Magnetoelectric effect in ytterbium aluminum borate YbAl$_3$(BO$_3$)$_4$

The anisotropic magnetoelectric properties of an ytterbium aluminum borate YbAl$_3($BO$_3)_4$ single crystal having noncentrosymmetric crystal structure (space group R32) are studied, including the orientational, field, and temperature dependences of the polarization in magnetic fields up to 5 T in the temperature range of 2–300 K. It has been shown experimentally for the first time that the symmetry of the observed magnetoelectric effects exactly corresponds to the trigonal structure of the crystal and is characterized by two quadratic magnetoelectric constants. The polarization in the basal plane $P_{a, b}$ is a quadratic function of the field at low fields and reaches 250–300 $\mu$C/m$^2$ in a field of 5 T at a temperature of 2 K, almost an order of magnitude exceeding the previously reported values. A theoretical model based on the spin Hamiltonian of the ground Kramers doublet of Yb$^{3+}$ ions in the crystal field is proposed including magnetoelectric interactions allowed by the symmetry. This model makes it possible to quantitatively describe all observed magnetic and magnetoelectric properties of YbAl$_3$(BO$_3$)$_4$.