Periodic vortex and current structures in superconductor-ferromagnet bilayer

Abstract

The formation of a periodic vortex and current structures in the ferromagnet/superconductor bilayer with finite interlayer distance $a$ is considered when the ferromagnetic film has a stripe domain structure with out-of-plane magnetization. The integrodifferential equation which determines the current and vortex distribution in the superconducting (SC) film is derived. The analytical solutions are obtained for two limiting cases: $L<\ensuremath{\lambda}$ (the narrow-domain structure) and $L⪢\ensuremath{\lambda}$ (the wide-domain structure), where $L$ is the width of the domain and $\ensuremath{\lambda}=\frac{{\ensuremath{\lambda}}_{L}^{2}}{{d}_{s}}$ is the effective penetration depth (where ${\ensuremath{\lambda}}_{L}$ is the London penetration depth and ${d}_{s}$ is the thickness of the SC film). The conditions for existence of two periodic vortex structures in the SC are found (i) for the chains of vortices/antivortices (one vortex/antivortex per domain) and (ii) for the domelike vortex distribution characterized by the average vortex density $n(x)$. The value of the critical current (along the domains) of the superconducting film is calculated. It is shown that there is the optimal interlayer distance ${a}^{\ensuremath{\ast}}$ corresponding to the maximal value of the critical current at a given value of the magnetization.