1：Experimental Design and Method Selection:

The study involved low-temperature magnetic and infrared measurements on BiFeO3 ceramic sample. The magnetic properties were measured using a vibrating sample magnetometer, and infrared reflectance spectra were obtained using a Fourier-transform IR spectrometer.

2：Sample Selection and Data Sources:

Single-phase polycrystalline BiFeO3 sample was synthesized using the modified sol-gel route. The structural properties were studied using various techniques, including x-ray diffraction and x-ray photoelectron spectroscopy.

3：List of Experimental Equipment and Materials:

Vibrating sample magnetometer (MPMS, Quantum Design, USA), Bruker Vertex 80v Fourier-transform IR spectrometer, pyroelectric DLaTGS and He-cooled Si bolometer detectors, Optistat-CFV cryostat.

4：Experimental Procedures and Operational Workflow:

Zero-field cooled (ZFC) and field-cooled (FC) magnetization data were measured at different magnetic fields. Near-normal incidence IR reflectance spectra were obtained with a resolution of

5：5 cm-Variable temperature measurements were carried out from 5 to 290 K. Data Analysis Methods:

The reflectance data were fitted using a generalized damped-harmonic oscillator model with the complex dielectric function.