  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.
