  Understanding the sticking coefficient $\sigma$, i.e., the probability of an
adatom sticking to a surface, is essential for controlling the stoichiometry
during epitaxial film growth. However, $\sigma$ on monolayer graphene-covered
surfaces and its impact on remote epitaxy are not understood. Here, using
molecular-beam epitaxial (MBE) growth of the magnetic shape memory alloy
Ni$_2$MnGa, we show that the sticking coefficients for metals on
graphene-covered MgO (001) are less than one and are temperature and element
dependent, as revealed by ion backscattering spectrometry (IBS) and energy
dispersive x-ray spectroscopy (EDS). This lies in stark contrast with most
transition metals sticking on semiconductor and oxide substrates, for which
$\sigma$ is near unity at typical growth temperatures ($T<800\degree$C). By
initiating growth below $400 \degree$ C, where the sticking coefficients are
closer to unity and wetting on the graphene surface is improved, we demonstrate
epitaxy of Ni$_2$MnGa films with controlled stoichiometry that can be
exfoliated to produce freestanding membranes. Straining these membranes tunes
the magnetic coercive field. Our results provide a route to synthesize
membranes with complex stoichiometries whose properties can be manipulated via
strain.
