Spin-polarized neutron reflectivity: A probe of vortices in thin-film superconductors

Abstract

It is demonstrated that the specular reflectivity of spin-polarized neutrons can be used to study vortices in a thin-film superconductor. Experiments were performed on a 6000 Å thick c-axis film of YBa 2 Cu 3 O 7Ϫx with the magnetic field applied parallel to the surface. A magnetic hysteresis loop was observed for the spinpolarized reflection and, from these data, the average density of vortices was extracted. A model is presented which relates the specular reflectivity to the one-dimensional spatial distribution of vortices in the direction perpendicular to the surface. Unlike other techniques, neutron reflectivity observes vortices in a geometry where they are parallel to the interface. ͓S0163-1829͑99͒07021-6͔

Orientation of vortices in a superconducting thin film: Quantitative comparison of spin-polarized neutron reflectivity and magnetization

“…a model presented previously. 8 Although this requires the spatial distribution of the vortices as input information, the analysis of the present experiments does not depend on the choice of distribution, as shown in Fig. 4 for data taken at 2000 Oe after the sample had been subjected to a field of 3000 Oe.…”

“…This reversible behavior is quite different from the previous SPNR study of a YBCO film, where ⌬R/R exhibited a large hysteresis loop. 8 The data were analyzed to extract the vortex density using FIG. 3.…”

“…For a field applied parallel to the surface of a superconductor, assuming a uniform distribution of vortices, the magnetization parallel to the surface M ʈ is obtained by direct integration of the equations in Ref. 8,…”

“…7 All of these studies were performed at low field, below H c1 . Recently, it was demonstrated 8,9 that SPNR is also useful at higher fields, above H c1 , where it can yield information on vortices. In particular, Han et al 8 extracted the average vortex density for the field parallel to a thin film of YBa 2 Cu 3 O 7-x ͑YBCO͒ and a large hysteresis loop was observed.…”

Neutron scattering studies of nanomagnetism and artificially structured materials

“…For example, small-angle neutron scattering has been used to map out the vortex lattice phase diagram as a function of magnetic field and temperature [165,166,167,168,169] for arrays of vortices forming an hexagonal or a square lattice at the surface [170]. For thin films, the vortex distribution parallel to the film has been determined from polarized neutron reflectometry [171,172,173,174].…”