  Nuclear spin systems in manganites, having separation of ferromagnetic and
antiferromagnetic phases, which are manifested as two lines in the NMR
spectrum, are studied. Taking into account the Ising nuclear interaction, we
obtain an analytical description of Rabi oscillations and free induction decay
in two-component nuclear spin systems when a radio-frequency pulse
non-resonantly excites the nuclei of one magnetic phase and resonantly the
nuclei of the other phase. It is revealed that the nonlinearity of interaction
between the nuclei of these phases results in additional harmonics in the Rabi
oscillations of the non-resonantly excited subsystem. We also show that the
Ising interaction inside this subsystem forms multiple echoes in the free
induction decay, whereas their non-monotonic damping and amplitude modulation
is caused by the spin coupling between the subsystems.
