Bifurcations observed in the spectra of coupled electron-phonon modes in multiferroic PrFe₃(BO₃)₄ subjected to a magnetic field

We report on bifurcations effect mediated by the electron-phonon coupling in a concentrated rare-earth-containing antiferromagnet, observed in the spectra of coupled $4f$-electron-phonon modes under the influence of an external magnetic field. The effect was observed in the low-temperature far-infrared (terahertz) reflection spectra of a multiferroic easy-axis antiferromagnet $PrFe_3(BO_3)_4$ in magnetic fields $\textbf{B}_{ext}||c$. Both paramagnetic and magnetically ordered phases (including a spin-flop one) were studied in magnetic fields up to 30 T. We show that the field behavior of the coupled modes can be successfully explained and modeled on the base of the equation derived in the frame of the theory of coupled electron-phonon modes, with the same field-independent electron-phonon interaction constant $|W| = 14.8 cm^{-1}$.