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 intratriangle exchange coupling constants and one weak intertriangle exchange coupling constant is proposed to model the interacting Cu²⁺ ions of the Cu₃MoO₄ planes in La₄Cu₃MoO₁₂. Depending on the ratio of the intratriangle 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 La₄Cu₃MoO₁₂ suggests that the spins in this material order antiferromagnetically along the x direction and ferromagnetically along the y direction of the Cu₃MoO₄ 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.