  By the first-principles electronic structure calculations, we find that the
ground state of the Fe-vacancies ordered TlFe$_{1.5}$Se$_2$ is a
quasi-two-dimensional collinear antiferromagnetic semiconductor with an energy
gap of 94 meV, in agreement with experimental measurements. This
antiferromagnetic order is driven by the Se-bridged antiferromagnetic
superexchange interactions between Fe moments. Similarly, we find that crystals
AFe$_{1.5}$Se$_2$ (A=K, Rb, or Cs) are also antiferromagnetic semiconductors
but with a zero-gap semiconducting state or semimetallic state nearly
degenerated with the ground states. Thus rich physical properties and phase
diagrams are expected.
