  We report Brownian dynamics (BD) simulation and theoretical results for a
system of spherical colloidal particles with permanent dipole moments in a
rotating magnetic field. Performing simulations at a fixed packing fraction and
dipole coupling parameter, we construct a full non-equilibrium phase diagram as
function of the driving frequency ($\omega_0$) and field strength ($B_0$). This
diagram contains both synchronized states, where the individual particles
follow the field with (on average) constant phase difference, and asynchronous
states. The synchronization is accompanied by layer formation, i.e. by spatial
symmetry-breaking, similar to systems of induced dipoles in rotating fields. In
the permanent-dipole case, however, too large $\omega_0$ yield a breakdown of
layering, supplemented by complex changes of the single-particle rotational
dynamics from synchronous to asynchronous behavior. We show that the limit
frequencies $\omega_c$ can be well described as a bifurcation in the nonlinear
equation of motion of a single particle rotating in a viscous medium. Finally,
we present a simple density functional theory, which describes the emergence of
layers in perfectly synchronized states as an equilibrium phase transition.
