  We investigate the pressure phase diagram of FeTe, predicting structural and
magnetic properties in the normal state at zero temperature within density
functional theory (DFT). We carefully examined several possible different
crystal structures over a pressure range up to $\approx 30 $ GPa: simple
tetragonal (PbO type), simple monoclinic, orthorhombic (MnP type), hexagonal
(NiAs and wurzite type) and cubic (CsCl and NaCl type). We predict pressure to
drive the system through different magnetic ordering (notably also some
ferromagnetic phases) eventually suppressing magnetism at around 17GPa. We
speculate the ferromagnetic order to be the reason for the absence of a
superconducting phase in FeTe at variance with the case of FeSe.
