  This study reveals a novel phenomenon demonstrating the elastic softening of
synthetic diamonds when cooled to very low temperatures below 1 K. We present
the results of ultrasonic measurements of single-crystalline synthetic diamonds
without irradiation, namely type-IIa (colorless) and Ib (yellow) diamonds grown
by high-pressure-high-temperature synthesis as well as type-IIa diamond grown
by chemical vapor deposition. We observed a divergent decrease of the elastic
stiffness constant $C_{44}$ in all samples at low temperatures down to 20 mK.
We argue for the existence of electric quadrupolar degrees of freedom with
irreducible representation $T_2$ in diamond as the origin of this elastic
softening. The possible ground state preserves local $T_d$ symmetry presumably
down to absolute zero. Of the ground states of atomic vacancies in diamond
proposed thus far, the only relevant one is the positively charged single
atomic vacancy V$^+$, which has not been observed in previous optical
measurements in diamonds.
