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Well-known examples of shears bands in the nuclei 198 Pb and 199 Pb are investigated within tilted axis cranking relativistic mean-field theory. Energy spectra, the relation between spin and rotational frequency, deformation parameters and reduced M1 and E2 transition probabilities are calculated. The results are in good agreement with available data and with calculations based on the phenomenological pairing plus-quadrupole-quadrupole tilted-axis cranking model. It is shown that covariant density functional theory provides a successful microscopic and fully self-consistent description of magnetic rotation in the Pb region showing the characteristic properties as the shears mechanism and relatively large B(M1) transitions decreasing with increasing spin.

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