Investigation of the Magnetic Model in Multiferroic NdFe${}_3$(BO${}_3$)${}_4$ by Inelastic Neutron Scattering

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.