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

Electronic and magnetic structures of ternary iron selenides AFe$_2$Se$_2$ (A=K, Cs, or Tl)