  We use the state-of-the-arts density-functional-theory method to study
various magnetic orders and their effects on the electronic structures of the
FeSe. Our calculated results show that, for the spins of the single Fe layer,
the striped antiferromagnetic orders with distortion are more favorable in
total energy than the checkerboard antiferromagnetic orders with tetragonal
symmetry, which is consistent with known experimental data, and the inter-layer
magnetic interaction is very weak. We investigate the electronic structures and
magnetic property of the distorted phases. We also present our calculated spin
coupling constants and discuss the reduction of the Fe magnetic moment by
quantum many-body effects. These results are useful to understand the
structural, magnetic, and electronic properties of FeSe, and may have some
helpful implications to other FeAs-based materials.
