Crystalline-field splittings in cerous magnesium nitrate*

Measurements of the magnetic susceptibility at low temperatures have been made on single crystals of cerous magnesium nitrate, with a view to determining the energies of the low-lying states and the coefficients of the crystalline potential. The analysis, in terms of a crystal field of C$_{3v}$ symmetry acting on one 4f electron, gives results which are qualitatively similar to those of Judd's earlier work, but the relative magnitudes of the six coefficients which fit the data suggest that a simple ionic crystal field model does not in fact describe the properties completely. A similar analysis of susceptibility measurements over a wider temperature range, recently reported by Hellwege, indicates substantially the same conclusion. A number of factors generally omitted from the theory of rare-earth salts are considered, but more detailed calculations are required to decide which, if any, are important here. In spite of the uncertainties, the analysis gives quite a good estimate of the energy of the first excited doublet, (38 $\pm$ 3)$^\circ$, in reasonable agreement with the results of measurements of the spin-lattice relaxation time.