  The bicollinear antiferromagnetic order experimentally observed in FeTe is
shown to be stabilized by the coupling $\tilde g_{12}$ between monoclinic
lattice distortions and the spin-nematic order parameter with $B_{\rm 2g}$
symmetry, within a three-orbital spin-fermion model studied with Monte Carlo
techniques. A finite but small value of $\tilde g_{12}$ is required, with a
concomitant lattice distortion compatible with experiments, and a
tetragonal-monoclinic transition strongly first order. Remarkably, the
bicollinear state found here displays a planar resistivity with the "reversed"
puzzling anisotropy discovered in transport experiments.Orthorhombic
distortions are also incorporated and phase diagrams interpolating between
pnictides and chalcogenides are presented. We conclude that the spin-lattice
coupling discussed here is sufficient to explain the challenging properties of
FeTe.
