Exotic order in frustrated magnets

研究的重点主要放在烧绿石磁体上，这是一个典型的几何受挫系统。在以下三个方面取得了进展：1)三角晶格Heisenberg反铁磁体中的涡旋有序，2)具有铁磁第二近邻相互作用的Heisenberg焦绿石反铁磁的有序化，以及3)具有长程RKKY相互作用的Ising焦绿石磁体的有序化。对于主题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关联长度和关联时间，揭示了模型的拓扑有序态是伴随着大而慢的自旋涨落的一种特殊的“自旋-凝胶”态。关于主题2)，通过广泛的蒙特卡罗模拟，建立了该模型到特殊有序状态的一级转变，在该状态下，尖锐的布拉格峰表征…在自旋结构因子中出现了更多受无公度波矢影响的自旋，但自旋仍在很大程度上波动。关于主题3)，由于最近人们对“自旋-冰”磁体的有序感兴趣，我们研究了具有长程RKKY相互作用的&lt；111&gt；Ising磁体的有序性，它旨在模拟金属“自旋-冰”磁体，如Pr_2Ir_2O_7。我们使用Ewald和技术进行了广泛的蒙特卡罗模拟，充分考虑了相互作用的长程性质。根据表示费米波矢的参数kF，该模型表现出丰富的有序化行为。特别是，我们发现与实验体系相对应的RKKY模型在反铁磁居里-魏斯常数下具有低温下的“2-in-2-out”局域自旋结构，与实验一致。相比之下，该模型总是表现出向磁性长程有序状态的热力学相变，这种自旋-液体行为从未实现。较少

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