Twinning of domains and spin anisotropy in K$_5$Fe$_4$Ag$_6$Te$_{10}$
The Fe-based superconductors are derived from metallic parent compounds with nematic and stripe magnetic orders, which lead to two types of magnetic domains. Recently it was found that K$_5$Fe$_4$Ag$_6$Te$_{10}$ (KFAT), an Fe-based semiconductor, exhibits similar nematic and stripe magnetic orders, and is thus an analogue to the Fe-based superconductors in the limit of localized electrons. In this work, the superstructure and magnetic domains of KFAT are elucidated by fully mapping the reciprocal space using time-of-flight single crystal neutron diffraction. In KFAT, Fe and Ag atoms order to form a $\sqrt{5}\times\sqrt{5}$ superstructure containing $2\times2$ Fe blocks, which leads to two superstructure domains with identical main Bragg peaks but distinct superstructure peaks. Below $T_{\rm N}\approx35$~K, magnetic and nematic orders break in-plane rotational symmetry of the tetragonal $\sqrt{5}\times\sqrt{5}$ superstructure, and further give rise to two magnetic domains. These four equally populated domains account for the complex scattering pattern observed in our time-of-flight elastic neutron scattering measurements. Using polarized neutron scattering, we demonstrate a prominent spin anisotropy with an easy-plane spanned by the $c$-axis and the intra-block antiferromagnetic Fe-Fe bond direction. Such an anisotropy at ${\bf q}\neq0$ persists well above $T_{\rm N}$, accounts for the in-plane ${\bf q}=0$ magnetic anisotropy observed in uniaxial-strained KFAT, and offers an indicator for discovering similar piezomagnetic effects in other materials.