  Time-odd mean fields (nuclear magnetism) and their impact on physical
observables in rotating nuclei are studied in the framework of covariant
density functional theory (CDFT). It is shown that they have profound effect on
the dynamic and kinematic moments of inertia. Particle number, configuration
and rotational frequency dependences of their impact on the moments of inertia
have been analysed in a systematic way. Nuclear magnetism can also considerably
modify the band crossing features such as crossing frequencies and the
properties of the kinematic and dynamic moments of inertia in the band crossing
region. The impact of time-odd mean fields on the moments of inertia in the
regions away from band crossing only weakly depends on the relativistic mean
field parametrization, reflecting good localization of the properties of
time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei
considerably deviate from the rigid body value. On the contrary, superdeformed
and hyperdeformed nuclei have the moments of inertia which are close to rigid
body value. The structure of the currents in rotating frame, their microscopic
origin and the relations to the moments of inertia have been systematically
analysed. The phenomenon of signature separation in odd-odd nuclei, induced by
time-odd mean fields, has been analysed in detail.
