Crystal-Field Effects onCe3+in the Ethyl Sulfate

Abstract

We have determined the crystal-field splitting $\Delta$ of the first excited state in the ground multiplet $4f^1{}_{}{}^2{}_{}{}^{}F_{\frac{5}{2}}^{}{}_{}{}^{}$ for ${\mathrm{Ce}}^{3+}$ magnetically dilute in a number of ethyl sulfate host crystals $X{\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{S}{\mathrm{O}}_4\right)}_3·9{\mathrm{H}}_2\mathrm{O}$, where $X$ is a rare-earth ion. The value of $\Delta$ in each case is extracted from the temperature dependence of the spin-lattice relaxation rate for the lowest doublet of ${\mathrm{Ce}}^{3+}$, in the liquid-helium range, at a microwave frequency of $\nu \sim 9.3$ GHz; data are taken for 2% ${\mathrm{Ce}}^{3+}$ in the magnetically concentrated ethyl sulfates of ${\mathrm{Nd}}^{3+}$, ${\mathrm{Sm}}^{3+}$, ${\mathrm{Gd}}^{3+}$, ${\mathrm{Dy}}^{3+}$, and ${\mathrm{Er}}^{3+}$. A simple calculation is made for the variation of $\Delta$ among the host crystals; agreement is found with the direction of the experimentally measured shift but not the magnitudes of $\Delta$. A brief discussion of this discrepancy and the obvious difficulties is given. It is also shown that the relaxation-rate measurements appear to verify the ${\Delta }^3$ dependence of the coefficient $B$ for the Orbach relaxation rate, where ${T_{10}}^{-1\mathrm{}}=B\exp (-\frac{\Delta }{T})$.