  We report the direct observation of two mid-gap core d-states of differing
symmetry for a single Fe atom embedded in GaAs. These states are distinguished
by the strength of their hybridization with the surrounding host electronic
structure. The mid-gap state of Fe that does not hybridize via sigma-bonding is
strongly localized to the Fe atom, whereas the other, which does, is extended
and comparable in size to other acceptor states. Tight-binding calculations of
these mid-gap states agree with the spatial structure of the measured wave
functions, and illustrate that such measurements can determine the degree of
hybridization via pi-bonding of impurity d-states. These single-dopant mid-gap
states with strong d-character, which are intrinsically spin-orbit-entangled,
provide an opportunity for probing and manipulating local magnetism and may be
of use for high-speed electrical control of single spins.
