  In the presence of P,T-violating interactions, the exchange of axion-like
particles between electrons and nucleons in atoms and molecules induces
electric dipole moments (EDMs) of atoms and molecules. We perform calculations
of such axion-exchange-induced atomic EDMs using the relativistic
Hartree-Fock-Dirac method including electron core polarisation (RPA)
corrections. We present analytical estimates to explain the dependence of these
induced atomic EDMs on the axion mass and atomic parameters. From the
experimental bounds on the EDMs of atoms and molecules, including $^{133}$Cs,
$^{205}$Tl, $^{129}$Xe, $^{199}$Hg, $^{171}$Yb$^{19}$F, $^{180}$Hf$^{19}$F$^+$
and $^{232}$Th$^{16}$O, we constrain the P,T-violating scalar-pseudoscalar
nucleon-electron and electron-electron interactions mediated by a generic
axion-like particle of arbitrary mass. Our limits improve on existing
laboratory bounds from other experiments by many orders of magnitude for $m_a
\gtrsim 10^{-2}~\textrm{eV}$. We also place constraints on CP violation in
certain types of relaxion models.
