Vibronic Transitions of Hexagonal Rare-Earth Trichlorides. I. ${\mathrm{Pr}}^{3+}$ and ${\mathrm{Nd}}^{3+}$ in Nd${\mathrm{Cl}}_3$

The absorption spectra of ${\mathrm{Pr}}^{3+}$ and ${\mathrm{Nd}}^{3+}$ in Nd${\mathrm{Cl}}_3$ have been obtained under high resolution in the 3000-6000 Å region at low temperatures, and under magnetic fields up to 36 kOe. Vibronic transitions are observed accompanying the strong electronic transitions of the rare-earth (RE) ions. The vibronic spectra show a broad, unpolarized absorption band in the phonon-energy region 0-80 ${\mathrm{cm}}^{-1\mathrm{}}$ which is attributed to acoustical phonons. Many sharp vibronic lines appear in the phonon energy region of 10-270 ${\mathrm{cm}}^{-1\mathrm{}}$. These are attributed to optical-phonon branches having k's at various regions of the Brillouin zone (B.Z.). The analysis of these transitions is done by assuming an interaction Hamiltonian between the RE ion and the lattice vibrations which is linear in the phonon normal coordinates. Electric dipole selection rules for single-phonon vibronic transitions are derived for points of high symmetry in the B.Z. The assignment of phonon branches which participate in the vibronic spectrum is made by comparing the polarization of the Zeeman components of the vibronic lines with the set of selection rules. It is found that the sharp polarized vibronic transitions are due to phonon branches which are flat over a wide range of k's along directions of high symmetry in the B.Z. The Zeeman effect of vibronic states is discussed. The energy correction to the energy of the vibronic states is estimated to be less than 1 ${\mathrm{cm}}^{-1\mathrm{}}$ for both ${\mathrm{Pr}}^{3+}$ and ${\mathrm{Nd}}^{3+}$.