Magneto-acoustic Faraday rotation in Tb₃Ga₅O₁₂

We report on observation of the magneto-acoustic Faraday effect in paramagnetic Tb₃Ga₅O₁₂ (TGG). This effect is the acoustic analog of the magneto-optical Faraday rotation. In cubic crystals, such as TGG, the two transverse sound waves propagating along the [100] direction are doubly degenerated. The magnetic field applied along the propagation direction breaks the time-reversal invariance and, therefore, lifts the degeneracy and induces a polarization rotation. This can be detected in the sound attenuation as oscillations as function of magnetic field, where each period corresponds to a polarization rotation of pi. Here, we present magneto-acoustic measurements performed at T = 1.4 K in fields up to 20 T in the frequency, f, range from 30 to 330 MHz. Indeed, we observed oscillations in the sound attenuation due to the Faraday effect. Theoretical studies predict an f² dependence of the Faraday rotation [1], whereas we observe a linear dependence. Such behavior has also been reported for CeAl2 in the paramagnetic phase [2]. We observed a softening of the sound velocity with increasing field with a minimum at about 19 T. At the same field the attenuation oscillations cease. These results can be attributed to a crystal-field level crossing. With the appropriate choice of crystal-field parameters an effective theory predicts this level crossing to occur at ~20 T. Taking the magneto-elastic interaction into account, the theory reproduces the qualitative features of our data.