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

Abstract

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.

Domain structure and magnetic pinning in ferromagnetic/superconducting hybrids

“…The latter is close to the domain shrinkage of 2.1 reported for a magnetic garnet film covered with a 300 nm Pb layer [40][41]. Such a value is well above 1.2, the maximum ratio achievable at the total Meissner screening of the stray fields of narrow (D<d F ) FM domains [42][43][44][45][46] and it is in contrast to the expected expansion of wide domains (D>d F ) [43] as is discussed below. This indicates that the screening effects are negligible, in accordance with our observations of B z below T c in domains over the Nb area where it is supported by vortices, and other mechanisms control the domain behavior.…”

“…However, at D >> d F the superconducting screening always suppresses the magnetostatic term and should increase the equilibrium domain size. Similar behavior was numerically predicted in [43].…”

“…On the other side of the FM film H s will stay intact. Then the total magnetostatic energy will increase 1.5 times causing the reduction of the domain width by (1.5) 1/2 [42][43][44][45][46]. If the SC film is thin and the FM domain width is smaller than the effective London penetration depth λ eff , the screening is negligible and the domain shrinkage should be small, ~0.08 (D/λ eff ) of the initial D [42].…”

Phase transitions in the domain structure of ferromagnetic superconductors

“…17 (see also later analysis in Refs. [18,19]). If one takes into account vortex pinning potentials the expansion of the domains at low temperatures takes place and the application of ac magnetic field, routinely used for equilibration of domains, may lead to their significant contraction.…”

Sudden magnetization drops in superconductor/ferromagnet bilayered structures

“…3a. Note also that as the film gets thicker the domains reduce in size, increasing the number of domain walls and Bloch lines that can fit in the same interface area [37] thus enlarging the local out of plane fields on the superconductor.…”