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 ${\mathrm{K}}_5{\mathrm{Fe}}_4{\mathrm{Ag}}_6{\mathrm{Te}}_{10}$ (KFAT), an Fe-based semiconductor, exhibits similar nematic and stripe magnetic orders, and is thus an analog 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 $2\times 2$ Fe blocks, which leads to two superstructure domains with identical main Bragg peaks but distinct superstructure peaks. Below $T_{\mathrm{N}}\approx 35\mathrm{K}$, 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 intrablock antiferromagnetic Fe-Fe bond direction. Such an anisotropy at $\mathbf{q}\ne 0$ persists well above $T_{\mathrm{N}}$, accounts for the in-plane $\mathbf{q}=0$ magnetic anisotropy observed in uniaxial-strained KFAT, and offers an indicator for discovering similar piezomagnetic effects in other materials.

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• Magnetic order
• Nematic order
• Neutron diffraction
• X-ray diffraction