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

Abstract

The distorted kagome lattice antiferromagnet ${\mathrm{Tb}}_{3}{\mathrm{Ru}}_{4}{\mathrm{Al}}_{12}$ with a hexagonal structure has the N\'eel temperature ${T}_{\mathrm{N}}=22$ K. To clarify the $4f$-electronic state and an influence of electric quadrupoles in ${\mathrm{Tb}}_{3}{\mathrm{Ru}}_{4}{\mathrm{Al}}_{12}$, ultrasonic measurements on a single-crystalline sample at zero magnetic field and under fields were carried. A characteristic elastic softening of the transverse modulus ${C}_{66}$ originating from a quadrupole interaction was found. The crystal electric field parameters were determined to reproduce ${C}_{66}$, 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 ${\mathrm{Tb}}_{3}{\mathrm{Ru}}_{4}{\mathrm{Al}}_{12}$ is a curious compound. The positive sign of the quadrupole-quadrupole coupling constant for ${C}_{66}$ indicates a ferroquadrupolar-type interaction of the electric quadrupole ${O}_{xy}$ or ${O}_{2}^{2}$. The anisotropic magnetic field dependencies of ${T}_{\mathrm{N}}$ in the field along [100] and [001] were also clarified.