  Time-odd mean fields (nuclear magnetism) are analyzed in the framework of
covariant density functional theory (CDFT). It is shown that they always
provide additional binding to the binding energies of odd-mass nuclei. This
additional binding only weakly depends on the RMF parametrization reflecting
good localization of the properties of time-odd mean fields in CDFT. The
underlying microscopic mechanism is discussed in detail. Time-odd mean fields
affect odd-even mass differences. However, our analysis suggests that the
modifications of the strength of pairing correlations required to compensate
for their effects are modest. In contrast, time-odd mean fields have profound
effect on the properties of odd-proton nuclei in the vicinity of proton-drip
line. Their presence can modify the half-lives of proton-emitters (by many
orders of magnitude in light nuclei) and affect considerably the possibilities
of their experimental observation.
