  The interaction of neutrino transition magnetic dipole moments with magnetic
fields can give rise to the phenomenon of neutrino spin-flavour precession
(SFP). For Majorana neutrinos, the combined action of SFP of solar neutrinos
and flavour oscillations would manifest itself as a small, yet potentially
detectable, flux of electron antineutrinos coming from the Sun. Non-observation
of such a flux constrains the product of the neutrino magnetic moment $\mu$ and
the strength of the solar magnetic field $B$. We derive a simple analytical
expression for the expected $\bar{\nu}_e$ appearance probability in the
three-flavour framework and we use it to revisit the existing experimental
bounds on $\mu B$. A full numerical calculation has also been performed to
check the validity of the analytical result. We also present our numerical
results in energy-binned form, convenient for analyses of the data of the
current and future experiments searching for the solar $\bar{\nu}_e$ flux. In
addition, we give a comprehensive compilation of other existing limits on
neutrino magnetic moments and of the expressions for the probed effective
magnetic moments in terms of the fundamental neutrino magnetic moments and
leptonic mixing parameters.
