The magnetization process in a layered superconductor composed of a periodic array of strongly and weakly superconducting layers is investigated near Hc1 in a field parallel to the layers, using a generalized Lawrence-Doniach model. In the case where the coupling between layers is weak the rate of increase of the flux line density for the raised external field is small. The magnetization in this case decreases with increasing the field (dm/dh<0) near Hc1. When the in-plane penetration depth of weakly superconducting layers is much greater than that of strongly superconducting layers, the interaction between flux lines has an attractive part along the layers. The transition at Hc1 is first order in this case.
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