Probing Magnetic Sublattices in Multiferroic Ho$_{0.5}$Nd$_{0.5}$Fe$_{3}$(BO$_{3}$)$_{4}$ Single Crystal using X-ray Magnetic Circular Dichroism

Using element-specific X-ray magnetic circular dichroism (XMCD) technique we have studied different magnetic sublattices in a multiferroic Ho$_{0.5}$Nd$_{0.5}$Fe$_{3}$(BO$_{3}$)$_{4}$ single crystal. The XMCD measurements at the emph{L}$_{2,3}$-edges of Ho and Nd, and at the Fe emph{K}-edge have been performed at emph{T}=2~K under a magnetic field up to 17~T applied along the trigonal emph{c}-axis as well as in the basal emph{ab}-plane. All three magnetic sublattices are shown to undergo a spin-reorientation transition under magnetic field applied along the emph{c}-axis. On the contrary, when magnetic field is applied in the emph{ab}-plane only the holmium atoms exhibit a magnetization jump. Thus, the element-specific magnetization curves revealed the Ho sublattice to be much stronger coupled to the Fe one than the Nd sublattice. The results demonstrate that the Ho$^{3+}$ subsystem plays even more dominant role in magnetic behavior of Ho$_{0.5}$Nd$_{0.5}$Fe$_{3}$(BO$_{3}$)$_{4}$ crystal than in pure HoFe$_{3}$(BO$_{3}$)$_{4}$ crystal.