We find anomalously large diamagnetic responses in the cage compounds AV2Al20 where A = Y and La, not A = Al0.3, Sc0.4, and Lu, despite the apparent similarities in crystal and electronic structures among these compounds. The magnetic susceptibilities of the Y and La compounds become -1.94 and -7.44 x 10-4 cm3 mol-1 at 10 K, respectively, the latter of which corresponds to approximately one-quarter of that of bismuth, a well-known diamagnetic material, in terms of unit volume. The origin is not clear but may be related to a specific evolution in the band structure, as the diamagnetic response increases with increasing lattice constant.
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