  Using the relativistic point-coupling model with density functional PC-PK1,
the magnetic moments of the nuclei $^{207}$Pb, $^{209}$Pb, $^{207}$Tl and
$^{209}$Bi with a $jj$ closed-shell core $^{208}$Pb are studied on the basis of
relativistic mean field (RMF) theory. The corresponding time-odd fields, the
one-pion exchange currents, and the first- and second-order corrections are
taken into account. The present relativistic results reproduce the data well.
The relative deviation between theory and experiment for these four nuclei is
6.1% for the relativistic calculations and somewhat smaller than the value of
13.2% found in earlier non-relativistic investigations. It turns out that the
$\pi$ meson is important for the description of magnetic moments, first by
means of one-pion exchange currents and second by the residual interaction
provided by the $\pi$ exchange.
