  We have observed a quadratic x-ray magneto-optical effect in near-normal
incidence reflection at the M-edges of iron. The effect appears as the
magnetically induced rotation of ca. 0.1$ degrees of the polarization plane of
linearly polarized x-ray radiation upon reflection. A comparison of the
measured rotation spectrum with results from x-ray magnetic linear dichroism
data demonstrates that this is the first observation of the Schaefer-Hubert
effect in the x-ray regime. Ab initio density-functional theory calculations
reveal that hybridization effects of the 3p core states necessarely need to be
considered when interpreting experimental data. The discovered magneto-x-ray
effect holds promise for future ultrafast and element-selective studies of
ferromagnetic as well as antiferromagnetic materials.
