  In this study, we have performed the magnetocaloric effect and the specific
heat measurements of chromium spinel oxide HgCr$_2$O$_4$, wherein the magnetic
Cr$^{3+}$ ions form a highly frustrated pyrochlore lattice with significant
spin-lattice coupling. In addition to the known magnetic-field-induced phases,
our thermodynamic measurements detect a novel quantum phase just before the
saturation of the magnetization, which has not been expected from the classical
theories of the pyrochlore lattice antiferromagnet with spin-lattice coupling.
Based on recent theoretical model calculation, we discuss the possibility of a
spin nematic state appearing for this quantum phase.
