Magnetic domain structures of ferromagnetic ultra-thin films deposited on superconducting substrates

The influence of bulk superconducting substrates and coatings on the domain structure parameters of a ferromagnetic ultra-thin film was analysed, assuming the validity of the London equation in the superconducting volumes. The problem was analysed for both easy plane and perpendicular easy axis films; however, as the effects of the superconducting substrate are relatively unimportant for films magnetized in plane, most of the article is devoted to easy axis films. Expressions for the demagnetization energy were found for arbitrary magnetization distribution. It was shown that a superconducting substrate changes the domain structure properties even if the layer is coated with a non-superconducting material. For sufficiently thin films the domain structure can be fully suppressed, which was shown by considering an isolated Bloch wall for larger anisotropy (Q > 1) and the critical domain structure for low anisotropy (Q < 1). The results of numerical calculations for critical ferromagnetic film thickness (as a function of anisotropy and London penetration depth) are presented.