  Size effects on vibrational modes in complex crystals remain largely
unexplored, despite their importance in a variety of electronic and energy
conversion technologies. Enabled by advances in a four-probe thermal transport
measurement method, we report the observation of glass-like thermal
conductivity in ~20 nm thick single crystalline ribbons of higher manganese
silicide, a complex, anisotropic crystal with a ~10 nm scale lattice constant
along the incommensurate c axis. The boundary scattering effect is strong for
many vibrational modes because of a strong anisotropy in their group velocities
or diffusive nature, while confinement effects are pronounced for acoustic
modes with long wavelengths along the c axis. Furthermore, the transport of the
non-propagating, diffusive modes is suppressed in the nanostructures by the
increased incommensurability between the two substructures as a result of the
unusual composition of the nanostructure samples. These unique effects point to
diverse, new approaches to suppressing the lattice thermal conductivity in
complex materials.
