Relativistic spin dynamics conditioned by dark matter axions

The relativistic spin dynamics defined by the pseudoscalar field of dark matter axions is rigorously determined. Hamiltonian in Foldy-Wouthuysen representation derived. It agrees with previously obtained nonrelativistic Hamiltonians and classical estimation axion wind effect. In Hamiltonian, biggest term describes extraordinary (three orders magnitude) enhancement effect storage ring experiments as compared immobile particles. This defines rotation about longitudinal axis. effects caused axion-induced oscillating EDM consist rotations different horizontal axes phases stimulating oscillations differ $\pi/2$. Experiments a search for has been discussed. two experimental designs rings have elaborated.