Concentration dependence of residual spin-lattice relaxation in theS324state ofEr3+:LaF3

Spin-lattice relaxation in the lower doublet of the excited ${}_{}{}^4{}_{}{}^{}S_{\frac{3}{2}}^{}{}_{}{}^{}$ state of ${\mathrm{Er}}^{3+}$:La${\mathrm{F}}_3$ shows a weak temperature dependence for low magnetic fields and at temperatures below $\approx 2.5$ K. Orbach relaxation is not yet effective in this temperature range and for magnetic fields $\lesssim 0.8$ T the residual relaxation process is field independent, which rules out the direct process as a relaxation mechanism. ${\mathrm{Er}}^{3+}$-${\mathrm{Er}}^{3+}$ cross relaxation can act as a relaxation process and depends on the ${\mathrm{Er}}^{3+}$ concentration. We measured the residual spin-lattice relaxation rates in the range 1.5-3 K for different ${\mathrm{Er}}^{3+}$ concentrations, using a laser spectroscopic method. No apparent correlation between the ${\mathrm{Er}}^{3+}$ concentration and the measured relaxation rates was observed. A model involving cross relaxation between ${\mathrm{Er}}^{3+}$ ions and impurities is used to fit the data.