  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.
