%0 Journal Article %T Magnetoelectricity in the system $RAl_3(BO_3)_4$ ($R$ = Tb, Ho, Er, Tm) %A K. -C. Liang %A R. P. Chaudhury %A B. Lorenz %A Y. Y. Sun %A L. N. Bezmaternykh %A I. A. Gudim %A V. L. Temerov %A C. W. Chu %J Physics %D 2012 %I arXiv %R 10.1088/1742-6596/400/3/032046 %X The magnetoelectric effect in the system $RAl_3(BO_3)_4$ ($R$ = Tb, Ho, Er, Tm) is investigated between 3 K and room temperature and at magnetic fields up to 70 kOe. We show a systematic increase of the magnetoelectric effect with decreasing magnetic anisotropy of the rare earth moment. A giant magnetoelectric polarization is found in the magnetically (nearly) isotropic $HoAl_3(BO_3)_4$. The polarization value in transverse field geometry at 70 kOe reaches 3600 $\mu C/m^2$ which is significantly higher than reported values for the field-induced polarization of linear magnetoelectric or even multiferroic compounds. The results indicate a very strong coupling of the f-moments to the lattice. They further indicate the importance of the field-induced ionic displacements in the unit cell resulting in a polar distortion and a change in symmetry on a microscopic scale. The system $RAl_3(BO_3)_4$ could be interesting for the technological utilization of the high-field magnetoelectric effect. %U http://arxiv.org/abs/1201.4890v1