  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.
