  Superconductor/ferromagnet/superconductor Josephson junctions with anomalous
phase shift $\varphi_0$ ($\varphi_0$-S/F/S JJs) realize a coupling between the
superconducting phase and the spin degrees of freedom. Consequently, the
anomalous phase shift is a hallmark effect of superconducting spintronics and
opens great perspectives for applications of such structures for controlling
magnetization. Besides controlling the magnetization of a single ferromagnet,
the direct coupling between the phase and the magnetization provides a
possibility to establish and control a collective behavior of magnetic moments
of different weak links in coupled chains of $\varphi_0$-S/F/S JJs. Here we
investigate voltage-driven dynamics of such chains and predict that the
spin-phase coupling makes the conventional voltage-driven regime unstable. As a
result the system undergoes a transition to other dynamical regimes, where
clear signatures of the spin-phase coupling and the collective behavior are
observed.
