Interspecies singlet pairing in a mixture of two spin-1 Bose condensates

We study the ground state properties of a mixture formed by two spin-1 condensates in the absence of an external magnetic field. As the collisional symmetry between interspecies bosonic atoms is broken, the interspecies coupling interaction ($\beta$) and interspecies singlet pairing interaction ($\gamma$) arise. The ground state can be calculated using the angular momentum theory analytically for $\gamma =0$. The full quantum approach of exact diagonalization is adopted numerically to consider the more general case as $\gamma \neq 0$. We illustrate the competition between the two interspecies interactions and find that as singlet pairing interaction dominates (or the total spin vanishes), there are still different types of singlet formations which are well determined by $\beta$.