  The PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) has
measured $\phi$ meson production and its nuclear modification in asymmetric
Cu$+$Au heavy-ion collisions at $\sqrt{s_{NN}}=200$ GeV at both forward
Cu-going direction ($1.2<y<2.2$) and backward Au-going direction
($-2.2<y<-1.2$), rapidities. The measurements are performed via the dimuon
decay channel and reported as a function of the number of participating
nucleons, rapidity, and transverse momentum. In the most central events,
0\%--20\% centrality, the $\phi$ meson yield integrated over $1<p_T<5$ GeV/$c$
prefers a smaller value, which means a larger nuclear modification, in the
Cu-going direction compared to the Au-going direction. Additionally, the
nuclear-modification factor in Cu$+$Au collisions averaged over all centrality
is measured to be similar to the previous PHENIX result in $d$$+$Au collisions
for these rapidities.
