Modified Orbach Relaxation Process in a La(Cl,Br)3Matrix

We have studied the spin-lattice relaxation rates of cerium and erbium in matrices of $\mathrm{La}{(1-x \mathrm{Cl}, x \mathrm{Br})}_3$. The substitution of ${\mathrm{Br}}^{-}$ for ${\mathrm{Cl}}^{-}$ in La${\mathrm{Cl}}_3$ was a technique for artificially introducing random local strains at the sites of paramagnetic impurities. The purpose was to test our earlier proposal that naturally occurring random strains were responsible for the frequent and sometimes large (≈15%) discrepancies between the excited-state energy levels as measured by optical techniques and by spin-lattice relaxation. Our model assumes that the variation from site to site of $\Delta$, the first-excited-state energy of the paramagnetic ion, can be described by a Gaussian distribution, with a standard deviation $\sigma$, centered at the optically determined value. From our relaxation data we extract the value of ${\sigma }^2$ for each sample. We observe the theoretically predicted modifications to the temperature dependence of the Orbach relaxation mechanism as ${\sigma }^2$ changes with the degree of ${\mathrm{Br}}^{-}$ substitution. Additional infrared and optical data, taken by other investigators on these samples, are briefly presented. These measurements give the actual distributions in $\Delta$, and the widths are found to be in excellent agreement with the values of $2\sigma$ inferred from our relaxation data.