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We examine magnetic structures of electron systems on an extended triangularlattice that consists of two types of bond triangles with electron transferenergies t_l and t'_l (l = 1, 2, and 3), respectively. We examine the groundstate in the mean-field theory when t_1 = t'_1, focusing on collinear stateswith two sublattices. It is shown that when the imbalance of the spatialanisotropies of the two triangles is large, up-up-down-down (uudd) phases arestable, and the most likely ground states of the lambda-(BETS)_2FeCl_4 systemare the Neel state with the modulation vector (\pi/c,\pi/a) and a uudd state,where c = a_1 = a'_1 and a = (a_2+a'_2)/2, with a_1, a_1', a_2, and a_2' beingthe lattice constants of the bonds with t_1, t'_1, t_2, and t'_2, respectively.These results are consistent with those from the classical spin system. Inaddition, this study reveals behaviors near the quantum critical point, whichcannot be reproduced in the localized spin model. As the imbalance of thespatial anisotropies increases, the U_c of the Neel state increases, and thatof the uudd state decreases. In the phase diagrams containing areas of theparamagnetic state, the Neel state with (\pi/c,\pi/a), and a uudd state, theirboundaries terminate at a triple point, near which all the transitions are ofthe first order. The phase boundary between the antiferromagnetic phases doesnot depend on U, and the transition is of the first order everywhere on theboundary. By contrast, the transitions from the two antiferromagnetic phases tothe paramagnetic phase are of the second order, unless the system is close tothe triple point.

Magnetic structures of electron systems on the extended spatially completely anisotropic triangular lattice near quantum critical points