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We study the ground-state magnetism of the half-filled Hubbard model on theanisotropic triangular lattice, where two out of three bonds have hopping $t$and the third one has $t^\prime$ in a unit triangle. Working in a spin-rotatingframe and using the density matrix renormalization group method as an impuritysolver, we provide a proper description of incommensurate magnetizations atzero temperature in the framework of the dynamical mean-field theory (DMFT). Itis shown that the incommensurate spiral magnetic order for $t^\prime/t\gtrsim0.7$ survives the dynamical fluctuations of itinerant electrons in the Hubbardinteraction range from the strong-coupling (localized-spin) limit down to theinsulator-to-metal transition. We also find that the magnetic moment reductionfrom the localized-spin limit is pronounced in the vicinity of the transitionbetween the commensurate N\'eel and incommensurate spiral phases at$t^\prime/t\sim 0.7$. When the anisotropy parameter $t^\prime/t$ increases fromthe N\'eel-to-spiral transition, the magnitude of the magnetic momentimmediately reaches a maximum and then rapidly decreases in the range of larger$t^\prime/t$ including the isotropic triangular lattice point $t^\prime/t=1$.This work gives a solid foundation for further extension of the study includingnonlocal correlation effects neglected at the standard DMFT level.

Incommensurate spiral magnetic order on anisotropic triangular lattice: Dynamical mean field study in a spin-rotating frame