  We study kinetic magnetism for the Fermi-Hubbard models in triangular type
lattices, including a zigzag ladder, four- and six-legged triangular cylinders
and a full two-dimensional triangular lattice. We focus on the regime of strong
interactions, $U\gg t$ and filling factors around one electron per site. For
temperatures well above the hopping strength, the Curie-Weiss form of the
magnetic susceptibility suggests effective antiferromagnetic correlations for
systems that are hole doped with respect to $\nu=1$, and ferromagnetic
correlations for systems with electron dopings. We show that these correlations
arise from magnetic polaron dressing of charge carrier propagating in a spin
incoherent Mott insulator. Effective interactions corresponding to these
correlations can strongly exceed the magnetic super-exchange energy. In the
case of hole doping, antiferromagnetic polarons originate from kinetic
frustration of individual holes in a triangular lattice. In the case of
electron doping, Nagaoka type ferromagnetic correlations are induced by
propagating doublons. These results provide a theoretical explanation of recent
experimental results in moire TMDC materials. To understand many-body states
arising from antiferromagentic polarons at low temperatures, we study hole
doped systems in finite magnetic fields. At low dopings and intermediate
magnetic fields we find a magnetic polaron phase, separated from the fully
polarized state by a metamagnetic transition. With decreasing magnetic field
the system shows a tendency to phase separate, with hole rich regions forming
antiferromagnetic spinbags. We demonstrate that direct observations of magnetic
polarons in triangular lattices can be achieved in experiments with ultracold
atoms, which allow measurements of three point hole-spin-spin correlations.
