\) crystal structure induces the formation of charge carrier traps, thereby promoting electron mobility. Simultaneously, these dopants create crystalline lattice distortions that generate oxygen vacancy defects, which act as recombination barriers to prolong charge carrier lifetimes. This dual mechanism synergistically increases reactive oxygen species production, ultimately elevating the quantum yield of photocatalytic reactions. To achieve the aim of recovery and prevent secondary pollution, a photocatalyst with magnetic nanoparticles (Fe\({}_{3}\)O\({}_{4}\)) as the magnetic nucleus, SiO\({}_{2}\) as the protective layer, and the core-shell structure of TiO\({}_{2}\) on the surface can be prepared.  
In this study, multilayer core-shell photocatalysts with Fe-doped TiO\({}_{2}\) were designed, and the magnetic FS-FT (0 g) and FS-FT (x g) composites were synthesized and characterized using XRD, TEM, UV-VIS-NIR spectroscopy, DRS, and XPS. Photocatalytic degradation experiments were implemented using pure methyl orange (MO) and MO-Na\({}_{2}\)SO\({}_{4}\)-blended solutions as model pollutants, and the underlying principles of photodegradation were investigated.