  We have investigated the magnetic-field induced phases of a typical
three-dimensional frustrated magnet, CdCr$_2$O$_4$, in magnetic fields of up to
120 T that is generated by the single-turn coil techniques. We focused on
magnetic phase transitions in proximity of a saturated magnetization moment. We
utilized both the electromagnetic induction method using magnetic pick-up coils
and magneto-optical spectroscopies of the $d$-$d$ transitions and the
exciton-magnon-phonon transitions to study the magnetic properties subjected to
ultra-high magnetic fields. Anomalies were observed in magneto-optical
absorption intensity as well as differential magnetization prior to a fully
polarized magnetic phase (a vacuum state in the magnon picture), revealing a
novel magnetic phase associated with changes in both crystal and magnetic
structures accompanied by the first order phase transition. Magnetic superfluid
state such as an umbrella-like magnetic structure or a spin nematic state, is
proposed as a candidate for the novel magnetic phase, which is found universal
in the series of chromium spinel oxides, $A$Cr$_2$O$_4$ ($A$ = Zn, Cd, Hg).
