Influence of the ground state of the $\mathrm{Pr}^{3+}$ ion on magnetic and magnetoelectric properties of the $\mathrm{PrFe}_3(\mathrm{BO}_3)_4$ multiferroic

The magnetic, magnetoelectric, and magnetoelastic properties of a $\mathrm{PrFe}_3(\mathrm{BO}_3)_4$ single crystal and the phase transitions induced in this crystal by the magnetic field are studied both experimentally and theoretically. Unlike the previously investigated ferroborates, this material is characterized by a singlet ground state of the rare-earth ion. It is found that, below $T_N=32$ K, the magnetic structure of the crystal in the absence of the magnetic field is uniaxial $({\mathbf l}\|c)$, while, in a strong magnetic field ${\mathbf H}\|{\mathbf c}$ ($H_{cr}\sim43$ kOe at T=4.2  K), a $\mathrm{Fe}^{3+}$ spin reorientation to the basal plane takes place. The reorientation is accompanied by anomalies in magnetization, magnetostriction, and electric polarization. The threshold field values determined in the temperature interval 2–32 K are used to plot an $H-T$ phase diagram. The contribution of the $\mathrm{Pr}^{3+}$ ion ground state to the parameters under study is revealed, and the influence of the praseodymium ion on the magnetic and magnetoelectric properties of praseodymium ferroborate is analyzed.