1：Experimental Design and Method Selection:

The study uses a sol–gel method to synthesize multi-doped bismuth ferrite thin films (BLxSFMC, x = 0.00–0.18) on FTO/glass substrates. The design rationale is to control La3+ doping to adjust oxygen vacancy concentration and improve multiferroic properties. Theoretical models include defect reaction equations and conduction mechanisms (Ohmic and SCLC).

2：00–18) on FTO/glass substrates. The design rationale is to control La3+ doping to adjust oxygen vacancy concentration and improve multiferroic properties. Theoretical models include defect reaction equations and conduction mechanisms (Ohmic and SCLC). Sample Selection and Data Sources:

2. Sample Selection and Data Sources: Samples are BLxSFMC thin films with varying La3+ doping levels (x = 0.00, 0.06, 0.12, 0.18). Data sources include synthesized films and characterization measurements.

3：00, 06, 12, 18). Data sources include synthesized films and characterization measurements. List of Experimental Equipment and Materials:

3. List of Experimental Equipment and Materials: Equipment includes Rigaku D/MAX-2200 XRD, Horiba JYHR800 Raman test system, Agilent B2901A source/measure unit, XPS (XSAM800, Kratos Ltd), Agilent E4980A LCR system, aix ACCT TF-Analyzer 2000, and SQUID-MPMS-XL magnetic measurement system. Materials include Bi(NO3)3·5H2O, La(NO3)3, Sr(NO3)3, Fe(NO3)3·9H2O, C6H9MnO6·2H2O, Co(NO3)3·6H2O, C3H8O2, C4H6O3, FTO/glass substrate, and Au electrode.

4：Experimental Procedures and Operational Workflow:

Precursor solution preparation with metal nitrates in C3H8O2 and C4H6O3. Substrate UV irradiation to reduce contact angle. Spin coating at 4000 rev/min for 15 s, baking at 180 °C for 7 min, annealing at 545 °C for 10 min, repeated 12 times. Au electrode sputtering and annealing at 300 °C for 25 min. Characterization via XRD, Raman, XPS, leakage current, dielectric, ferroelectric, and magnetic measurements.

5：Substrate UV irradiation to reduce contact angle. Spin coating at 4000 rev/min for 15 s, baking at 180 °C for 7 min, annealing at 545 °C for 10 min, repeated 12 times. Au electrode sputtering and annealing at 300 °C for 25 min. Characterization via XRD, Raman, XPS, leakage current, dielectric, ferroelectric, and magnetic measurements. Data Analysis Methods:

5. Data Analysis Methods: XRD data analyzed with Rietveld refinement using MAUD software. Raman data fitted with Lorentz function. XPS data analyzed with Avantage software. Leakage current data fitted piecewise-linearly for conduction mechanisms. Ferroelectric and magnetic data analyzed for parameters like residual polarization, coercive field, and saturation magnetization.