Spin Hamiltonian ParameterDversus Axial Crystal Field forS-State Ions

Measurements have been made, in a Mössbauer absorption experiment, of the nuclear quadrupole splitting of the ${}_{}{}^6{}_{}{}^{}S_{\frac{5}{2}}^{}{}_{}{}^{}$ state ion ${\mathrm{Fe}}^{3+}$ substituted in several compounds. The compounds chosen were those for which electron spin resonance measurements had previously been made of the quantity $D$ in the electron spin resonance Hamiltonian. The measured quadrupole coupling $\frac{\mathrm{eqQ}}{h}$ is directly proportional to the axial crystal field, $V_{\mathrm{ax}}$. Hence, it is possible to compare the results of the dependence of $D$ on the axial crystal field with theoretical predictions of Watanabe and Pryce. It is found that considerable scatter of data points occurs about any smooth curve one might draw. This scatter is possibly the result of covalent bonding or the distortion of the iron wave functions by the surrounding ions. Moreover, a functional dependence of any smooth curve through the experimental points disagrees with the theoretical calculations. If the data are to be even crudely fit by a smooth curve, the sign of the coefficient of $V_{\mathrm{ax}}^{}{}_{}{}^2$ should be positive and not negative as theory indicates. Finally, there is serious disagreement between theory and experiment on the dependence of the $D$ vs $V_{\mathrm{ax}}$ curve on the particular paramagnetic ion (i.e., on whether the substituted ion is ${\mathrm{Fe}}^{3+}$ or ${\mathrm{Mn}}^{2+}$).