Multiple-Phonon Interactions in Ultrasonic Paramagnetic Resonance of Uranium Ions in Calcium Fluoride

The method of ultrasonic paramagnetic resonance (UPR) has been used to study direct spin‐lattice interactions between tetravalent uranium ions in sites of trigonal symmetry and the host lattice, ${\mathrm{CaF}}_2$ . Intense absorption and dispersion of 9.0‐GHz longitudinal elastic waves propagated along the [111] direction of calcium fluoride were observed when an external magnetic field was adjusted to the spin‐resonance value $B_1$ , characteristic of the absorption of one phonon by each paramagnetic ion. Resonant phonon absorption of progressively lower intensity was observed at multiples of two, three, four, and five of the one‐phonon resonant field, $B_1$ . The absorption was measured as a function of magnetic field, angle between ${B}$ and the symmetry axis of the paramagnetic ion, ultrasonic intensity, ultrasonic pulsewidth, and temperature in the range 1.5° to 4.2°K. Analysis of the results indicates that two processes are extant: (1) the generation of phonons at harmonics of the applied frequency due to the anharmonic lattice interaction and the UPR absorption of these phonons, and (2) multiple‐phonon UPR absorption by each paramagnetic ion.