The investigation of the magnetic phase transitions in the parent compounds of Fe-based superconductors is regarded essential for an understanding of the pairing mechanism in the related superconducting compounds. Even though the chemical and electronic properties of these materials are often strongly inhomogeneous on a nanometer length scale, studies of the magnetic phase transitions using spatially resolved experimental techniques are still scarce. Here, we present a real space spin-resolved scanning tunneling microscopy investigation of the surface of Fe$_{1+y}$Te single crystals with different excess Fe content, $y$, which are continuously driven through the magnetic phase transition. For Fe$_{1.08}$Te, the transition into the low-temperature monoclinic commensurate antiferromagnetic phase is accompanied by the sudden emergence of ordering into four rotational domains with different orientations of the monoclinic lattice and of the antiferromagnetic order, showing how structural and magnetic order are intertwined. In the low-temperature phase of Fe$_{1.12}$Te one type of the domain boundaries disappears, and the transition into the paramagnetic phase gets rather broad, which is assigned to the formation of a mixture of orthorhombic and monoclinic phases.
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