We consider a superconducting film with a magnetic dots array (MDA) placed upon it. Magnetic moments of the dots are normal to the film and strong enough to create vortices in the superconducting film. Magnetic interaction between dots is negligible. Zero-field cooling leads to random magnetization of the MDA well above the superconducting temperature. With this cooling, the film is in a resistive state below the (expected) superconducting transition. Paradoxically, when field cooled, the film with MDA can be superconducting.
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Lyuksyutov et al. (1998) studied this question.
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