多スピン交換相互作用を含む系の理論的研究

本文从理论上研究了具有多重交换相互作用的自旋系统以及相关的无多重交换自旋系统，得到了如下结果：1）利用分子场近似方法，确定了外磁场作用下三角晶格上具有2-、3-和4-自旋交换的自旋系统的基态相图.结果表明，相图是相当复杂的。当反铁磁相互作用较强时，出现6-亚晶格和12-亚晶格结构，其标量和矢量手征序接近120度结构。在铁磁相附近还存在144和72亚晶格的大尺度空间结构。这些大结构的稳定性还有待进一步的研究。2）利用分子场理论研究了5-和6-自旋交换对三角晶格上系统的影响。结果表明，5-自旋交换对铁磁相的稳定有很强的作用，而6-自旋交换对基态的影响不大。3）证明了在4-自旋交换的梯形晶格上，自旋序与手征序之间存在严格的对偶关系。从而严格证明了某些梯形自旋系统具有标量手征的基态。4）我们从理论上研究了一个由四面体团簇组成的一维自旋系统，并证明了它将表现出一个特殊的磁化过程和磁化平台。5）我们研究了自旋晶格相互作用对二维阻挫自旋系统SrCu_2（BO_3）_2中磁平台的影响。我们提出了一个自旋-晶格模型来描述实验观察到的磁平台。

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.