Effective Hamiltonian and phase diagram of the square lattice of antiferromagnetic spin-12triangles inLa4Cu3MoO12

Abstract

The effective Hamiltonian for the square lattice of antiferromagnetic spin-1/2 triangles in La4Cu3MoO12 is obtained with the help of a bond operator representation for three S=1/2 spins. In the weak intertriangle Coupling limit (J'much less thanJ(1), J(2), J(3), with J' the intertriangle interaction and J(1), J(2), and J(3) the intratriangle interactions), the magnetism of the effective Hamiltonian is studied with second-order perturbation theory and the site-dependent mean-field approach. Various long-range-ordered phases are shown to compete and the spin configurations corresponding to the phases with wave vectors of (0,pi) or (pi,0) are given. Up to second order, a spiral state is obtained along the lines of J(1)=J(3)<J(2) and J(2)=J(3)<J(1). At the symmetric Point of J(1)=J(2)=J(3), the system shows a long-range-ordered state with a wave vector of (pi,pi) in spin freedom and a wave of (0,pi) in chirality freedom.