4f instability and elastic properties in the metal system TmS in high magnetic fields

We have made an investigation of the elastic properties of TmS in high magnetic fields. A pronounced softening was observed in elastic constants C₁₁ and (C₁₁-C₁₂)/2 at low temperatures, while no softening was observed in C₄₄. An analysis based on crystalline electric field splitting of Tm ions indicates that ferroelectric quadrupolar interactions among quadrupolar moments with Γ₃ symmetry developed at low temperatures. Two distinct anomalies in C₁₁ were found in magnetic fields. We propose an (H-T) phase diagram based on present and former results. This phase diagram implies that a field-induced ferromagnetic quadrupolar transition may occur in addition to an antiferromagnetic transition. Furthermore, the bulk modulus CB exhibits a softening at low temperature, implying an instability of the $4f$ state in the Tm ions.