  We discuss an experiment in which two magnetic insulators that both show a
field-induced magnetic-ordering transition are weakly coupled to one another
and are placed into an ex- ternal magnetic field. If the respective magnetic
states can be interpreted as phase coherent Bose-Einstein condensates of
magnetic bosonic quasiparticles, one expects the occurrence of Josephson
effects. For two identical systems, the resulting d.c. Josephson effect
formally represents a constant quasiparticle Josephson current across the weak
link, which turns out to be unobservable in an experiment. For magnetic
insulators with different critical fields, a spontaneous alternating
quasiparticle current develops with a leading oscillation frequency
{\omega}a.c. that is determined by the difference between the critical fields.
As a result of the coupling, additional sidebands appear in the energy spectrum
of the coupled device that would be absent without phase coherence. We discuss
the primary conditions for such an effect to take place and conclude that its
detection can be feasible for a proper choice of compounds with suitable and
realistic material parameters.
