Magnetic resonances of multiferroic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>TbFe</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>BO</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>

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Low-energy magnetic excitations of the easy-axis antiferromagnet TbFe$_3$(BO$_3$)$_4$ are investigated by far-infrared absorption and reflection spectroscopy in high magnetic fields up to 30 T. The observed field dependence of the resonance frequencies and the magnetization are reproduced by a mean-field spin model for magnetic fields applied both along and perpendicular to the easy axis. Based on this model we determined the full set of magnetic interactions, including Fe-Fe and Fe-Tb exchange interactions, single-ion anisotropy for Tb ions and $g$-factors, which describe the ground-state spin texture and the low-energy spin excitations of TbFe$_3$(BO$_3$)$_4$. Compared to earlier studies we allow a small canting of the nearly Ising-like Tb moments to achieve a quantitative agreement with the magnetic susceptibility measurements. The additional high energy magnetic resonance lines observed, besides the two resonances expected for a two-sublattice antiferromagnet, suggest a more complex six-sublattice magnetic ground state for TbFe$_3$(BO$_3$)$_4$.

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