Features of the magnetic and magnetoelectric properties of HoAl$_3$(BO$_3)_4$

The main features of the magnetic and record magnetoelectric properties of a HoAl$_3$(BO$_3)_4$ aluminoborate single crystal have been studied experimentally and theoretically. It has been found that the electric polarization that was previously detected in HoAl3(BO3)4 and is record for multiferroics is significantly larger, $\Delta P_{ba}(B_a)\approx-5240\,\mu$C/m$^2$, with an increase in the magnetic field to $9$ T at $T = 5$ K. The measured magnetic properties and revealed features have been interpreted within a united theoretical approach based on the molecular field approximation and on calculations in the crystal field model for a rare-earth ion. The experimental temperature (from $3$ to $300$ K) and field (up to $9$ T) dependences of the magnetization have been described. The parameters of the crystal field of trigonal symmetry for a Ho$^{3+}$ ion in HoAl$_3$(BO$_3)_4$ have been determined from the interpretation of the experimental data.