Analytic calculation of polarized neutron reflectivity from superconductors

Abstract

We have obtained an analytic expression for the reflectivity R±(θ,λ) of polarized neutrons from a superconductor in the Meissner state, where λ is the magnetic-field penetration depth and θ is the incident angle of the neutron beam. The result is derived as an exact solution of the 1D Schrödinger equation in the continuum limit, with an interaction potential V±(x)=VN±μH[exp(-x/λ)-1], where VN is a constant representing the nuclear interaction, μ is the neutron magnetic moment, and H is the applied magnetic field. The solution for R±(θ,λ) reveals surprising features in its λ dependence that have not been discovered in previous numerical studies. In particular, R−(θ,λ) displays an oscillatory dependence on λ within a narrow angular range immediately above the total reflection angle (θ≳θc−), instead of a monotonic dependence as inferred from earlier numerical calculations. The solution also reveals that complete transmission for the down-spin state [R−(θ,λ)=0] may occur when λ and H satisfy certain conditions. In addition to the analytic expression of the reflectivity for a semi-infinite sample, we have also obtained the reflectivity R̃ ±(θ,λ) from a thick superconducting film where the magnetic field can penetrate from both sides. In the case of a free-standing film of which the two surfaces are identical, we have simply R̃ ±=2R±/(1+R±), and therefore all the interesting features of the exact solution R± persist in R̃ ±. Finally, the exact solution can also be applied to other systems where the scattering potential has an exponential dependence with distance, such as for the magnetization at the surface of a ferromagnet.

Source-reported materials — not catalogue approval

Similar papers