Theoretical Study of the Multiferroic Properties of Pure and Ion-Doped Pb5M3F19, M = Fe, Cr, Al

In a first theoretical investigation of the multiferroic properties of Pb5Fe3F19 (PFF) and Pb5Cr3F19 (PCF), we analyze their magnetic, ferroelectric, and dielectric characteristics as functions of temperature, magnetic field, and ion doping concentration using a microscopic model and Green's function theory. The temperature-dependent polarization in PFF and PCF shows a distinctive kink at the magnetic Neel temperature TN, which vanishes when an external magnetic field is applied, indicating the multiferroic behavior of these two compounds. Ion doping effectively tunes the properties of PFF and PCF. In PFF, Cr ion doping leads to a decrease in the Neel temperature TN, while Cr and Al ion doping lowers the ferroelectric Curie temperature TC. In the case of PCF, we observe the enhancement of TC by Fe ion doping and the reduction by Al ion doping. The last result coincides well quantitatively with the experimental data. Additionally, the magnetodielectric coefficient of PFF is enhanced with the increasing magnetic field.