Spin–Lattice Relaxation and Elastic Properties for Rare-Earth Substituted LaCl3

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Abstract
We develop a new theory of spin–lattice relaxation in an effort to improve the agreement between detailed predictions and experiment. Our work is based on (a) a uniquely general and convenient formulation of the crystal field problem utilizing the superposition model developed by Newman and co‐workers and (b) a knowledge of the detailed lattice motions, in particular the eigenvectors of long wavelength acoustic modes, in LaCl3. In conjunction with the latter, we give elastic constants, tables for the stress‐induced crystal field, and sound velocities. While the velocities agree with experiment, they are sufficiently low to reveal the inadequacy of earlier spin–lattice relaxation calculations on these systems. Relaxation data due to Stapleton and co‐workers permit a sensitive test of our model. It is possible to improve agreement with experiment and to achieve a consistent picture of direct and double direct (Orbach) relation with the dopants Pr3+, Nd3+, Tb3+, and to suggest an improved phenomenological estimated scheme. However, Raman rates are consistently overpredicted; also we find (as did earlier workers) special problems in connection with LaCl3:Er3+.
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