Quadrupole Susceptibility of Γ3 Pseudo-Doublet Ground State in Rare-Earth Garnet Tb3Ga5O12

We have investigated elastic properties of a garnet-type single crystal Tb 3 Ga 5 O 12 by ultrasonic measurements. Temperature dependence of the transverse elastic constants ( C 11 – C 12 )/2 and C 44 shows strong Curie-type softening below 150 K with minima around 30–50 K and also below 5 K. These effects are due to quadrupole susceptibilities for the crystalline electric field system with a pseudo-doublet Γ 3 ground state and an excited triplet Γ 5 at 57.3 K. Magnetic field dependence of the ( C 11 – C 12 )/2 mode in H ∥[110] shows step-like anomaly due to a level crossing at around 9.5 T.