Magnetoelectricity and magnetostriction due to the rare-earth moment in TmAl$_{3}$(BO$_{3}$)$_{4}$

We investigated the magnetic, magnetostriction and magnetoelectric properties of d-electron free rare-earth aluminum borate TmAl$_3$(BO$_3$)$_4$ between room temperature and 2 K. The magnetoelectric polarization along the `a' and `c' directions reaches up to 300 $\mu$ C/m$^2$ at 70 kOe with the field is applied along the `a' axis. `c' axis magnetic field does not show any significant effect, which correlates with the fact that $\chi_a$ changed very rapidly compared to $\chi_c$. We find that the polarization is proportional to the magnetostriction. The result of this investigation prove the existence of a significant coupling between the rare-earth magnetic moment and the lattice in RAl$_3$(BO$_3$)$_4$ compounds (R=rare earth). This compound shows that the rare-earth moment is sufficient enough to generate a large magnetoelectric effect. This is comparatively a simpler system to study and understand the origin of magnetoelectric effect.