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Imbalance of Mn3+ and Mn4+ ions between surface and bulk in layered manganites is investigated on the basis of an orbital degenerate double-exchange model with surfaces. For two types of t2g spin structures, the number of Mn4+ ions on the surface is found to be larger than that in the bulk, explained by the surface-induced Friedel oscillation. In particular, for the sheet-type antiferromagnetic state, quantum beat phenomenon appears due to the interference among Friedel oscillations and the number of Mn4+ ions tends to increase on the surface. The present results are believed to be useful to develop high-efficient cathodes in Li-ion batteries and catalysts.

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