  We develop a general scheme for detecting spin correlations inside a
two-component lattice gas of bosonic atoms, stimulated by the recent
theoretical and experimental advances on analogous systems for a single
component quantum gas. Within a linearized theory for the transmission spectra
of the cavity mode field, different magnetic phases of a two-component (spin
1/2) lattice bosons become clearly distinguishable. In the Mott-insulating (MI)
state with unit filling for the two-component lattice bosons, three different
phases: antiferromagnetic, ferromagnetic, and the XY phases are found to be
associated with drastically different cavity photon numbers. Our suggested
study can be straightforwardly implemented with current cold atom experiments.
