  A unique type of frustrated lattice is found in two A-site ordered spinel
oxides, LiGaCr4O8 and LiInCr4O8. Because of the large size mismatch between Li+
and Ga3+/In3+ ions at the A site, the pyrochlore lattice, made up of Cr3+ ions
carrying spin 3/2, becomes an alternating array of small and large tetrahedra,
i.e., a "breathing" pyrochlore lattice. We introduce a parameter, the breathing
factor Bf, which quantifies the degree of frustration in the pyrochlore
lattice: Bf is defined as J'/J, where J' and J are nearest-neighbor magnetic
interactions in the large and small tetrahedra, respectively. LiGaCr4O8 with Bf
~ 0.6 shows magnetic susceptibility similar to that of conventional Cr spinel
oxides such as ZnCr2O4. In contrast, LiInCr4O8 with a small Bf ~ 0.1 exhibits a
spin-gap behavior in its magnetic susceptibility, suggesting a proximity to an
exotic singlet ground state. Magnetic long-range order occurs at 13.8 and 15.9
K for LiGaCr4O8 and LiInCr4O8, respectively, in both cases likely owing to the
coupling to structural distortions.
