Size and doping effects on the magnetic and electric properties of Bi $$_2$$ 2 Fe $$_4$$ 4 O $$_9$$ 9 nanoparticles

In the present paper we propose a microscopic model to study the multiferroic properties of Bi $$_2$$ 2 Fe $$_4$$ 4 O $$_9$$ 9 nanoparticles. The spontaneous magnetization $$M_s$$ M s increases with decreasing nanoparticle size. $$M_s$$ M s is shape dependent. It is larger for cylindrical than for spherical nanoparticles. $$M_s$$ M s increases with increasing Co and Ho concentration, whereas by Mn doping it decreases. These tunable magnetic properties can be widely applied in spintronics. The polarization $$P_s$$ P s increases also with decreasing nanoparticle size. Mn ion doping leads to increase of $$P_s$$ P s , the phase transition temperature $$T_C$$ T C and the dielectric constant and so to enhanced electric and dielectric properties of Bi $$_2$$ 2 Fe $$_4$$ 4 O $$_9$$ 9 nanoparticles. Applying an external magnetic field $$P_s$$ P s is enhanced, which is indirect evidence for a strong magnetoelectric coupling. The specific heat $$C_p$$ C p shows an anomaly at the Neel temperature $$T_N$$ T N which vanishes by applying an external magnetic field. The band gap energy $$E_g$$ E g decreases with increasing Ti, Co and Ho dopants whereas by Mn doping $$E_g$$ E g increases.