Magnetization, magnetoelectric polarization, and specific heat of HoGa$_3$(BO$_3$)$_4$

A comprehensive experimental and theoretical study of magnetic, magnetoelectric, thermal, and spectroscopic characteristics of HoGa$_3$(BO$_3$)$_4$ gallium borate single crystals has been performed. A large magnetoelectric effect exceeding its values found in all iron and aluminum borates except HoAl$_3$(BO$_3$)$_4$ has been observed. The magnetoelectric polarization of HoGa$_3$(BO$_3$)$_4$ equals $\Delta P_{ba}(B_a)\approx-1020\,$C/m$^2$ at $T = 5$ K in a magnetic field of $9$ T. The theoretical treatment based on the crystal field model for rare-earth ions provides a unified approach for the consistent interpretation of all measured characteristics. The crystal-field parameters are determined. The temperature (in the $3$–$300$ K range) and magnetic field (up to $9$ T) dependences of the magnetization, the Schottky anomaly in the temperature dependence of the specific heat, and its shift in the field ${\mathbf B}\|{\mathbf c}$ are described. To compare the thermal properties of HoGa$_3$(BO$_3$)$_4$ with those of HoAl$_3$(BO$_3$)$_4$ exhibiting record values of the polarization, the specific heat of HoAl$_3$(BO$_3$)$_4$ at various B values and the temperature dependence of the polarization $\Delta P_b(T)$ in the applied magnetic field of $9$ T have been measured.