  The magnetic properties and electronic structure of (K,Tl)y Fe1.6 Se2 is
studied using first-principles calculations. The ground state is checkerboard
antiferromagnetically coupled blocks of the minimal Fe4 squares, with a large
block spin moment ~11.2{\mu}B . The magnetic interactions could be modelled
with a simple spin model involving both the inter- and intra-block, as well as
the n.n. and n.n.n. couplings. The calculations also suggest a metallic ground
state except for y = 0.8 where a band gap ~400 - 550 meV opens, showing an
antiferromagnetic insulator ground state for (K,Tl)0.8 Fe1.6 Se2 . The
electronic structure of the metallic (K,Tl)y Fe1.6 Se2 is highly 3-dimensional
with unique Fermi surface structure and topology. These features indicate that
the Fe-vacancy ordering is crucial to the physical properties of (K,Tl)y Fe2-x
Se2 .
