  Isolated hydrogen atoms absorbed on graphene are predicted to induce magnetic
moments. Here we demonstrate that the adsorption of a single hydrogen atom on
graphene induces a magnetic moment characterized by a ~20 meV spin-split state
at the Fermi energy. Our scanning tunneling microscopy (STM) experiments,
complemented by first-principles calculations, show that such a spin-polarized
state is essentially localized on the carbon sublattice complementary to the
one where the H atom is chemisorbed. This atomically modulated spin-texture,
which extends several nanometers away from the H atom, drives the direct
coupling between the magnetic moments at unusually long distances. Using the
STM tip to manipulate H atoms with atomic precision, we demonstrate the
possibility to tailor the magnetism of selected graphene regions.
