  The Mn-terminated (001) surface of the stable anti-ferromagnetic insulating
phase of cubic perovskite CaMnO$_3$ is found to undergo a magnetic
reconstruction consisting on a spin-flip process at surface: each Mn spin at
the surface flips to pair with that of Mn in the subsurface layer. In spite of
very little Mn-O charge transfer at surface, the surface behavior is driven by
the $e_g$ states due to $d_{xy}$ $\to$ $d_{z^2}$ charge redistribution. These
results, based on local spin density theory, give a double exchange like
coupling that is driven by $e_g$ character, not additional charge, and may have
relevance to CMR materials.
