The origin of extra hyperfine lines in two optical transitions in the ${}_{}{}^5{}_{}{}^{}$${\mathit{I}}_8$${\to }^5$${\mathit{F}}_5$ region of the trigonal center of ${\mathrm{Ho}}^{3+}$ in ${\mathrm{CaF}}_2$ has been investigated by using optically detected nuclear magnetic resonance and two-laser hole burning. Specific mixing of the excited-state hyperfine wave functions is established by the experimental measurements and, in a theoretical analysis, it is shown that such a mixing can arise from the off-diagonal hyperfine interaction between adjacent E and A states. Normally forbidden transitions gain intensity from the mixing and lead to the appearance of the extra hyperfine lines in the optical spectra. The strengths of the quadrupole, hyperfine, and off-diagonal hyperfine interaction in the ground and excited states are obtained in the analysis.

• Received 5 October 1992

DOI:https://doi.org/10.1103/PhysRevB.47.14696