  Using bulk magnetization along with elastic and inelastic neutron scattering
techniques, we have investigated the phase diagram of
Fe$_{1+y}$Se$_{x}$Te$_{1-x}$ and the nature of magnetic correlations in three
nonsuperconducting samples of Fe$_{1.01}$Se$_{0.1}$Te$_{0.9}$,
Fe$_{1.01}$Se$_{0.15}$Te$_{0.85}$ and Fe$_{1.02}$Se$_{0.3}$Te$_{0.7}$. A cusp
and hysteresis in the temperature dependence of the magnetization for the
$x=0.15$ and 0.3 samples indicates spin-glass (SG) ordering below $T_{\rm sg} =
23$K. Neutron scattering measurements indicate that the spin-glass behavior is
associated with short-range spin density wave (SDW) ordering characterized by a
static component and a low-energy dynamic component with a characteristic
incommensurate wave vector of ${\bf Q}_m = (0.46, 0, 0.50)$ and an anisotropy
gap of $\sim$ 2.5 meV. Our high ${\bf Q}$-resolution data also show that the
systems undergo a glassy structural distortion that coincides with the
short-range SDW order.
