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Reorientation of the bicollinear antiferromagnetic structure at the surface of Fe$_{1+y}$Te bulk and thin films

Establishing the relation between the ubiquitous antiferromagnetism in the non-superconducting parent compounds of unconventional superconductors and their superconducting phase is believed to be important for the understanding of the complex physics in these materials. Going from the bulk systems to thin films strongly affects the phase diagram of unconventional superconductors. For Fe$_{1+y}$Te, the parent compound of the Fe$_{1+y}$Se$_{1-x}$Te$_x$ superconductors, bulk sensitive neutron diffraction has revealed an in-plane oriented bicollinear antiferromagnetic structure. Here, we show by spin-resolved scanning tunneling microscopy that on the surfaces of bulk Fe$_{1+y}$Te, as well as on thin films grown on the topological insulator Bi$_2$Te$_3$, the spin direction is canted both away from the surface plane and from the high-symmetry directions of the surface unit cell, while keeping the bicollinear magnetic structure. Our results demonstrate that the magnetism at the Fe-chalcogenide surface markedly deviates from a simple in-plane oriented bicollinear antiferromagnetic structure, which implies that the pairing at the surface of the related superconducting compounds might be different from that in the bulk.