Ferromagnetic film on a superconducting substrate

We study th equilibrium domain structure and magnetic flux around a ferromagnetic film with perpendicular magnetization M-o on a superconducting (SC) substrate. At 4 pi M-o<H-cl the SC is in the Meissner state and the equilibrium domain width in the film, l, scales at (l/4<pi>lambda (L)) = (l(N)/4 pi lambda (L))(2/3) with the domain width on a normal (nonsuperconducting) substrate, l(N)/4 pi lambda (L)>>1; lambda (L) being the London penetration length.