  We report neutron scattering measurements of the spinel oxide
LiGaCr$_{4}$O$_{8}$, in which magnetic ions Cr$^{3+}$ form a breathing
pyrochlore lattice. Our experiments reveal the coexistence of a nearly
dispersionless resonance mode and dispersive spin wave excitations in the
magnetically ordered state, which can be quantitatively described by a quantum
spin model of hexagonal loops and linear spin wave theory with the same set of
exchange parameters, respectively. Comparison to other Cr spinel oxides reveals
a linear relationship between the resonance energy and lattice constant across
all these materials, which is in agreement with our hexagonal loop
calculations. Our results suggest a unified picture for spin resonances in Cr
spinel oxides.
