Ferromagnetically coupled dimers on the distorted Shastry-Sutherland lattice: Application to (CuCl)LaNb₂O₇

A recent study has proposed a remarkable spin model for (CuCl)LaNb ₂O₇, in which dimers are ferromagnetically coupled to each other on the distorted Shastry-Sutherland lattice. In this model, the intradimer exchange coupling J>0 is antiferromagnetic, while the interdimer exchange couplings are ferromagnetic and take different values, J _x,J_y<0, in the two bond directions. Anticipating that the highly frustrated character of this model may lead to a wide range of behaviors in (CuCl)LaNb₂O₇ and related compounds, we theoretically investigate the ground-state phase diagram of this model in detail using the following three approaches: a strong-coupling expansion for small J_x and J_y, exact diagonalization for finite clusters, and a Schwinger boson mean-field theory. When |J_x|,|J_y| J, the system stays in a dimer singlet phase with a finite spin gap. This state is adiabatically connected to the decoupled-dimer limit J_x=J _y=0. We show that the magnetization process of this phase depends crucially on the spatial anisotropy of the interdimer couplings. The magnetization shows a jump or a smooth increase for weak and strong anisotropy, respectively, after the spin gap closes at a certain magnetic field. When |J_x| or |J_y| J, quantum phase transitions to various magnetically ordered phases (ferromagnetic, collinear stripe, and spiral) occur. The Schwinger boson analysis demonstrates that quantum fluctuations split the classical degeneracy of different spiral ground states. Implications for (CuCl)LaNb₂O₇ and related compounds are discussed in light of our theoretical results and existing experimental data.