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

A recent study [Tassel et al., Phys. Rev. Lett. 105, 167205 (2010)] has proposed a remarkable spin model for (CuCl)LaNb2O7, 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 vertical bar J(x)vertical bar,vertical bar J(y)vertical bar less than or similar to 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 vertical bar J(x)vertical bar or vertical bar J(y)vertical bar greater than or similar to 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.