We explore the Mott insulating phases of dual-species bosonic spinor lattice gases, emphasizing the intriguing interplay between synthetic flux and interspecies spin exchange interaction. One of the species is subjected to Raman-assisted tunneling, which leads to a synthetic flux within the framework of synthetic dimensions. In the deep Mott regime, the low-energy physics is governed by an unconventional and highly tunable spin model, which is characterized by two distinct spin chains. The synthetic flux serves as an effective spin-orbit coupling, inducing Dzyaloshinskii-Moriya (DM) interactions in one of the spin chains. The interspecies spin exchange interaction gives rise to the inter-chain coupling embodied as an isotropic $\mathit{XX}$ interaction. Using time-evolving block decimation method for tensor network states, we compute order parameters, correlation functions and structure factors to identify the ground state magnetic phases. The DM interaction in one species, when combined with the interspecies spin-exchange interaction, can induce spiral magnetic order in the second, otherwise nonchiral species. Additionally, the interplay of a transverse field applied to one spin chain and the interspecies coupling can drive both spin chains into a paramagnetic phase simultaneously. These results reveal that interspecies coupling serves as a powerful conduit for transmitting magnetic correlations, enabling exotic phases beyond the single-component perspective.

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• Cold gases in optical lattices
• Mixtures of atomic and/or molecular quantum gases
• Quantum phase transitions
• Mott superfluids
• Ultracold gases
• Bose-Hubbard model