Quasi-two-dimensional non-collinear magnetism in the Mott insulator Sr$_2$F$_2$Fe$_2$OS$_2$*

We study the magnetism of Sr$_2$F$_2$Fe$_2$OS$_2$ through neutron powder diffraction and thermodynamic and transport measurement. Quasi-two-dimensional magnetic order develops below $T_{\rm N}$=106K with an in-plane correlation length exceeding 310 {\AA} and an out-of-plane correlation length of only 17(3) {\AA}. The data are well described by a two-k structure with k$_1$=(1/2,0,1/2) and k$_2$=(0,1/2,1/2). The ordered moment is 3.3(1) $\mu_B$ oriented along the in-plane components of k. This structure is composed of orthogonal AFM chains intersecting at super-exchange mediating O sites. The Density Function Theory ( by Liang L.Zhao, Jiakui K. Wang, etc.) also leads to this structure and a narrower Fe 3d band than for the iron pnictides from which electronic correlations produce a Mott insulator.