Iron telluride doped lightly with selenium is known to undergo a first order magneto-structural transition before turning superconducting at higher doping. We study the effects of magneto-elastic couplings on this transition using symmetry considerations. We find that the magnetic order parameters are coupled to the uniform monoclinic strain of the unit cell with one iron per cell, as well as to the phonons at high symmetry points of the Brillouin zone. In the magnetic phase the former gives rise to monoclinic distortion while the latter induces dimerization of the ferromagnetic iron chains due to alternate lengthening and shortening of the nearest-neighbour iron-iron bonds. We compare this system with the iron arsenides and propose a microscopic magneto-elastic Hamiltonian which is relevant for all the iron based superconductors. We argue that this describes electron-lattice coupling in a system where electron-electron interaction is crucial.
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