High-field studies of spin-lattice relaxation processes in an optically excited Kramers doublet of LaF3:Er3+

Spin-lattice relaxation by the direct process and by the orbach process has been studied for the lower Kramers doublet $S\left(1\right)\mathrm{}$ of the optically excited ${}_{}{}^4{}_{}{}^{}S_{\frac{3}{2}}^{}{}_{}{}^{}$ quartet state of ${\mathrm{Er}}^{3+}$ ions in La${\mathrm{F}}_3$ up to a magnetic field $B=8\mathrm{}$ T. The direct process dominates at a crystal temperature of 2 K; this is concluded from a $B^5$ dependence of the relaxation rate found for a very large range of the magnetic field. At 4.2 K, on the other hand, an Orbach process via the upper Kramers doublet $S\left(2\right)\mathrm{}$, which is at zero field 30 ${\mathrm{cm}}^{-1\mathrm{}}$ above $S\left(1\right)\mathrm{}$, gives a strong contribution to the relaxation rate. We found evidence that the Orbach relaxation rate increases with the magnetic field strength. This observation is explained by the magnetic field dependence of the energy separations between the $S\left(1\right)\mathrm{}$ and $S\left(2\right)\mathrm{}$ Zeeman levels.