  By the first-principles electronic structure calculations, we find that the
ground state of ternary iron selenides AFe$_2$Se$_2$ (A=K, Cs, or Tl) is in a
bi-collinear antiferromagnetic order, in which the Fe local moments
($\sim2.8\mu_B$) align ferromagnetically along a diagonal direction and
antiferromagnetically along the other diagonal direction on the Fe-Fe square
lattice. This bi-collinear antiferromagnetic order results from the interplay
among the nearest, the next nearest, and the next next nearest neighbor
superexchange interactions, mediated by Se $4p$-orbitals.
