## 3 Results and Discussion
### Antiferroelectricity of La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) Ceramics  
The _P_-_E_ hysteresis loop was measured on a ferroelectric measurement system based on the Sawyer-Tower circuit. The measurement results are shown in the Figure 5. It can be clearly identified that La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) had obvious AFE characteristics in the fully separated double _P_-_E_ loops. It can be seen from Figure 5 that its critical forward phase field _E_\({}_{F}\) was about 1100 kV/cm, and its critical backward phase field _E_\({}_{A}\) was about 850 kV/cm. When the external electric field strength was greater than E\({}_{F}\), La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) would change from the AFE phase to FE phase due to an electric-field-induced phase transition. Then, when the external electric field was less than E\({}_{A}\), the FE phase would transform back to the AFE phase, resulting in a double hysteresis loop. Figure 4: (**A**) XPS survey spectrum of La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\); XPS spectra of Fe 2p (**B**), La 3d (**C**), and Ba 3d (**D**) in La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\). Figure 5: The fully separated double electric polarization hysteresis (_P_–_E_) loops of La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) ceramic. The ceramic was sintered at 1400 \({}^{\circ}\)C for 3 h and subsequently heat-treated in O\({}_{2}\) for 15 h in 3 steps. When the external electric field is small, the adjacent dipoles inside La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) are arranged in reverse order and are in an anti-parallel plane state, thus showing zero macroscopic polarization in the \(P\)-\(E\) diagram. When the external electric field is greater than the E\({}_{\rm F}\), the poles in the adjacent dipoles opposite to the external electric field cannot maintain the status due to the enhancement of the electric field, and turn to the same direction as the electric field, thus showing a double hysteresis loop in the \(P\)-\(E\) diagram. Figure 5 thus fits the definition of AFE very well. In a previously published paper, it was demonstrated that BaFe\({}_{12}\)O\({}_{19}\) is distinctly FE at room temperature and undergoes an FE-AFE transition at a frequency of 100 Hz and a temperature of 194 \({}^{\circ}\)C [28]. While [PERSON] et al. reported extensive work on PLZT x/95/5 ceramics [47; 48; 49], and concluded that La doping destroys the long-range dipole order of the FE phase, thereby suppressing the FE phase and stabilizing the AFE phase. Therefore, it is reasonable to suggest that doping La into BaFe\({}_{12}\)O\({}_{19}\) can weaken the FE phase in BaFe\({}_{12}\)O\({}_{19}\), while the opposite AFE phase is gradually stabilized, as it did in PLZT. Figure 6 shows the recoverable energy density of La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) ceramics under different electric fields. It can be seen from Figure 6 that when the electric field was less than 850 kV/cm, it stored almost no energy, and when the electric field was 850-920 kV/cm, its energy storage density increased dramatically. At field range of 920-1100 kV/cm, the energy storage density still increased but the increasing trend began to weaken. At around 1100 kV/cm, its recoverable energy density was the highest, which was 15.31 J/cm\({}^{3}\). This phenomenon can be explained as follows. When the electric field goes into the AFE region, the macroscopic polarization is close to zero, which makes it almost impossible to store energy. However, the electric field induces it to transform from the AFE phase to the FE one at \(E_{A}\), where its macroscopic polarization increases rapidly, and the energy storage density increases accordingly. Finally, when the electric field increases to a certain level, the internal AFE phase has been completely transformed into the FE phase, and the energy storage density reaches the highest value in this region.