Spin-Lattice Relaxation Times of ${\mathrm{Cu}}^{2+}$ in CuS${\mathrm{O}}_4$·5${\mathrm{H}}_2$O and ${\mathrm{Yb}}^{3+}$ in Ca${\mathrm{F}}_2$ by Nuclear Dynamic Polarization

Dynamic polarization of protons in CuS${\mathrm{O}}_4$·5${\mathrm{H}}_2$O-doped ZnS${\mathrm{O}}_4$·7${\mathrm{H}}_2$O and ${\mathrm{F}}^{19}$ nuclei in ${\mathrm{Yb}}^{3+}$-doped calcium fluoride (trigonal sites) has been observed in the range 1.6-4.2°K. Concentration, temperature, and microwave-power dependencies of the polarization and relaxation times of the nuclei are measured, and these dependencies are deduced for the ${\mathrm{Cu}}^{2+}$ and ${\mathrm{Yb}}^{3+}$ electron relaxation times. Copper electrons are found to relax mainly by the direct process, but the Orbach process is observed for ytterbium electrons above the range 3.6-4.2°K. Below this range, the direct process predominates. All samples indicate spin-diffusion-limited processes. A general expression is derived for the Orbach process of a Kramer's salt; it is applied to ${\mathrm{Cu}}^{2+}$ and ${\mathrm{Yb}}^{3+}$ and compared with the values deduced from the measurements. The wave functions of the ground states of ${\mathrm{Yb}}^{3+}$ in a trigonal site are calculated from ESR measurements and used in the above analysis. The first excited orbital-level splitting of ytterbium is calculated from the temperature at which the Orbach process relaxation rate becomes greater than that of the direct process. A lower bound for this splitting is obtained for copper.