We present an ab initio study of the magnetic surface reconstructions of th
e B2 FeV alloy using a self-consistent tight-binding linearized muffin tin
orbital method developed in the atomic spheres approximation. For (001) and
(111), the surface reconstruction stabilizes configurations unstable in th
e bulk alloy. When Fe is at the (001) surface, a c(2 x 2) in-plane antiferr
omagnetic order is found to be tile ground state with magnetic moments of -
2.32 muB and 2.27 muB. A p(1 x 1)down arrow ferromagnetic order is displaye
d in case of V toplayer with a magnetic moment of -1.83 muB. At the (111) s
urface, we obtain for Fe toplayer two solutions p(1 x 1)up arrow and p(2 x
1). The configuration p(1 x 1)up arrow is found to be the ground state with
a magnetic moment per atom of 2.34 muB. For V toplayer, only the p(1 x 1)d
own arrow solution is obtained with a moment of -0.84 muB. In all cases, th
e Fe-V coupling is always antiparallel like in the bulk. Our results are di
scussed and compared to experiments.