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By applying density functional theory calculations to iron chalcogenides, wefind that magnetic order in Fe$_{1+y}$Te and magnetic instability at$(\pi,\pi)$ in K$_y$Fe$_2$Se$_2$ are controlled by interstitial and interlayercations, respectively. While in Fe$_{1+y}$Te, magnetic phase transitions occuramong collinear, exotic bicollinear and plaquette-ordered antiferronmagneticstates when the height of interstitial irons measured from iron plane or theconcentration of interstitial irons is varied, the magnetic instability at$(\pi,\pi)$ which is believed to be responsible for the Cooper pairing in ironpnictides is significantly enhanced when $y$ is much smaller than $1$ inK$_y$Fe$_2$Se$_2$. Our results indicate that, similar to iron pnictides,itinerant electrons play important roles in iron chalcogenides, even though thefluctuating local moments become larger.

Magnetic Properties Controlled by Interstitial or Interlayer Cations in Iron Chalcogenides