Giant biquadratic interaction-induced magnetic anisotropy in the iron-based superconductorAxFe2−ySe2

The emergence of the electron-pocket-only iron-based superconductor ${A}_x\mathrm{F}{\mathrm{e}}_{2\ensuremath{-}y}\mathrm{S}{\mathrm{e}}₂ (A=\mathrm{alkali}\phantom{\rule{0.28em}{0ex}}\mathrm{metal})$ challenges the Fermi-surface nesting picture established in iron pnictides. It was widely believed that magnetism is correlated with the superconductivity in ${A}_x\mathrm{F}{\mathrm{e}}_{2\ensuremath{-}y}\mathrm{S}{\mathrm{e}}₂$. 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 ${A}_x\mathrm{F}{\mathrm{e}}_{2\ensuremath{-}y}\mathrm{S}{\mathrm{e}}₂$. 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 to include other high-energy configurations as in the conventional energy-mapping method. We show that our model successfully captures the magnetic interactions in ${A}_x\mathrm{F}{\mathrm{e}}_{2\ensuremath{-}y}\mathrm{S}{\mathrm{e}}₂$ 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 ${A}_x\mathrm{F}{\mathrm{e}}_{2\ensuremath{-}y}\mathrm{S}{\mathrm{e}}₂$, which sheds new light on the future study of the high-${T}_{\mathrm{c}}$ iron-based superconductors.