The emergence of the electron-pocket only iron-based superconductor AxFe2-ySe2 (A = alkali metal) challenges the Fermi-surface nesting picture established in iron-pnictides. It was widely believed that magnetism is correlated with the superconductivity in AxFe2-ySe2. Unfortunately, the highly anisotropic exchange parameters and the disagreement between theoretical calculations and experimental results triggered a fierce debate on the nature of magnetism in AxFe2-ySe2. Here we find that the strong magnetic anisotropy is from the anisotropic biquadratic interaction. In order to accurately obtain the magnetic interaction parameters, we propose a universal method, which does not need including other high energy configurations as did in conventional energy mapping method. We show that our model successfully captures the magnetic interactions in AxFe2-ySe2 and correctly predicts the spin wave spectrum, in quantitative agreement with the experimental observation. These results suggest that the local moment picture, including the biquadratic term, can describe accurately the magnetic properties and spin excitations in AxFe2-ySe2, which sheds new light on the future study of the high-Tc iron-based superconductors.
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