  The spin-orbit coupling (SOC) affecting the center of mass of ultracold atoms
can be simulated using a properly chosen periodic sequence of magnetic pulses.
Yet such a method is generally accompanied by micro-motion which hinders a
precise control of atomic dynamics and thus complicating practical
applications. Here we show how to by-pass the micro-motion emerging in the
magnetically induced SOC by switching on and off properly the oscillating
magnetic fields at the initial and final times. We consider the exact dynamics
of the system and demonstrate that the overall dynamics can be immune to the
micro-motion. The exact dynamics is shown to agree well with the evolution of
the system described by slowly changing effective Floquet Hamiltonian including
the SOC term. The agreement is shown to be the best when the phase of the
periodic driving takes a specific value for which the effect of the spin-orbit
coupling is maximum.
