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The robustness of the gapless topological surface state hosted by a 3Dtopological insulator against perturbations of magnetic origin has been thefocus of recent investigations. We present a comprehensive study of themagnetic properties of Fe impurities on a prototypical 3D topological insulatorBi$_2$Se$_3$ using local low temperature scanning tunneling microscopy andintegral x-ray magnetic circular dichroism techniques. Single Fe adatoms on theBi$_2$Se$_3$ surface, in the coverage range $\approx 1%$ are heavily relaxedinto the surface and exhibit a magnetic easy axis within the surface-plane,contrary to what was assumed in recent investigations on the opening of a gap.Using \textit{ab initio} approaches, we demonstrate that an in-plane easy axisarises from the combination of the crystal field and dynamic hybridizationeffects.

In-plane magnetic anisotropy of Fe atoms on Bi$_2$Se$_3$(111)