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The acoustic Faraday rotation in the 4f paramagnet Tb3Ga5O12 has recentlybeen observed by Sytcheva et al (arXiv:1006.0141). As in earlier examples therotation angle per unit length of transverse acoustic modes was found to dependlinearly on sound frequency. Existing theories for this effect consistentlyrequire that it should vary with the square of the frequency. In the presentwork a solution for this long-standing problem is provided. We propose a modelbased on magnetoelastic interactions with 4f quadrupole moments that includesboth acoustic and optical phonons. The symmetry allows a direct and inducedcoupling between the latter. This leads to an indirect acoustic Faradayrotation via the field induced splitting of doubly degenerate optical phononmodes. It varies linearly with frequency in accordance with experiment anddominates the rotation angle. It also explains the observed resonance of therotation angle in the field range between 17-20 T. The mechanism is of generalvalidity for non-Bravais lattices and applies to previous examples of theacoustic Faraday effect.

Paramagnetic Acoustic Faraday Rotation in Tb3Ga5O12