## 2 Methods and Experiment Details  
Tetrabutyl titanate AR 98%, polyethylene glycol-4000 AR, ferric chloride hexahydrate (FeCl\({}_{3}\).6H\({}_{2}\)O) AR 99% and L-ascorbic acid 99.99% were purchased from Shanghai Macklin Biochemical Technology Co., Ltd. (Shanghai, China). Sodium hydroxide (NaOH) AR, hydrofluoric acid (HF) GR 40%, sodium acetate AR, ethylene glycol AR and absolute ethanol AR were obtained from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China). The test water was ultrapure water. The power of the high-pressure mercury lamp (GGZ300) was 300 W. The concentration of Acid Red 73 solution before and after the photocatalytic experiment was determined with a TU-1950 Beijing Puxi UV-VIS spectrophotometer at the maximum absorption wavelength of 508 nm. The morphology of all samples was characterized by a field emission scanning electron microscope (FESEM: JSM-7800, Tokyo, Japan) operated at 3 kV. The elemental analysis of samples was performed with an energy dispersive spectrometer (EDS). The Raman spectra were obtained using a Raman spectrometer, and the excitation source was a 532 nm Ar laser. The crystalline structure of all samples was characterized by X-ray diffraction (XRD: Empyrean, Panaco Netherlands, Cu-K\({}_{\alpha}\) radiation). The 2\(\theta\) scan range was 20 to 80\({}^{\circ}\), the step length was 0.06 and the scan speed was 4\({}^{\circ}\)/min. The diffuse reflectance spectra (DRS) of all samples were measured using a ultraviolet-visible-near-infrared spectrophotometer (UV-VIS-NIR: Shimadzu Solid Spec-3700) equipped with an integrating sphere; the test wavelength range was 200-800 nm at room temperature, and barium sulfate was used as a reference. The DRS were converted to absorption coefficient F(R) by Kubelka-Munk function. The energy band gap (E\({}_{\text{bg}}\)) of the samples was determined according to the Tauc method from the plot of (F(R)h\(\
u\))\({}^{1/2}\) versus h\(\
u\)[1]. The preparation method of TiO\({}_{2}\) was the solvothermal method, with tetrabutyl titanate as the titanium source, HF as (101) surface inhibitor of the anatase phase and absolute ethanol as dispersant [16]. Firstly, 80 mL ethanol and 3 mL HF were stirred magnetically for 10 min. After stirring evenly, 10 mL tetrabutyl titanate was slowly put into the solution and stirred for 30 min. Then the mixture was moved to a Teflon-lined autoclave. The reaction temperature was 180 \({}^{\circ}\)C, and the reaction time was 10 h. After the reactor was cooled, TiO\({}_{2}\) was washed alternately with absolute ethanol and 1% NaOH solution and finally washed with ultrapure water and filtered. Then, the white TiO\({}_{2}\) powder was put into a vacuum drying box; the drying temperature was 40 \({}^{\circ}\)C, and the drying time was 24 h.  
The preparation method of Fe\({}_{3}\)O\({}_{4}\) particles was as follows: Firstly, 80 mL ethylene glycol and 2.7 g FeCl\({}_{3}\cdot\)6H\({}_{2}\)O were magnetically stirred for 30 min, and then 2 g polyethylene glycol-4000 was added into the above solution and stirred until the solution color was orange red. Finally, 7.2 g sodium acetate was added and stirred until the color of the solution was orange red, and then the solution was moved to the Teflon-lined autoclave. The reaction temperature was 200 \({}^{\circ}\)C, and the reaction time was 10 h. After the reaction, the black Fe\({}_{3}\)O\({}_{4}\) powder was selected by magnetic separation, washed three times with absolute ethanol, and put into the vacuum drying box and dried at 40 \({}^{\circ}\)C.  
The preparation process of Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) particles was as follows: Firstly, 0.1 g of L-ascorbic acid and 0.25 g of Fe\({}_{3}\)O\({}_{4}\) prepared nanoparticles were dispersed into 80 mL of ethanol; then, 10 mL tetrabutyl titanate and 3 mL HF were added successively and stirred until they become evenly dispersed, and the above solution was transferred to the Teflon-lined autoclave.