Magnetic-crystallographic phase diagram of the superconducting parent compound Fe1+xTe

hrough neutron diffraction experiments, including spin-polarized\nmeasurements, we find a collinear incommensurate spin-density wave with\npropagation vector $ \\mathbf k = $ ($0.4481(4) \\, \\,0 \\, \\, \\frac1 2$) at base\ntemperature in the superconducting parent compound Fe$_{1+x}$Te. This critical\nconcentration of interstitial iron corresponds to $x \\approx 12%$ and leads\ncrystallographic phase separation at base temperature. The spin-density wave is\nshort-range ordered with a correlation length of 22(3) \\AA, and as the ordering\ntemperature is approached its propagation vector decreases linearly in the\nH-direction and becomes long-range ordered. Upon further populating the\ninterstitial iron site, the spin-density wave gives way to an incommensurate\nhelical ordering with propagation vector $ \\mathbf k =$ ($0.3855(2) \\, \\,0 \\,\n\\, \\frac1 2$) at base temperature. For a sample with $x \\approx 9(1) %$, we\nalso find an incommensurate spin-density wave that competes with the\nbicollinear commensurate ordering close to the N\\'eel point. The shifting of\nspectral weight between competing magnetic orderings observed in several\nsamples is supporting evidence for the phase separation being electronic in\nnature, and hence leads to crystallographic phase separation around the\ncritical interstitial iron concentration of 12%. With results from both powder\nand single crystal samples, we construct a magnetic-crystallographic phase\ndiagram of Fe$_{1+x}$Te for $ 5% < x <17%$\n