Spin Structures and Phase Diagrams of Extended Spatially Completely Anisotropic Triangular Lattice Antiferromagnets

Motivated by recently discovered organic antiferromagnets, we examine an extended triangular lattice that consists of two types of triangles of bonds with exchange coupling constants J(l) and J'(l) (l = 1, 2, and 3), respectively. The simplified system with J(l) = J'(l) > 0 is the spatially completely anisotropic triangular lattice (SCATL) antiferromagnet examined previously. The extended system, which we call an extended SCATL (ESCATL), has two different spatial anisotropy parameters J(3)/J(2) and J'(3)/J'(2) when J(1) = J'(1) is assumed. We derive classical phase diagrams and spin structures. It is found that the ESCATL antiferromagnet exhibits two up-up-down-down (uudd) phases when the imbalance of the anisotropy parameters is significant, in addition to the three Neel phases that occur in the SCATL. When the model parameters vary, these collinear phases are continuously connected by the spiral-spin phase. Using the available model parameters for the organic compounds lambda-(BETS)(2)XCl4 (X = Fe and Ga), we examine the stabilities of the spin structures of the independent pi-electron system, which is considered to primarily sustain the magnetic order, where BETS represents bis(ethylenedithio) tetraselenafulvalene. It is found that one of the uudd phases has an energy close to the ground-state energy for lambda-(BETS)(2)FeCl4. We discuss the relevance of the magnetic anion FeCl4 and the quantum fluctuation to the magnetism of these compounds. When J'(3) = 0, the system is reduced to a trellis lattice antiferromagnet. The system exhibits a stripe spiral-spin phase, which comprises one-dimensional spiral-spin states stacked alternately.