Magneto-Acoustic Faraday Effect in Tb₃Ga₅O₁₂

The transverse acoustic wave propagating along the [100] axis of the cubic paramagnet Tb₃Ga₅O₁₂ (TGG) exhibits amplitude oscillations as a function of magnetic field applied in the direction of propagation. This magneto-acoustic Faraday effect shows a linear frequency dependence contrary to theoretical expectation which demands a quadratic frequency dependence. The c₄₄ mode demonstrates also a strong softening of 6% up to 19 T, the magnetic field where an energy level of the CEF triplet branch starts to cross the quasi-doublet branch. This softening has the same origin, the magneto-elastic coupling, as the anomalies in the temperature dependence of the elastic constants and the magneto-acoustic Faraday effect.