  Strong dependence of the Josephson energy on the magnetization orientation in
Josephson junctions with ferromagnetic interlayers and spin-orbit coupling
opens a way to control magnetization by Josephson current or Josephson phase.
Here we investigate the perspectives of magnetization control in
superconductor/ferromagnet/superconductor (S/F/S) Josephson junctions on the
surface of a 3D topological insulator hosting Dirac quasiparticles. Due to the
spin-momentum locking of these Dirac quasiparticles a strong dependence of the
Josephson current-phase relation on the magnetization orientation is realized.
It is demonstrated that this can lead to splitting of the ferromagnet's
easy-axis in the voltage driven regime. We show that such a splitting can lead
to stabilization of an unconventional four-fold degenerate ferromagnetic state.
