Flux-line row-transitions determine the magnetic behaviour of thin superconducting films in the mixed state in the configuration of an external field parallel to the film surface, as shown schematically in the upper panel for increasing field values.
Polarised neutron reflectometry reveals the number of flux-line rows and yields the magnetisation curve, which exhibits unusual behaviour arising from the reduced dimensionality. The filled circles in the lower panel mark the positions of the flux-line rows in an external magnetic field.
a) Schematic representation of the arrangement of 1 to 3 flux-line rows inside a superconducting thin film in an external magnetic field.
b) The ideal profile of the magnetic scattering-length density (= magnetisation profile) from the flux-line rows as seen by polarised neutron reflectometry. The two spin states of the neutrons in the external field yield the two magnetic scattering length densities marked with green and pink lines. The nuclear scattering-length density is omitted.
c) The experimentally deduced magnetic scattering-length density (= magnetisation profile) in a step-function presentation. The data have been taken at a temperature of 4 K and the sample was cooled in zero field.
(Courtesy of V. Lauter-Pasyuk)