Magnetic excitations and exchange interactions in the substituted multiferroics ( Nd , Tb ) Fe 3 ( BO 3 ) 4 revealed by inelastic neutron scattering

Inelastic neutron scattering spectra in the antiferromagnetic ferroborates ${\mathrm{Nd}}_{1\ensuremath{-}x}{\mathrm{Tb}}_{x}{\mathrm{Fe}}_{3}{({\mathrm{BO}}_{3})}_{4}$ ($x$ = 0, 0.1, 0.2, and 1) reveal various magnetic excitations of the interacting iron and rare-earth subsystems. We observe an evolution of the magnetic system from ``easy-plane'', in the Tb-free ($x$ = 0) case, to ``easy-axis'' anisotropy for samples substituted with Tb. The spectra show hybridized Fe and Nd branches, which are determined by the Fe-Nd exchange splitting of the ground-state ${\mathrm{Nd}}^{3+}$ doublet. In the easy-plane configuration, near the Brillouin zone center, there are two different pairs of anticrossing quasiacoustic Fe and Nd modes in contrast to the easy-axis state, where the two corresponding pairs of the branches are degenerated. The high-energy (exchange) branches are similar in both spin configurations. The Ising-type anisotropy of the Tb ion prevents the magnetic moment from precession. The increasing of the Tb content changes the effective magnetic anisotropy and stabilizes the easy-axis state. The spin-wave dispersion in the substituted and pure $\mathrm{Tb}{\mathrm{Fe}}_{3}{({\mathrm{BO}}_{3})}_{4}$ compounds, which have the same, easy-axis magnetic structure, but different crystal symmetry, strongly differ. The observed spectra were analysed in the frame of linear spin-wave theory and the exchange parameters were determined.