  We study magnetic solitons, solitary waves of spin polarization (i.e.,
magnetization), in binary Bose-Einstein condensates in the presence of Rabi
coupling. We show that the system exhibits two types of magnetic solitons,
called $2\pi$ and $0\pi$ solitons, characterized by a different behavior of the
relative phase between the two spin components. $2\pi$ solitons exhibit a
$2\pi$ jump of the relative phase, independent of their velocity, the static
domain wall explored by Son and Stephanov being an example of such $2\pi$
solitons with vanishing velocity and magnetization. $0\pi$ solitons instead do
not exhibit any asymptotic jump in the relative phase. Systematic results are
provided for both types of solitons in uniform matter. Numerical calculations
in the presence of a one-dimensional harmonic trap reveal that a $2\pi$ soliton
evolves in time into a $0\pi$ soliton, and vice versa, oscillating around the
center of the trap. Results for the effective mass, the Landau critical
velocity, and the role of the transverse confinement are also discussed.
