We performed ultrasonic measurements on a single crystal of PrMg3. The characteristic Curie-type softening was observed in temperature dependence of transverse mode (C11 - C12) / 2 below 8 K down to 0.8 K. This softening in PrMg3 is caused by a non-Kramers Γ3 doublet ground state having electric quadrupoles Ou and Ov and magnetic octupole Txyz. The elastic constant (C11 - C12) / 2 shows a minimum at 25 K, which cannot be explained by the quadrupole susceptibility based on the crystal electric field (CEF) levels. However, considering higher order (l = 4) multipole, namely electric hexadecapole, the minimum around 25 K was well reproduced. At lower temperatures, a shoulder anomaly in elastic constant being deviated from the Curie-type softening was observed around 100-800 mK in (C11 - C12) / 2. This anomaly is unaffected by magnetic fields up to 14 T.
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