Ultrasonic Study of the Properties of the Ferrous and Ferric Ions in Corundum

Abstract

Acoustic paramagnetic resonance was observed directly for the first time in ${\mathrm{Fe}}^{3+}$-doped ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ at 9366 MHz using fields between 0 and 5000 G in various directions. The transitions were identified by comparing the angular dependence of the resonance lines with the theoretically expected positions. From the observed attenuation for each line in conjunction with the matrix elements of the interaction Hamiltonian, it was possible to determine some of the elements of the magnetoelastic coupling tensor. The following values were found: ${[\frac{1}{4}{(G_{11}-G_{12})}^2+{G_{16}}^2]}^{\frac{1}{2}}=0.42\mathrm{}\pm 0.11$ ${\mathrm{cm}}^{-1\mathrm{}}$/(unit strain); ${[{G_{52}}^2+{G_{41}}^2]}^{\frac{1}{2}}=2.9\mathrm{}\pm 0.9$ ${\mathrm{cm}}^{-1\mathrm{}}$/(unit strain) for ${\mathrm{Fe}}^{3+}$. In order to obtain these values, we calculated explicitly the line shape as a function of the field strength. One line was identified as an ${\mathrm{Fe}}^{2+}$ line. The dependence of the attenuation of this line on the angle was in complete agreement with our predictions. A comparison is made with experimental data obtained for the magnetoelastic tensor using EPR experiments under stress, and with available theories.