Optical-absorption Zeeman spectroscopy of HoFeO3

Detailed optical-absorption Zeeman spectra of the ${}_{}{}^5{}_{}{}^{}I_8^{}{}_{}{}^{}\to {}_{}{}^5{}_{}{}^{}F_5^{}{}_{}{}^{}$ $4f$-shell transitions in HoFe${\mathrm{O}}_3$ are obtained at liquid-helium and liquid-nitrogen temperatures. With these data all ${}_{}{}^5{}_{}{}^{}F_5^{}{}_{}{}^{}$ states (and the lowest ${}_{}{}^5{}_{}{}^{}I_8^{}{}_{}{}^{}$ states) are identified in terms of representations of the ${\mathrm{Ho}}^{3+}$ $C_{1h}$ site-symmetry group. The strong polarization behavior observed is discussed in terms of important time-reversal symmetry considerations that are shown to be responsible for strong polarization in this compound as they are in other even-electron systems. An explanation of the frequent occurrence of nearly degenerate pairs in the even-electron rare-earth spectra where low site symmetry is involved is given based on a proposed dominance of axial terms in the crystal field. The theory limits the number of such pairs to three less than the total angular momentum eigenvalue of the multiplet in which they are found and allows the interpretation of the interesting polarization phenomenon exhibited by transitions between such pairs.