Nuclear magnetic relaxation in rare earth-doped CAF2 [i.e. CaF2] crystals at low temperatures

Abstract

The spin-lattice relaxation times or fluorine nuclei in single calcium fluoride crystals doped with three paramagnetic rare earth ions, Tb3+, Tm3+, and Sm3+, have been measured over a temperature range of 28°K to 300°K. The measurements were made using 90° - 90° pulse sequences, with the static magnetic field along the [111] directions. Each sample was annealed several times, the process having been repeated until the values of the nuclear relaxation time measured before and after the last anneal agreed within the experimental accuracy. The data show that the relaxation mechanism which is operative over the range of temperatures investigated is one previously proposed involving the paramagnetic impurities. In this process, energy is transferred from the nuclear spins to the impurity spins by means of the dipole-dipole interactions. It is assumed that the process by which the impurity spins relax to the lattice is characterized by a spin-lattice relaxation time T_e which is much Shorter than the nuclear T_1. The theory predicts a minimum in the nuclear T_1, versus temperature curve. This was observed at 41°K for both the Tb3+ -doped sample and that containing Tm3+. From these minima, the diffusion coefficients characterizing a process of mutual spin flips, by which energy is transmitted from nuclei distant from impurity spins to those near the impurities, have been obtained. Theoretically, this diffusion constant is independent of both temperature and the impurity in the crystal; reasonable agreement was obtained between the values tor the two samples. Using these constants and the measured values of nuclear T_1, the correlation times T_e for these two impurity ions in CaF2 have been calculated over the temperature range of the experiment. The values of T_e Calculated for Tb3+ range from 5.8 x 10^-7 seconds at 28°K to 1.4 x 10^-15 seconds at room temperature. The corresponding range of values obtained for Tm3+ is from 4.9 x 10^-8 seconds to 4.5 x 10^-12 seconds. No minimum was observed in the temperature range investigated in the case of the Sm3+ -doped sample. The correlation time T_e or this ion in CaF2 has, however; been estimated using the measured values or the nuclear relaxation time and the average or the diffusion coefficients obtained for the other two samples. the values of T_e obtained in this case extend from 1.36 x 10^13 seconds at 32°K to 4.41 x 10^16 seconds at room temperature. Well above the minima in the T_1 versus temperature curves, the product or the central Larmor frequency of the fluorine and the correlation time T_e of the impurity ion is much less than one. In this region; the samples doped with Tb3+ and Tm3+ both yielded curves having two linear portions. At about 165°K, both curves have knees, above which the slopes are smaller than below. The data obtained for the SM3+ sample is linear above 130°K. The linear dependences of the nuclear T_1 on temperature indicate T^-4 dependences of T_e.