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Motivated by the importance of non-collinear and non-coplanar magnetic phasesin determining various electrical properties of magnetic materials, weinvestigate the phase diagrams of the extended Hubbard model on anisotropictriangular lattice. We make use of a mean-field scheme that treats collinear,non-collinear and non-coplanar phases on equal footing. In addition to theferromagnetic and 120{\deg} antiferromagnetic phases, we find thefour-sublattice flux, the 3Q non-coplanar and the non-collinear charge-orderedstates to be stable at specific values of filling fraction $n$. Inter-siteCoulomb repulsion leads to intriguing spin-charge ordered phases. Most notableof these are the collinear and non-collinear magnetic states at $n=2/3$, whichoccur together with a pinball-liquid-like charge order. Our results demonstratethat the elementary single-orbital extended Hubbard model on a triangularlattice hosts unconventional spin-charge ordered phases, which have beenreported in more complex and material-specific electronic Hamiltonians relevantto layered triangular systems.

Noncollinear and noncoplanar magnetic order in the extended Hubbard model on anisotropic triangular lattice