To investigate the $4f$-electronic states under a crystal electric field (CEF) and the phase transition in ${\mathrm{Dy}}_3{\mathrm{Ru}}_4{\mathrm{Al}}_{12}$ with the antiferromagnetic transition temperature $T_{\mathrm{N}}=7$ K, we performed ultrasonic measurements on a single-crystalline sample at zero magnetic field and under fields. The transverse elastic modulus $C_{44}$ shows a characteristic elastic softening. The CEF analyses indicate that the softening is caused by an interlevel quadrupole interaction between the ground and excited Kramers doublets. Under fields, we found a magnetic-field-induced phase transition along both the [100] and [001] directions in addition to the antiferromagnetic ordering. A plausible origin of the field-induced transition is quadrupolar ordering, which is estimated from our CEF calculation. These results and the negative sign of a quadrupole-quadrupole coupling constant suggest that the effect of geometrical frustration alignment due to the kagome lattice also appears on the electric quadrupoles of the Dy ions with the antiferroquadrupolar-type interaction.

• Received 30 March 2018

DOI:https://doi.org/10.1103/PhysRevB.97.235130