1. (a) Summary of multifunctional properties in HIF with R-P structure; (b) Number of articles published on R-P oxides in recent years based on the Web of Science database

2. Energetics of a transition from paraelectric to ferroelectric phase for (a) proper and (b) improper ferroelectric system^[23]

3. Symmetry mode decomposition of the (a) paraelectric to (b) ferroelectric structure in R-P A′₂AB₂O₇, and (c) representation of anti-ferrodistortive displacements (X) at every layer and total ferroelectric polarization (P_total) in ferroelectric structure^[25]

4. (a) Ferroelectric a⁻a⁻c⁺ structure of A₃B₂O₇ R-P phase; (b) First principles amplitudes of two octahedral rotations and induced polar mode for a suite of A₃B₂O₇ materials, arranged by increasing τ of ABO₃ parent^[26]

5. (a, b) Schematic diagrams of two octahedral tilt modes of a⁰a⁰c⁺and a⁻a⁻c⁰ of (Ca,Sr)₃Ti₂O₇ single crystal; (c) Photographic and (d) circular differential interference contrast image of a cleaved (001) surface of Ca_2.46Sr_0.54Ti₂O₇ single crystal; (e) Ferroelectric hysteresis loops of Ca_3−xSr_xTi₂O₇ (x=0, 0.54, 0.85) single crystal along [110] orientation; (f) Schematic picture of IP-PFM measurement^[49]

6. Comparison of ferroelectric properties for Ca₃Ti₂O₇-based compounds with double-layered R-P structure^[40]

7. (a) DF-TEM image obtained at room temperature (RT) using the g=100 diffraction spot showing the ferroelectric domains, with blue and red arrows indicating directions of ferroelectric polarization along [100]; (b) DF-TEM image obtained at RT using the reflection g=220; (c) PFM measurements for Ca₃[Mn_0.5(Fe_0.5Nb_0.5)_0.5]₂O₇ ceramics at RT: mappings of topography, amplitude contrast, phase contrast, and contact resonant frequency; (d) First and second harmonic responses versus AC voltage; (e, f) Local switching spectroscopy for (e) amplitude voltage butterfly loops and (f) phase voltage hysteresis loops under various DC bias^[45]

8. Comparison of ferroelectric properties for Sr-based oxides with R-P structure (Sr₃Sn₂O₇ single crystal^[112], (Sr,Ba)₃Sn₂O₇ ceramics^[84], (Sr,Ca)₃Sn₂O₇ ceramics^[85], (Sr,Ba)₃Zr₂O₇ ceramics^[86], and Sr₃(Sn,Zr)₂O₇ ceramics^[113])

9. (a) Crystal structures of four phases observed experimentally for Sr₃Sn₂O₇, specified by space group symmetry and Glazer tilt notation^[118]; (b) Phase diagram of Sr₃Sn₂O₇ established in the present study^[118]; (c) Calculated layer-resolved polarization using a point-charge approximation for the crystal structure refined against NPD data at 300 K (left panel), [010] projected crystal structure (right panel) with Sr, Zr, and O atoms in gray, blue, and red, respectively^[119]; (d) Atomic contributions and layer-by-layer contributions to polarization in Sr₃Hf₂O₇, in which Sr1-O represents the SrO layer between perovskite layers, and Sr2-O represents the SrO layer between rock-salt and perovskite layers^[120]

10. T_C of double-layered R-P ferroelectrics against τ of their perovskite unit^[40]

11. Dependence of dielectric constant on temperature and ferroelectric phase transition schematic of Li₂Sr(Nb_1−xTa_x)₂O₇ oxides^[65]

12. (a) Crystal structures, room temperature P-E loops and the A-site cation ordering dependence of DFT calculated energy for La₂SrSc₂O₇ ceramics^[123]; (b) P-E loops for La₂Sr(Sc_1−xFe_x)₂O₇ ceramics under a electric field of 400 kV/cm and a frequency of 2 Hz^[121] ; (c) Temperature dependence of dielectric constant for La₂Sr(Sc_1−xFe_x)₂O₇ ceramics over the temperature range of 150-600 K during heating and cooling processes^[121]; (d) Temperature dependence of DC magnetic susceptibility of La₂Sr(Sc_1−xFe_x)₂O₇ (x=0.15) ceramics, with inset showing Curie-Weiss fitting results^[121]; (e) Isothermal field dependence of magnetization of La₂Sr(Sc_1−xFe_x)₂O₇ (x=0.15) ceramics at various temperatures^[121]

13. Comparison of ferroelectric properties of double-layered R-P materials (Ca₃Ti₂O₇ ceramics^[80], Sr₃Sn₂O₇ ceramics^[84], Sr₃Zr₂O₇ ceramics^[86], Li₂CaTa₂O₇ ceramics^[26], and Li₂SrNb₂O₇ ceramics^[130])

14. (a) Phase diagram of (1−x)(Ca_ySr_1−y)_1.15Tb_1.85Fe₂O₇-xCa₃Ti₂O₇ (0≤x≤0.3, y=0.60); (b) Ferroelectric polarization and saturated magnetic moment versus composition; (c) Linear magnetoelectric susceptibility versus composition at 60 and 100 K^[136]

15. (a) Crystal structure of several oxides with single layer R-P structure^[143]; (b) Schematic diagram of the intercalation structure of HRTiO₄ and NaRTiO₄^[139]; (c, d) Temperature dependence of SHG for (c) A_ASmTiO₄ and (d) A_AEuTiO₄ with A_A representing Na (yellow circles) and K (purple circles)^[141]

16. (a) Room temperature P−E loop and J−E curves measured at 390 kV/cm by PUND method^[149]; (b) Calculated energies for Li₂La₂Ti₃O₁₀ with different crystal symmetries in the triple-layered R-P structure relative to the lowest energy Pc phase at 0 K^[149]; (c) Room temperature P−E loops of Li₂Nd₂Ti₃O₁₀ ceramics measured through PUND method^[150]; (d) Rotation (θ_R) and tilt (θ_T) angles of Li₂La₂Ti₃O₁₀ (LLTO) and Li₂Nd₂Ti₃O₁₀ (LNTO) ceramics, respectively^[150]; (e) Schematic diagrams of crystal structures for Li₂La₂Ti₃O₁₀ ceramics based on the Rietveld refinement (the green, brown, and red balls represent Li⁺, La³⁺, and O²⁻ ions, respectively, while Ti⁴⁺ cations reside in the oxygen octahedra center)^[149]; (f) Layer-by-layer contributions to polarization in Li₂La₂Ti₃O₁₀ calculated by the Born effective charge mode^[149]