  Detecting axionic dark matter induced electron or nucleon oscillating
electric dipole moment (OEDM) has become a new way for dark matter searches. We
re-examine such axion-spin couplings in external electromagnetic fields. We
point out that axion-photon interaction induces an electron spin effective
coupling, which is different from an OEDM. In particular, the axion-spin
effective coupling is directly related to magnetic field rather than electric
field. For axion-electron or axion-nucleon couplings, an OEDM of fermion is
introduced, whose effect in ultralight axion cases depends on whether axion
shift symmetry is manifest. Specifically, ultralight axionic dark matter
interactions that do not obey the shift symmetry will be strongly constrained.
We also extend the results to the case where axion has a finite velocity.
