Due
to the magnetoelastic coupling, the magnetic properties of
many flexible magnetic films (such as Fe, Co, and Ni) are sensitive
to mechanical stress, which deteriorates the performance of flexible
magnetoelectronic devices. We show that by stacking Co and Pt alternatively
to form multilayers with strong perpendicular magnetic anisotropy
(PMA), both magnetic hysteresis and magnetic domain measurements reveal
robust PMA against external stress. As the PMA weakens at increased
Co thickness, the magnetic anisotropy is vulnerable to external stress.
These results were understood based on a micromagnetic model, which
suggests that the strength of magnetoelastic anisotropy with respect
to initial effective magnetic anisotropy affects the stress-stability
of the film. Although the stress coefficient of magnetoelastic anisotropy
is enhanced at reduced Co thickness, the concomitant increase of initial
effective magnetic anisotropy guarantees a robust PMA against external
stress. Our results provide a route to constructing flexible magnetoelectronic
devices with enhanced stress stability.