## 3 Results and Discussion
The Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) spectrum shows a'red shift' compared with the TiO\({}_{2}\) spectrum, indicating that Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) can absorb light in a wider wavelength range compared with TiO\({}_{2}\), and its photocatalytic activity is significantly improved. According to the Kubelka-Munk function, the absorption threshold is estimated. The energy band gap (E\({}_{\rm{bg}}\)) of Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) and TiO\({}_{2}\) is determined by the relationship between (F(R)h\(v\))\({}^{1/2}\) and h\(v\) (Tauc plot). The value of E\({}_{\rm{bg}}\) is measured in the high absorption region. The zero F(R) (i.e., E\({}_{\rm{bg}}\)) is measured by extrapolating the linear region to the horizontal axis in the high absorption region [22]. Figure 5c shows band gap spectra of TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) obtained by Kubelka-Munk method. The band gaps of TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) are 2.9 eV and 2.5 eV, respectively. The possible reasons for the decrease in the band gap of composite materials are that after HF ionization, H\({}^{+}\) ions react with Fe\({}_{3}\)O\({}_{4}\) to promote ionization and increase the concentration of F\({}^{-}\), causing it to have a stronger inhibitory effect on the (101) surface. The photogenerated electron-hole rate of Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) is higher than that of TiO\({}_{2}\), and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) has good light absorption in the wider wavelength range. The dark reaction showed that both Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) and TiO\({}_{2}\) had good adsorption of AR73, as shown in Figure 6. In the initial stage of photocatalytic reaction, the concentration of AR73 was high, and the rate of dye degradation was not high, but the rate of dye degradation increased rapidly. The intermediate products generated by the degraded AR73 occupied the activity of the photocatalyst and increased as time went on, so the photocatalytic degradation rate was high, but the rate of dye degradation increased slowly, as shown in Figure 6c. After the combination of Fe\({}_{3}\)O\({}_{4}\) and TiO\({}_{2}\), the band gap decreased and the exposure ratio of (001) high-energy facets increased, which improved the photocatalytic activity. This result is consistent with Figures 2 and 5c. With the extension of the photocatalytic time, there were too many intermediates generated by AR73, which led to a significant reduction in the contact dimensions between the AR73 and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\), inhibiting the photocatalytic degradation and causing the degradation rate to increase slowly or even not increase. The photocatalytic degradation rates of TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) at 24 min were 74.47% and 93.56%, respectively, which indicated that under the same experimental conditions, the rate of dye degradation by Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) was better than that by TiO\({}_{2}\). Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) was recovered by magnetism, as shown in Figure 6d. Figure 4: FESEM elemental mapping and EDS patterns of Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\). (**a**) oxygen elements; (**b**) Fe elements; (**c**) Ti elements; (**d**) EDS patterns of Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\). Figure 5: UV-VIS DRS of (**a**) Fe\({}_{3}\)O\({}_{4}\), (**b**) TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\); (**c**) Plot of transferred Kubelka\(-\)Munk values versus the energy of the light absorbed by TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\). Figure 6: Photocatalytic degradation of AR73 by (**a**) Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) and (**b**) TiO\({}_{2}\); (**c**) the rate of degradation of AR73 by Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) and TiO\({}_{2}\) in a dark reaction time of 25 min and irradiation time of 24 min; (**d**) magnetically adsorbed Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\). The recovered photocatalyst degraded AR73 under the same experimental conditions.