Electron-nuclear double resonance of divalent holmium in calcium fluoride

The fluorine electron-nuclear-double-resonance (ENDOR) spectrum of ${\mathrm{Ho}}^{2+}$ in cubic sites in Ca${\mathrm{F}}_2$ has been measured at 24 GHz. The analysis of the spectrum was complicated by the large magnitude of the hyperfine interaction. This caused the effective spin projection in the field direction, $<S_z>$, to differ appreciably from ± 1/2. The value of this reduced spin $<S_z>$ was calculated from the eigenfunctions for each hyperfine state, obtained by diagonalization of the Hamiltonian. By using $<S_z>$, it became possible to predict the ENDOR spectrum for all eight hyperfine levels, and also to specify uniquely to which $m$ state each ENDOR transition belonged. This allowed absolute determination of sign and magnitude of the superhyperfine interaction constants for the first to the fourth nearest-neighbor ${\mathrm{F}}^{-}$ ions. For the first shell, $T_s=+3.54\mathrm{}$ MHz, $T_p=-15.84\mathrm{}$ MHz. Anomalies of the order of 1 MHz in the ENDOR frequencies were successfully accounted for by a superhyperfine pseudonuclear Zeeman effect. These results are discussed in relation to results on other rare-earth ions, and with respect to mechanisms for the superhyperfine interaction.