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We investigate the ground-state phase diagram of interacting binary Bosegases trapped in two-dimensional optical lattices by means of quantum MonteCarlo simulations. Our simulations reveal a magnetic phase transition from a$x-y$ ferromagnetic-order to a spin insulator inside the Mott insulating phasewith two particles per site for quasi-balanced on-site inter- andintra-particle interactions, i.e., $U_{\uparrow \downarrow} \lesssim U$. This3D-XY transition is characterized by the establishment of a finite localmagnetic moment along the $z$-axis, ferromagnetic correlations in the $x-y$plan and by counterflow superfluidity inside the Mott phase. When decreasing$U_{\uparrow \downarrow}/U$, this transition merges with the Mott-superfluidtransition and becomes first-order. The merging of the two transitions isinvestigated with respect to $U_{\uparrow \downarrow}/U$ parameter.

Magnetic Phase Transition in the Ground-State Phase Diagram of Binary Bose Gases in Optical Lattices