Relative intensities in the vibronic Zeeman effect in cubic crystals

Vibronic Zeeman intensity ratios are predicted for circularly polarized light propagation parallel to an externally applied magnetic field along [100] and [111] directions. A unique relative-intensity pattern is predicted for each type of site-symmetry vibration appearing in vibronic Zeeman patterns involving $T_{1g}$ or $T_{2g}$ electronic states. Experimental results in fields up to 62.8 kOe show semiquantitative agreement in most cases with predicted results for the ideal case of a limiting approximation in which $T_{1u}$ and $T_{2u}$, etc., site-symmetry vibrations are not degenerate. Such degeneracy, rather than accidental, is typical of that required by the space-group symmetry of the crystal, and leads to departures from the limiting intensity ratios. Measurements of the departure from the limiting ratios can lead to the determination of the relative contribution of degenerate $T_{1u}$, $T_{2u}$, etc., site-symmetry vibrations. This information should provide quantitative data beyond that of zero-field vibronic intensity profiles in testing models for lattice-dynamics calculations applied to the vibronic interaction, or in evaluating necessary parameters of such models. Ideal $\frac{\pi }{\sigma }$ vibronic intensity ratios for $D_{3d}$ distortion of a cubic crystal field in zero magnetic field are also presented which explain certain observed polarizations not predicted by exact vibronic selection rules.