  We study theoretically the transverse spin associated with the eigenmodes of
a thin metal film embedded in a dielectric. We show that the transverse spin
has a direct dependence on the nature and strength of the coupling leading to
two distinct branches for the long- and short- range modes. We show that the
short-range mode exhibits larger extraordinary spin because of its more
'structured' nature due to higher decay in propagation. In contrast to some of
the earlier studies, calculations are performed retaining the full lossy
character of the metal. In the limit of vanishing losses we present analytical
results for the extraordinary spin for both the coupled modes. The results can
have direct implications for enhancing the elusive transverse spin exploiting
the coupled plasmon structures.
