Bicollinear Antiferromagnetic Order, Monoclinic Distortion, and Reversed Resistivity Anisotropy in FeTe as a Result of Spin-Lattice Coupling

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.