Theoretical Study of the Raman Relaxation of Ni2+ and Cr3+ Ions in MgO Crystals

Abstract

The Raman relaxation rates for ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Cr}}^{3+}$ ions in MgO crystals have been calculated using a shell model of phonons which is in good agreement with the results of neutron scattering experiments. These shell-model results are compared with those obtained with the Debye model for the phonons and, also, with the available experimental results for ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Cr}}^{3+}$ in MgO. In the case ${\mathrm{Ni}}^{2+}$, 50\ifmmode^\circ\else\textdegree\fi{}K is the highest temperature for which the relaxation time is sufficiently long to be directly measureable. As might be expected, in this low-temperature region the results based on the shell model and the Debye model of phonons are not significantly different. However, the values of relaxation rates at 123 and 136\ifmmode^\circ\else\textdegree\fi{}K obtainable from the recent line-shape measurements for ${\mathrm{Ni}}^{2+}$ in MgO are in good agreement with those calculated on the basis of the shell model of phonons. In the case of ${\mathrm{Cr}}^{3+}$ ions, the relaxation time can be measured directly up to temperatures as high as 200\ifmmode^\circ\else\textdegree\fi{}K, and in this range of temperature the two sets of results differ considerably. With the shell model, we obtain good agreement with the experimental results on the functional dependence of the relaxation rate $\frac{1}{{T}_{1}}$ on temperature. However, the absolute values of $\frac{1}{{T}_{1}}$ for ${\mathrm{Cr}}^{3+}$ obtained with this phonon model are on the average less than the experimental measurements by a factor of 5. The possible sources which might be important in bridging the gap between the theoretical and experimental results are discussed.