  On a lattice with 2+1-flavor dynamical domain-wall fermions at the physical
pion mass, we calculate the decay constants of $D_{s}^{(*)}$, $D^{(*)}$ and
$\phi$. The lattice size is $48^3\times96$, which corresponds to a spatial
extension of $\sim5.5$ fm with the lattice spacing $a\approx 0.114$ fm. For the
valence light, strange and charm quarks, we use overlap fermions at several
mass points close to their physical values. Our results at the physical point
are $f_D=213(5)$ MeV, $f_{D_s}=249(7)$ MeV, $f_{D^*}=234(6)$ MeV,
$f_{D_s^*}=274(7)$ MeV, and $f_\phi=241(9)$ MeV. The couplings of $D^*$ and
$D_s^*$ to the tensor current ($f_V^T$) can be derived, respectively, from the
ratios $f_{D^*}^T/f_{D^*}=0.91(4)$ and $f_{D_s^*}^T/f_{D_s^*}=0.92(4)$, which
are the first lattice QCD results. We also obtain the ratios
$f_{D^*}/f_D=1.10(3)$ and $f_{D_s^*}/f_{D_s}=1.10(4)$, which reflect the size
of heavy quark symmetry breaking in charmed mesons. The ratios
$f_{D_s}/f_{D}=1.16(3)$ and $f_{D_s^*}/f_{D^*}=1.17(3)$ can be taken as a
measure of SU(3) flavor symmetry breaking.
