  We use cold neutron spectroscopy to study the low-energy spin excitations of
superconducting (SC) FeSe$_{0.4}$Te$_{0.6}$ and essentially non-superconducting
(NSC) FeSe$_{0.45}$Te$_{0.55}$. In contrast to BaFe$_{2-x}$(Co,Ni)$_{x}$As$_2$,
where the low-energy spin excitations are commensurate both in the SC and
normal state, the normal-state spin excitations in SC FeSe$_{0.4}$Te$_{0.6}$
are incommensurate and show an hourglass dispersion near the resonance energy.
Since similar hourglass dispersion is also found in the NSC
FeSe$_{0.45}$Te$_{0.55}$, we argue that the observed incommensurate spin
excitations in FeSe$_{1-x}$Te$_{x}$ are not directly associated with
superconductivity. Instead, the results can be understood within a picture of
Fermi surface nesting assuming extremely low Fermi velocities and spin-orbital
coupling.
