  Magnetometry measurements of Fe/U and Ni/U bilayer systems reveal a
non-monotonic dependence of the magnetic anisotropy for U thicknesses in the
range 0 nm - 8 nm, with the Fe/U bilayers showing a more prominent effect as
compared to Ni/U. The stronger response for Fe/U is ascribed to the stronger
3d-5f hybridization of Fe and U. This non-monotonic behaviour is thought to
arise from quantum well states in the uranium overlayers. Estimating an
oscillation period from the non-monotonic data, and comparing it to Density
Functional Theory calculations, we find that wavevector matches to the
experimental data can be made to regions of high spectral density in (010) and
(100) cuts of the electronic structure of{\alpha}-U, consistent with the
measured texture in the films. Unexpectedly, there are also indications of
perpendicular magnetic anisotropy in a subset of Fe/U samples at relatively
large U thickness.
