Hyperfine effects on spin-lattice relaxation rates of rare-earth salts: Theory and experimental data

Abstract

Two papers in the literature dealing with the theory of hyperfine (hf) effects on the direct spin-lattice relaxation process in Kramers ions are shown to contain an identical error, which invalidates their results except when the external magnetic field is parallel to the crystalline symmetry axis. Here we derive relaxation expressions which are valid for any magnetic field orientation and present data for two salts of ${\mathrm{Er}}^{167}$ which at $X$-band frequencies are examples of dominant allowed and dominant forbidden relaxation processes. The vast differences in the hf relaxation behvior of these two similar salts can be explained only by the corrected theory and are associated with minor differences in the wave functions of Er in these two salts.