畸变Shastry-Sutherland晶格上的铁磁耦合二聚体：对（CuCl）LaNb2O7的应用
Ferromagnetically coupled dimers on the distorted Shastry-Sutherland lattice: Application to (CuCl)LaNb2O7
摘要：
最近的一项研究[Tassel { \it et al.}，物理修订信函{ \bf 105}，167205（2010）]提出了（CuCl）LaNb 2 O 7的显著自旋模型，其中二聚体在扭曲的Shastry-Sutherland晶格上彼此铁磁耦合。在该模型中，二聚体内的交换耦合J>0是反铁磁的，而二聚体间的交换耦合是铁磁的，并且在两个键方向上取不同的值，J_x，J_y<0。考虑到该模型的高阻挫特性可能导致（CuCl）LaNb_2 O_7及其相关化合物的广泛行为，我们采用以下三种方法：小J_x和J_y的强耦合展开、有限团簇的精确对角化和Schwinger玻色子平均场理论，对该模型的基态相图进行了详细的理论研究.当|J_x|，|J_y| <~ J时，体系处于具有有限自旋能隙的二聚体单重态相.这种状态与双链二聚体极限J_x=J_y=0有着密切的联系。我们发现，这一阶段的磁化过程取决于至关重要的二聚体间耦合的空间各向异性。当自旋能隙在一定的磁场下闭合后，磁化强度分别在弱各向异性和强各向异性下出现跳跃或平滑增加。当|J_x|或|J_y| >~ J时，发生到各种磁有序相（铁磁、共线条纹和螺旋）的量子相变。Schwinger玻色子分析表明，量子涨落分裂不同的螺旋基态的经典简并。根据我们的理论结果和现有的实验数据，（CuCl）LaNb 2 O 7和相关化合物的影响进行了讨论。
英文摘要：
A recent study [Tassel {\it et al.}, Phys. Rev. Lett. {\bf 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 intra-dimer exchange coupling J>0 is antiferromagnetic, while the inter-dimer 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 inter-dimer 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.
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