Investigations have been made of long-wavelength collective lattice vibrations and long-wavelength spin wave modes in ferromagnetic insulators such as the rare-earth iron garnets. These materials have many different sites for the rare earth ions and generally have unquenched orbital moments. In this paper both theoretical and experimental work are reported with the main consideration being strong coupling effects between acoustic and spin wave modes. The strong coupling produces a field dependence of the resonant frequency and acoustic $Q$ of long-wavelength acoustic modes in saturated (i.e., single domain) samples. The sample shapes employed are spheres and thin disks. Satisfactory agreement is obtained between theory and experiment concerning the field dependences, rare earth concentration dependences, and correlation of acoustic effects with spin resonance quantities, such as linewidth. Also from these results values are obtained of the cubic magnetoelastic coupling constants $B_1$ and $B_2$ for terbium and europium iron garnets.

• Received 19 September 1962

DOI:https://doi.org/10.1103/PhysRev.130.50