We study the equilibrium domain structure and magnetic flux around a ferromagnetic film with perpendicular magnetization M₀ on a superconducting (SC) substrate. At 4πM₀<Hc1 the SC is in the Meissner state and the equilibrium domain width in the film, l, scales as (l/4πλL)=(lN/4πλL)2/3 with the domain width on a normal (nonsuperconducting) substrate, lN/4πλL1; λL being the London penetration length.
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Bulaevskiǐ et al. (2000) studied this question.