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Based on first principle calculations we have investigated the evolution ofmagnetism in free-standing monolayer FeSe with respect to lattice constant andmagnetism in bulk FeSe. The computational results show that the magnetic orderin free-standing monolayer FeSe will change from anti-ferromagneticpair-checkboard order to stripe collinear order along with enlarging latticeconstant. The magnetic order in bulk FeSe will change from stripe collinearorder to anti-ferromagnetic pair-checkboard order only if structurereconstruction is allowed. We use J$_1$-J$_2$-K$_1$ model to fit the calculatedtotal energies of different magnetic orders to study magnetic interactionstrengths in FeSe. The fitting results of J$_1$-J$_2$-K$_1$ indicate thatmagnetic interactions in FeSe are quite strong and highly frustrated, andincrease slowly with enlarging lattice parameter.

Magnetic interactions in FeSe studied by first principle calculations