We report on ultrasonic measurements of the rare-earth altermagnet ${\mathrm{TbPt}}_6{\mathrm{Al}}_3$ in which the Tb magnetic moments in a honeycomb lattice form a collinear antiferromagnetic structure below $T_{\mathrm{N}}=3.4\mathrm{K}$. All elastic moduli show a distinct downward peak at $T_{\mathrm{Q}}=1.6\mathrm{K}$, suggesting an additional phase transition. The transverse moduli $C_{44}$ and $C_{66}$ exhibit significant softening toward $T_{\mathrm{Q}}$, accompanied by ultrasound attenuation. Crystal field analysis of the temperature dependences of elastic moduli reveals that the elastic softening arises from quadrupole-mediated interactions of the ground non-Kramers doublet of the Tb ions. The field-temperature phase diagram in a magnetic field applied along [001] shows an increase in $T_{\mathrm{Q}}$ with increasing field up to 0.8 T. Our crystal field model with the mean-field approximation displays spontaneous occurrence of an expectation value of electric quadrupole at $T_{\mathrm{Q}}$. The agreement between our experimental and calculated results suggests quadrupolar ordering in an altermagnetic ordered state.

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• Altermagnetism
• Elastic modulus
• Multipole order
• Phase diagrams
• Altermagnets
• Rare-earth magnetic materials
• Ultrasound techniques