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We study the magnetism and lattice distortion of Fe_{1+y}Te_{1-x}Se_x with ageneral field theory formalism, motivated by recent neutron scatteringexperiments. Besides the Ising nematic order parameter which can be naturallydefined in the 1111 and 122 materials, We show that the collinear orderobserved in $\mathrm{Fe_{1+y}Te}$ materials is stabilized by an extra Isingorder parameter which doubles the generalized unit cell of the system. Bytuning this Ising order parameter, one can drive a transition between collinearand noncollinear spin density wave orders, both of which are observed in theFeTe family. The nature of the quantum and classical phase transitions are alsostudied in this field theory formalism, with lattice strain tensor fluctuationconsidered.

Field theory for magnetic and lattice structure properties of Fe_{1+y}Te_{1-x}Se_x