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Diverging Giant Magnetoresistance in the Limit of Infinitely Conducting Spacer

The relevance of pair-breaking by exchange and dipolar fields, and by injected spins in a low carrier density cuprate Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_7$ sandwiched between two ferromagnetic La$_{2 / 3}$Sr$_{1 / 3}$MnO$_{3}$ layers is examined. At low external field ($H_{ext}$), the system shows a giant magnetoresistance(MR), which diverges deep in the superconducting state. We establish a distinct dipolar contribution to MR near the switching field(H$_c$) of the magnetic layers. At H$_{ext} \gg$ H$_c$, a large positive MR, resulting primarily from the motion of Josephson vortices and pair breaking by the in-plane field, is seen.