  We develop a low energy effective field theory of a mixture of two species of
pseudospin-1/2 atoms with interspecies spin-exchange, in addition to
density-density interaction. This approach is beyond the single orbital-mode
approximation. In a wide parameter regime, it indicates the existence of the
four elementary excitations, especially a gapped mode due to interspecies
spin-exchange. On the other hand, the spectrum of the effective spin
Hamiltonian yielded by the single mode approximation can be obtained by
quantizing the homogeneous excitation, which is spin excitation and is the
long-wavelength limit of the gapped mode of elementary excitations. These low
energy excitations can be experimentally measured by using Bragg spectroscopy.
