多スピン交換相互作用を含む系の理論的研究

我们从理论上研究了具有多重交换作用的自旋体系和不具有多重交换作用的自旋体系，得到了以下结果：1)利用分子场近似确定了外加磁场作用下具有2、3、4自旋交换的三角晶格体系的基态相图。结果表明相图是相当复杂的。当反铁磁相互作用较强时，存在6亚晶格结构和12亚晶格结构，其标量和矢量手性有序度接近120度结构。还有144和72亚晶格接近铁磁相的大尺度空间结构。需要更多的研究来证实这些大型结构的稳定性。2)利用分子场理论研究了三角晶格上5-和6-自旋交换对体系的影响。结果表明，5-自旋交换对稳定铁磁相有较强的作用，而6-自旋交换对基态影响不大。3)证明了具有4-自旋交换的阶梯晶格自旋系统的自旋序与手性序之间存在严格的对偶关系。结果证明了一些阶梯自旋系统具有具有标量手性的基态。将这种对偶关系推广到阶梯上的相关电子系统。4)我们从理论上研究了由四面体团簇组成的一维自旋系统，并证明了它会表现出具有磁化平台的特殊磁化过程。5)研究了二维受挫自旋体系SrCu_2(BO_3)_2中自旋晶格相互作用对磁平台的影响。我们提出了一个可以描述实验观测到的磁平台的自旋晶格模型。

We have investigated the spin systems with multiple exchange interactions as well as related spin systems without multiple exchanges theoretically, and obtained following results.1)The ground state phase diagram of the system on the triangular lattice with 2-, 3- and 4-spin exchanges were determined under external magnetic field by means of the molecular field approximations. As the result it turned out that the phase diagram is quite complex. There appear 6-sublattice as well as 12-sublattice structures with scalar and vector chiral order close to the 120 degree structure when the antiferromagnetic interactions are strong. There are also large scale spatial structures with 144 and 72 sublattices close to ferromagnetic phase. More studies are necessary to confirm the stability of these large structures.2)Effects of the 5- and 6-spin exchanges on the system on the triangular lattice were studied by means of the molecular field theory. It turned out that the 5-spin exchanges have strong effect in stabilizing the ferromagnetic phase while 6-spin exchanges do not affect the ground state too much.3)We proved that there exists a rigorous duality relation between spin orders and chirality orders in spin systems on the ladder lattice with 4-spin exchanges. As a result we could rigorously proved that some ladder spin systems have ground states with scalar chirality. This duality relation was extended to the systems of correlated electrons on the ladder.4)We have investigated a 1D spin system which cnsists of tetrahedral clusters theoretically and have shown that it will show a peculiar magnetization process with magnetization plateaus.5)We investigated the effect of spin lattice interactions on magnetic plateaus in a 2D frustrated spin system SrCu_2(BO_3)_2. We proposed a spin-lattice model which can describe the magnetic plateaus experimentally observed.