The Fe1+xTe phase diagram consists of two distinct magnetic structures with collinear order present at low interstitial iron concentrations and a helical phase at large values of x with these phases separated by a Lifshitz point. We use unpolarized single crystal diffraction to confirm the helical phase for large interstitial iron concentrations and polarized single crystal diffraction to demonstrate the collinear order for the iron deficient side of the Fe1+xTe phase diagram. Polarized neutron inelastic scattering show that the fluctuations associated with this collinear order are predominately transverse at low energy transfers, consistent with a localized magnetic moment picture. We then apply neutron inelastic scattering and polarization analysis to investigate the dynamics and structure near the boundary between collinear and helical order in the Fe1+xTe phase diagram. We first show that the phase separating collinear and helical order is characterized by a spin-density wave with a single propagation wave vector of (~ 0.45, 0, 0.5). We do not observe harmonics or the presence of a charge density wave. The magnetic fluctuations associated with this wavevector are different from the collinear phase being strongly longitudinal in nature and correlated anisotropically in the (H,K) plane. The excitations preserve the C4 symmetry of the lattice, but display different widths in momentum along the two tetragonal directions at low energy transfers. While the low energy excitations and minimal magnetic phase diagram can be understood in terms of localized interactions, we suggest that the presence of density wave phase implies the importance of electronic and orbital properties.
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