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Band calculations for supercells of La$_{(2-x)}$Ba$_x$CuO$_4$ show that therigid band model for doping is less adequate than what is commonly assumed. Inparticular, weak ferromagnetism (FM) can appear locally around clusters of highBa concentration. The clustering is important at large dilution and averagedmodels for magnetism, such as the virtual crystal approximation, are unable tostabilize magnetic moments. These results give a support to the idea that weakFM can be the cause of the destruction of superconductivity at high holedoping.

The importance of local band effects for ferromagnetism in hole doped La$_2$CuO$_4$