Periodicity in the appearance of intervals of the reversal of the magnetic moment of a $\phi_0$ Josephson junction

The dynamics of the magnetization under the action of a current pulse in a $\phi_0$ Josephson junction with the direct coupling between the magnetic moment and a superconducting current has been analyzed. Time dependences of the components of the magnetic moment at different parameters of the $\phi_0$ junction have been calculated. These dependences have been used to determine intervals of the parameters where the magnetic moment is reversed from $m_z=1$ to $m_z=-1$. Periodicity has been revealed in the appearance of intervals of the reversal of the magnetic moment under the variation of the spin-orbit coupling, Gilbert damping parameter, and Josephson-to-magnetic energy ratio. The results obtained can be used in various fields of superconducting spintronics, in particular, to create a memory unit based on the Josephson $\phi_0$ junction.