Origin of magnetoelectric response induced by respective magnetic ions $R^{3+}$/Fe$^{3+}$ in a chiral antiferromagnet $R$Fe$_{3}$(BO$_{3})_{4}$

Recent discoveries of the spin-induced ferroelectricity in frustrated magnets and the strong ME correlation in noncentrosymmetric magnets have stimulated the revived interest on the ME phenomena [1]. Rare earth iron borates $R$Fe$_{3}$(BO$_{3})_{4}$, whose structures possess a noncentrosymmetric space group ($R$32 or $P$3$_{1}$21), have recently been discovered to show multiferroicity [2]. While their magnetic and ME properties were extensively investigated, the origin of the $P$, or specifically the relationship between the electricity and the respective magnetism of iron ions (Fe) and rare-earth ions ($R)$, remains elusive. We measured the $P$ under a magnetic field and observed the linear ME effect and/or the spontaneous $P$ which are ascribed to spins of Fe and/or magnetic moments of $R$. We constructed a model for the spin-induced $P$ at the Fe/$R$ sites, with which we could reproduce the observed behavior of the magnetic field dependence of $P$. Thus, we could extract the respective contributions to $P$ from Fe and $R$ magnetic ions. \\[4pt] [1] T. Arima, J. Phys. Soc. Jpn. 80 (2011) 052001 \\[0pt] [2] A. M. Kadomtseva et al. Low Temp. Phys. 36 (2010) 511