Solitonic spin-liquid state due to the violation of the Lifshitz condition in Fe${}_{1+y}$Te

A combination of phenomenological analysis and M"ossbauer spectroscopy experiments on the tetragonal Fe${}_{1+y}$Te system indicates that the magnetic ordering transition in compounds with higher Fe-excess, $y\ge$ 0.11, is unconventional. Experimentally, a liquid-like magnetic precursor with quasi-static spin-order is found from significantly broadened M"ossbauer spectra at temperatures above the antiferromagnetic transition. The incommensurate spin-density wave (SDW) order in Fe${}_{1+y}$Te is described by a magnetic free energy that violates the weak Lifshitz condition in the Landau theory of second-order transitions. The presence of multiple Lifshitz invariants provides the mechanism to create multidimensional, twisted, and modulated solitonic phases.