  We simulate the dynamics of paramagnetic colloidal particles that are placed
above a magnetic hexagonal pattern and exposed to an external field
periodically changing its direction along a control loop. The conformation of
three colloidal particles above one unit cell adiabatically responds with half
the frequency of the external field creating a time crystal at arbitrary low
frequency. The adiabatic time crystal occurs because of the non-trivial
topology of the stationary manifold. When coupling colloidal particles in
different unit cells, many body effects cause the formation of topologically
isolated time crystals and dynamical phase transitions between different
adiabatic reversible and non-adiabatic irreversible space-time-crystallographic
arrangements.
