  The quasi-one-dimensional Chevrel phases, A$_2$Mo$_6$Se$_6$ (A = Tl, In, K,
Rb, Cs), are of interest due to their atypical electronic properties. The Tl
and In analogues undergo a superconducting transition whereas the alkali metal
analogues show charge gapping of another, not well understood type. We report
the results of inelastic neutron scattering on polycrystalline
In$_2$Mo$_6$Se$_6$ ($T_c=2.85\,$K) and Rb$_2$Mo$_6$Se$_6$ (non-superconducting)
samples, which reveal a column of intensity with linear dispersion from [0 0
1/2] to [0 0 1] in both compounds. The observed temperature and |$Q$|
independence together suggest the presence of unconventional carriers with a
spin contribution to the excitation. This is contrary to the prevailing model
for these materials, which is that they are non-magnetic. The excitation has
similar dispersion and $S(Q,E,T)$ behavior as one observed in the structurally
related superconducting compounds A$_2$Cr$_3$As$_3$ and A$_2$Mo$_3$As$_3$ (A =
K, Rb, Cs), which has been interpreted as magnetic in origin and related to
Fermi surface nesting. The connection is unexpected because the calculated
Fermi surface of the arsenides differs substantially from the A$_2$Mo$_6$Se$_6$
compounds, and many consider them distinct classes of materials. The new
observation suggests a hidden link in the physics between both classes of
superconductors, perhaps originating from their quasi-low-dimensional
character.
