Phase Diagram and Thermodynamic Properties of the Square Lattice of Antiferromagnetic Spin-1/2 Triangles in La₄Cu₃MoO₁2

The magnetic phase diagram and the thermodynamic properties of a square lattice containing antiferromagnetically coupled spin-1/2 triangles are studied. A Heisenberg Hamiltonian with three strong intra-triangle exchange coupling constants and one weak inter-triangle exchange coupling constant is proposed to model the interacting Cu^2+ ions of the Cu_3MoO_4 planes in La_4Cu_3MoO_12. Depending on the ratio of the intra-triangle coupling constants, various long-ranged magnetic phases are shown to compete at low temperatures. A comparison of numerical calculations of thermodynamic properties in the model Hamiltonian with recent experiments on La_4Cu_3MoO_12 suggests that the spins in this material order antiferromagnetically along the x-direction and ferromagnetically along the y-direction of the Cu_3MoO_4 planes. The temperature dependence of the uniform magnetic susceptibility, the heat capacity, and the entropy are calculated and are shown to be in qualitative agreement with the experiments on this compound.