  We report a sequence of continuous phase transformations in iron telluride,
Fe1+yTe (y~0.1), which is observed by combining neutron diffraction, magnetic
susceptibility, and specific heat measurements on single crystal samples. While
a gradual increase of magnetic scattering near the wave vector (0.5, 0, 0.5) is
seen below T = 70 K, a temperature where the discontinuous first order
magneto-structural phase transition is found in systems with small y (< 0.06),
the reduction of the lattice symmetry in Fe1.1Te only occurs at Ts = 63 K.
Below TN = 57.5 K the long-range magnetic order develops, whose incommensurate
wave vector Qm varies with temperature. Finally, at Tm ~ 45 K the system enters
the low-T phase, where Qm is locked at (0.48, 0, 0.5). We conclude that these
instabilities are weak compared to the strength of the underlying interactions,
and we suggest that the impact of the Fe interstitials on the transitions can
be treated with random-field models.
