  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.
