Magnetic transition due to the inter-singlet spin-exchange interaction and elastic softening by the interplay of electric quadrupoles in the distorted kagome lattice antiferromagnet Tb3Ru4Al12

The distorted kagome lattice antiferromagnet Tb3Ru4Al12 with a hexagonal structure has the Néel temperature TN=22 K. To clarify the 4f-electronic state and an influence of electric quadrupoles in Tb3Ru4Al12, ultrasonic measurements on a single-crystalline sample at zero magnetic field and under fields were carried. A characteristic elastic softening of the transverse modulus C66 originating from a quadrupole interaction was found. The crystal electric field parameters were determined to reproduce C66, magnetic susceptibilities, and magnetization curves. The obtained level scheme is that the ground and first excited states are singlets, despite the existence of both the magnetic transition and the quadrupole interaction, indicating that Tb3Ru4Al12 is a curious compound. The positive sign of the quadrupole-quadrupole coupling constant for C66 indicates a ferroquadrupolar-type interaction of the electric quadrupole Oxy or O22. The anisotropic magnetic field dependencies of TN in the field along [100] and [001] were also clarified.