Exotic order in frustrated magnets

研究的重点是火绿石磁体，这是一种典型的几何挫折系统。在三角晶格Heisenberg反铁磁体的涡旋有序、Heisenberg焦绿石反铁磁体与第二近邻铁磁相互作用的有序以及Ising焦绿石磁体与远程RKKY相互作用的有序三个方面取得了进展。关于课题1)，通过广泛的蒙特卡罗模拟，我们估计了经典三角晶格海森堡反铁磁体的相关长度和相关时间，揭示了该模型的拓扑有序态是一种特殊的“自旋-凝胶”态，伴随着大而慢的自旋涨落。关于主题2)，通过广泛的蒙特卡罗模拟，建立了该模型呈现一阶跃迁到特殊的有序状态，其中自旋结构因子中出现了一个明显的Bragg峰特征，更多的是由于不相称的波矢量，但自旋仍然存在很大的波动。关于主题3)，由于最近对“自旋-冰”磁体的排序感兴趣，我们研究了<111>的Ising磁体与远程RKKY相互作用的排序，旨在模拟金属“自旋-冰”磁体，如Pr_2Ir_2O_7。我们通过使用埃瓦尔德和技术进行了广泛的蒙特卡罗模拟，以充分考虑相互作用的长程性质。取决于参数k_F。作为费米波矢量的代表，该模型显示出丰富的有序行为。特别是，我们发现实验系统对应的RKKY模型在反铁磁居里-魏斯常数下，低温下呈现“2进2出”的局部自旋结构，与实验结果一致。相比之下，该模型总是表现出向磁性长程有序态的热力学相变，而从未实现自旋液体样行为。少

Main emphasis of the research has been put on the pyrochlore magnet, a typical system showing geometrical frustration. Progress has been achieved on the following three topics, 1) vortex order in the triangular-lattice Heisenberg antiferromagnet, 2) the ordering of the Heisenberg pyrochlore antiferromagnet with the ferromagnetic second-neighbor interaction, and 3) the ordering of the Ising pyrochlore magnet with the long-range RKKY interaction. Concerning the subject 1), by means of extensive Monte Carlo simulation, we estimate the correlation length and the correlation time of the classical triangular-lattice Heisenberg antiferromagnet, revealing that the topological ordered state of the model is a peculiar "spin-gel" state which accompanies large and slow spin fluctuations. Concerning the subject 2), by means of extensive Monte Carlo simulations, it was established that the model exhibited a first-order transition into the peculiar ordered state in which a sharp Bragg peak characteri … More zed by an incommensurate wavevector appeared in the spin structure factor, yet the spin remained largely fluctuating. Concerning the subject 3), motivated by the recent interest in the ordering of "spin-ice" magnets, we have studied the ordering of the <111> Ising magnet with the long-range RKKY interaction, which is intended to model metallic "spin-ice" magnets such as Pr_2Ir_2O_7. We performed extensive Monte Carlo simulation by using the Ewald sum technique to fully take account of the long-range nature of the interaction. Depending on the parameter k_F. representing the Fermi wavevector, the model has turned out to exhibit rich ordering behaviors. In particular, we have found that the RKKY model corresponding to the experimental system takes "2-in 2-out" local spin structure at low temperatures under the antiferromagnetic Curie-Weiss constant, consistently with the experiment. By contrast, the model always exhibits a thermodynamic phase transition into the magnetic long-range ordered state, a spin-liquid-like behavior being never realized. Less