Ferromagnetic Film on a Superconducting Substrate

We study the equilibrium domain structure and magnetic flux around a ferromagnetic (FM) film with perpendicular magnetization M 0 on a super-conducting (SC) substrate. At 4πM 0 < H c1 the SC is in the Meissner state and the equilibrium domain width in the film, l, scales as (l/4πλ L) = (l N /4πλ L) 2/3 with the domain width on a normal (non-superconducting) substrate, l N /4πλ L ≫ 1. Here λ L is the London penetration length. For 4πM 0 > H c1 and l N in excess of about 35λ L , the domains are connected by SC vortices. We argue that pinning of vortices by magnetic domains in FM/SC multilayers can provide high critical currents.