The magnetic, electric, magnetoelectric, and magnetoelastic properties of rare-earth ferroborates $\mathrm{R}{\mathrm{Fe}}_3{\left(\mathrm{B}{\mathrm{O}}_3\right)}_4$ ($\mathrm{R}=\mathrm{Pr}$ , Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er) as well as yttrium ferroborate $\mathrm{Y}{\mathrm{Fe}}_3{\left(\mathrm{B}{\mathrm{O}}_3\right)}_4$ have been studied comprehensively. A strong dependence not only of the magnetic but also magnetoelectric properties on the type of rare-earth ion, specifically, on its anisotropy, which determines the magnetic structure and the large contribution to the electric polarization, has been found. This is manifested in the strong temperature dependence of the polarization below the Néel point $T_N$ and its specific field dependence, which is determined by the competition between the external and exchange $f\text{-}d$ fields. A close correlation has been found between the magnetoelastic properties of ferroborates and the magnetoelastic and magnetic anomalies at magnetic-field induced phase transitions. It is found that in easy-plane ferroborates, together with magnetic-field induced electric polarization spontaneous polarization also arises below the Néel point. The ferroelectric ordering in ferroborates is of extrinsic character, giving rise to strong magnetoelectric coupling below $T_N$ . Aside from the antiferromagnetic phase transition, the particulars of the structural phase transition accompanied by anomalies of the dielectric and magnetoelectric properties are examined for the first time. The character of the dielectric anomalies at a structural transition is analyzed for the first time on the basis of Landau’s approach.

The stability regions of the trigonal (Tb,Er)(Fe,Ga)₃(BO₃)₄ phases are established in (Bi₂Mo₃O₁₂)-based fluxes. The specific features of heterogeneous nucleation and the subsequent phase transformations during transition to the equilibrium are studied in the vicinity of the boundaries. The temperature modes of single crystal growth on seeds are suggested with due regard for the “nonequilibrium effect.”

We have studied the thermodynamic properties of single-crystalline $\mathrm{Tb}{\mathrm{Fe}}_3{\left(\mathrm{B}{\mathrm{O}}_3\right)}_4$. Magnetization measurements have been carried out as a function of magnetic field (up to $50\mathrm{T}$) and temperature up to $350\mathrm{K}$ with the magnetic field both parallel and perpendicular to the trigonal $c$ axis of the crystal. The specific heat has been measured in the temperature range $2–300\mathrm{K}$ with a magnetic field up to $9\mathrm{T}$ applied parallel to the $c$ axis. The data indicate a structural phase transition at $192\mathrm{K}$ and antiferromagnetic spin ordering at $T_N\approx 40\mathrm{K}$. A Schottky anomaly is present in the specific-heat data around $20\mathrm{K}$, arising due to two low-lying energy levels of the ${\mathrm{Tb}}^{3+}$ ions being split by $f\text{−}d$ coupling. Below $T_N$, magnetic fields parallel to the $c$ axis drive a spin-flop phase transition, which is associated with a large magnetization jump. The highly anisotropic character of the magnetic susceptibility is ascribed mainly to the Ising-like behavior of the ${\mathrm{Tb}}^{3+}$ ions in the trigonal crystal field. We describe our results in the framework of a unified approach which is based on mean-field approximation and crystal-field calculations.