  We investigate the Johari-Goldstein (JG) $\beta$-relaxation process in a
model metallic glass-forming (GF) material (Al90Sm10), previously studied
extensively by both frequency-dependent mechanical measurements and simulation
studies devoted to equilibrium properties, by molecular dynamics simulations
based on validated and optimized interatomic potentials with the primary aim of
better understanding the nature of this universal relaxation process from a
dynamic heterogeneity (DH) perspective. The present relatively low temperature
and long-time simulations reveal a direct correspondence between the JG
$\beta$-relaxation time $\tau_{JG}$ and the lifetime of the mobile particle
clusters $\tau_M$, defined as in previous DH studies, a relationship dual to
the corresponding previously observed relationship between the
$\alpha$-relaxation time $\tau_\alpha$ and the lifetime of immobile particle
clusters $\tau_{IM}$. Moreover, we find that the average diffusion coefficient
D nearly coincides with D$_{Al}$, of the smaller atomic species (Al), and that
the hopping time associated with D coincides with $\tau_{JG}$ to within
numerical uncertainty, both trends being in accord with experimental studies.
This indicates that the JG $\alpha$-relaxation is dominated by the smaller
atomic species and the observation of a direct relation between this relaxation
process and rate of molecular diffusion in GF materials at low temperatures
where the JG $\beta$-relaxation becomes the prevalent mode of structural
relaxation. As an unanticipated aspect of our study, we find that Al90Sm10
exhibits fragile-to-strong (FS) glass-formation, as found in many other
metallic GF liquids, but this fact does not greatly alter the geometrical
nature of DH in this material and the relation of DH to dynamical properties.
