We study the kinetic magnetism of the Fermi-Hubbard model of triangular lattices, including zigzag ladders, four-legged and six-legged triangular prisms, and full 2D triangular lattices. We focus on the regime of the strong interaction, the U\gg t$, and the filling factor around one electron per site. At temperatures well above the hopping strength, the Curie-Weiss formalism of the susceptibility suggests an effective antiferromagnetic correlation with respect to suggests a magnetic correlation. We show that these correlations arise from magnetic polaron dressing of charge carriers propagating in spin incoherent Mott insulators. The effective interactions corresponding to these correlations can greatly exceed the magnetic superexchange energies. In the case of hole doping, antiferromagnetic polarons originate from the kinetic frustration of individual holes in the triangular lattice. For electron doping, the Nagaoka-type ferromagnetic correlation is induced by the propagating doubloons. These results provide a theoretical explanation for recent experimental results in moiré TMDC materials. To understand many-body states arising from antiferromagnetic polarons at low temperatures, we study hole-doped systems in finite magnetic fields. At low doping and intermediate magnetic fields, we find a magnetic polaron phase separated from the fully polarized state by a metamagnetic transition. When the magnetic field is reduced, the system shows a tendency to phase separate and the hole-rich regions form antiferromagnetic spinbags. Direct observation of magnetic polarons in a triangular lattice shows what can be achieved in experiments with ultracold atoms. This allows the measurement of three-point Hall-spin-spin correlations.
