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 4 f -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 O2 2. The anisotropic magnetic field dependencies of TN in the field along [100] and [001] were also clarified.This work was supported by JSPS KAKENHI Grants No.17H06136, No. 18KK0078, and No. 19K03719. This work was also supported by CResCent (Chirality Research Center) in Hiroshima University (the MEXT program for promoting the enhancement of research universities, Japan) and by JSPS Core-to-Core Program, A. Advanced Research Networks. The work was supported by Projects No. 19-00925S and No. 19-07931Y of the Czech Science Foundation and by MGML within the Program of Czech Research Infrastructures (Project No. LM2018096)