Nuclear Spin-Lattice Relaxation in CaF2Crystals via Paramagnetic Centers

The results of nuclear spin-lattice relaxation-time measurements in the laboratory reference frame ($T_1$) and the rotating reference frame (${T_1}^r$), made on ${\mathrm{F}}^{19}$ nuclei in Ca${\mathrm{F}}_2$ crystals doped either with ${\mathrm{Eu}}^{3+}$, ${\mathrm{Ce}}^{3+}$, or ${\mathrm{Mn}}^{2+}$ paramagnetic centers, are reported. From 0.25 to 0.36 of the Debye temperature, values of the correlation time ${\tau }_c$ are found from ${T_1}^r$ minima for ${\mathrm{Mn}}^{2+}$ ions. Over this range ${\tau }_c\propto T^{-3.2\mathrm{}\pm 0.1}$, compared to $T^{-3.2\mathrm{}}$ computed from Leushin's theory. For ${\mathrm{Eu}}^{3+}$ over 0.15 to 0.19 of the Debye temperature, measurements yield ${\tau }_c\propto T^{-4.9\mathrm{}\pm 0.1}$, compared to $T^{-4.7\mathrm{}}$ computed from Leushin's theory. From the $T_1$ data for a ${\mathrm{Mn}}^{2+}$ -doped Ca${\mathrm{F}}_2$ crystal, a value of 1.9×${10}^{-12\mathrm{}}$ ${\mathrm{cm}}^2$/sec for the spin-diffusion constant $D$ is computed. From the $T_1$ data for a ${\mathrm{Eu}}^{3+}$-doped Ca${\mathrm{F}}_2$ crystal, $D$ is computed to be 1.2×${10}^{-12\mathrm{}}$ ${\mathrm{cm}}^2$/sec. A NMR measurement of the effective number of paramagnetic centers per unit volume, $N_p$, increases the measured $D$ to 2.6×${10}^{-12\mathrm{}}$ ${\mathrm{cm}}^2$/sec. The computed value of $D$ (Lowe and Gade) is 5.1×${10}^{-12\mathrm{}}$ ${\mathrm{cm}}^2$/sec. Indirect evidence leads to the conclusion that the spin-diffusion barrier radius is at least a factor of 2 smaller than predicted by Rorschach's formula. In the short-${\tau }_c$ region, $T_1$ and ${T_1}^r$, are found to be field-independent, with $\frac{{T_1}^r}{T_1}>1\mathrm{}$. The experimental data are consistent with $T_1\propto {B_0}^{\frac{1}{2}}{{\tau }_c}^{\frac{1}{4}}{N_p}^{-1\mathrm{}}$ (diffusion-limited region), $T_1\propto {B_0}^1{{\tau }_c}^{\frac{1}{2}}{N_p}^{\frac{-4\mathrm{}}{3}}$ (diffusion-vanishing region). The initial decay of the magnetization in the measurements of ${T_1}^r$ is found to be proportional to $t^{\frac{1}{2}}$ in the long-correlation-time region. The coefficient of $t^{\frac{1}{2}}$ is used to obtain an experimental value for $N_p$ that is ½ as large as the value supplied by the manufacturer of the crystal.