  We performed inelastic neutron scattering measurements on single crystals of
NdFe$_{3}$($^{11}$BO$_{3}$)$_{4}$ to explore the magnetic excitations, to
establish the underlying Hamiltonian, and to reveal the detailed nature of
hybridization between the 4$f$ and 3$d$ magnetism. The observed spectra
exhibiting a couple of key features, i.e., anti-crossing of Nd- and
Fe-excitations and anisotropy gap at the antiferromagnetic zone center, are
explained by the magnetic model including spin interaction in the framework of
weakly-coupled Fe$^{3+}$ chains, interaction between the Fe$^{3+}$ and
Nd$^{3+}$ moments, and single-ion anisotropy derived from Nd$^{3+}$ crystal
field. The combination of the measurements and calculations reveals that the
hybridization between 4$f$ and 3$d$ magnetism propagates the local magnetic
anisotropy of the Nd$^{3+}$ ion to the Fe$^{3+}$ network, resulting in the bulk
structure of multiferroics.
