Bifurcations of Coupled Electron-Phonon Modes in an Antiferromagnet Subjected to a Magnetic Field

We report on a new effect caused by the electron-phonon coupling in a stoichiometric rare-earth antiferromagnetic crystal subjected to an external magnetic field, namely, the appearance of a nonzero gap in the spectrum of electronic excitations in an arbitrarily small field. The effect was registered in the low-temperature far-infrared (terahertz) reflection spectra of an easy-axis antiferromagnet ${\mathrm{PrFe}}_3{\left({\mathrm{BO}}_3\right)}_4$ in magnetic fields $B_{\text{ext}}\parallel c$. Both paramagnetic and magnetically ordered phases (including a spin-flop one) were studied in magnetic fields up to 30 T, and two bifurcation points were observed. We show that the field behavior of the coupled modes can be successfully explained and modeled on the basis of the equation derived in the framework of the theory of coupled electron-phonon modes, with the same field-independent electron-phonon interaction constant $\left|W\right|=14.8{\mathrm{cm}}^{-1}$.

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