1：Experimental Design and Method Selection:

Solid-state reaction method was used to synthesize ceramic samples of BaTi1-xNixO3 with nominal compositions x = 0, 2.5, 5, 7.5 and 10 mol%. High purity BaCO3, TiO2 and NiO powders were mixed in the stoichiometric amount after that ball milled for 8h. These samples were subsequently calcined at 1100 °C for 12h. After that, resultant powder was pressed to a disc shape using a uniaxial hydraulic press to form pellets, and sintered at 1350 °C for 4 h.

2：5, 5, 5 and 10 mol%. High purity BaCO3, TiO2 and NiO powders were mixed in the stoichiometric amount after that ball milled for 8h. These samples were subsequently calcined at 1100 °C for 12h. After that, resultant powder was pressed to a disc shape using a uniaxial hydraulic press to form pellets, and sintered at 1350 °C for 4 h. Sample Selection and Data Sources:

2. Sample Selection and Data Sources: The phase formation and crystal structure of Ni-doped BaTiO3 sintered pellets were characterized by X-Ray diffractometer (XRD) with CuKa (1.54 ?) radiation. Fullprof suite was used for the Rietveld refinement of the X-ray data.

3：54 ?) radiation. Fullprof suite was used for the Rietveld refinement of the X-ray data. List of Experimental Equipment and Materials:

3. List of Experimental Equipment and Materials: X-Ray diffractometer (PANalytical X'PERT Pro MPD), TF Analyzer 2000 (aixACCT GmbH Germany), high-resolution Alpha A analyzer (Novocontrol GmbH, Germany), superconducting quantum interference device (SQUID, Quantum Design, USA), DC electromagnet and Alpha A analyzer (Novocontrol GmbH, Germany), SR830 dual phase lock in amplifier (SRS Inc. USA).

4：Experimental Procedures and Operational Workflow:

For electrical measurements, both sides of sintered pellets were smoothly polished and silver pasted. Ferroelectric hysteresis loop measurements were carried out with TF Analyzer 2000 at 10 Hz. Dielectric properties were studied using high-resolution Alpha A analyzer at 1Vrms, spanning the frequency range 102-106 Hz. Magnetization hysteresis (M-H) measurement of the sample was performed using a SQUID. Magnetodielectric (MD) measurement was studied using a DC electromagnet and Alpha A analyzer at 10 kHz. Magnetoelectric coefficient was recorded as a function of applied DC magnetic field (Hdc) up to 6 kOe, superimposing 1 Oe AC magnetic field generated through the Helmholtz coils at 1 kHz. The induced magnetoelectric voltage was recorded using the SR830 dual phase lock in amplifier.

5：Data Analysis Methods:

Rietveld refinement has been employed to refine the crystal structure and phase transition of BTNO ceramics.