Measurement of Signal Velocity in a Region of Resonant Absorption by Ultrasonic Paramagnetic Resonance

Measurements of signal velocity for wave propagation at frequencies within a narrow absorption band are reported. The measurements were made on pulsed microwave ultrasonic waves propagating in single crystal MgO and interacting with paramagnetic resonance absorption lines of ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Fe}}^{2+}$ impurity ions, present in low concentrations. The lines are inhomogeneously broadened, and a comparison of observed velocities with theory then requires knowledge of homogeneous spin packet linewidths. These are estimated from the theory of dipolar broadening. The experimental results are found to lie within theoretical limits established by calculations of Brillouin and Baerwald, provided that the spatial scale of the random magnetic inhomogeneities, which cause inhomogeneous line broadening, is assumed large compared with the acoustic wavelength. If this assumption is not made, the observed changes in signal velocity were larger than theory predicts by as much as three orders of magnitude. Thus, as byproducts of these experiments, it is found that ultrasonic velocity measurements may be used to estimate the scale of inhomogeneities, and also to measure spin packet linewidths in the presence of inhomogeneous broadening.