Abstract
The magnetic-field--temperature $(H\ensuremath{-}T)$ phase diagram of a superconductor is significantly altered when domains are present in an underlying ferromagnet with perpendicular magnetic anisotropy. When the domains have a bandlike shape, the critical temperature ${T}_{c}$ of the superconductor in zero field is strongly reduced and the slope of the upper critical field as a function of T is increased by a factor of 2.4 due to the inhomogeneous stray fields of the domains. Field compensation effects can cause an asymmetric phase boundary with respect to H when the ferromagnet contains bubble domains. For a very inhomogeneous domain structure, ${T}_{c}\ensuremath{\propto}{H}^{2}$ for low H and ${T}_{c}\ensuremath{\propto}H$ for higher fields, indicating a dimensional crossover from a one-dimensional networklike to a two-dimensional behavior in the nucleation of superconductivity.
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