We present x-ray resonant magnetic reflectivity (XRMR) as a very sensitive tool to detect proximity induced interface spin polarization in Pt/Fe, Pt/Ni$_{33}$Fe$_{67}$, Pt/Ni$_{81}$Fe$_{19}$ (permalloy), and Pt/Ni bilayers. We demonstrate that a detailed analysis of the reflected x-ray intensity gives insight in the spatial distribution of the spin polarization of a non-magnetic metal across the interface to a ferromagnetic layer. The evaluation of the experimental results with simulations based on optical data from ab initio calculations provides the induced magnetic moment per Pt atom in the spin polarized volume adjacent to the ferromagnet. We find the largest spin polarization in Pt/Fe and a much smaller magnetic proximity effect in Pt/Ni. Additional XRMR experiments with varying photon energy are in good agreement with the theoretical predictions for the energy dependence of the magnetooptic parameters and allow identifying the optical dispersion $delta$ and absorption $beta$ across the Pt L3-absorption edge.
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