Competing Orders in Frustrated Magnets and Nanostructures

该奖项支持理论研究，以调查低维强相关电子系统（如受挫量子磁体和制造和自组装纳米结构）中不同有序趋势之间的竞争。这两个领域都处于现代凝聚态物理的前沿。该研究有三个目标：1)发展空间各向异性量子反铁磁体中自旋激发的一致理论描述。这种描述将包括一维链的分数化高能自旋子以及弱有序基态的低能磁振子。特别关注的是由两个自旋为1/2的自旋子组成的复合自旋-1对，通过沿链横向方向的离域降低能量时的运动学结合机制。将包括降低对称性的Dzyaloshinskii-Moriya相互作用、热波动和外磁场的影响。PI还旨在研究多自旋连续体的单重态扇区，该扇区可以通过共振非弹性x射线散射，声子辅助光学吸收和拉曼散射来探测。确定两族空间各向异性三角形反铁磁体的相图。这两个体系在共线自旋涨落、二聚体有序倾向和经典螺旋不稳定性之间表现出强烈的竞争，但在声子所起的作用上有所不同。结合重整化群、链平均场理论、相互作用自旋波和大n Schwinger玻色子技术，分析了该材料对外加磁场的各向异性响应，并计算了场诱导有序相的实验性质。此外，还将对准一维几何中对称性降低的各向异性Dzyaloshinskii-Moriya相互作用进行细致的分析。根据不同的静电约束和/或表面纳米结构，分析低维相互作用电子在显著的结构反转不对称性下自旋轨道诱导的不稳定性。我将研究强相关电子维格纳晶体的极限，其中自旋轨道效应必然占指数弱交换相互作用的主导地位。本项目研究生将接受玻色子化、重整化群、量子场和多体理论等现代理论技术的培训。该项目将为本科生提供夏季研究机会。在犹他大学的定期本科物理研讨会上，将对一般物理水平的研究进行定性讨论。此外，将开发一个网站，以研究生水平描述概述的研究主题及其相互联系，以便将结果传达给更广泛的受众。该奖项支持凝聚态物理前沿的理论研究和教育。这项研究的重点是理解通过对最近发现的材料进行实验所揭示的不寻常的磁性，例如herbertsmithite和volborthite。这些材料具有成为磁铁的必要成分，但不表现出磁性。在原子的尺度上，相互作用之间存在着一种竞争，这种相互作用有利于排列磁性的基本组成部分和原子的几何排列。这阻碍了磁性秩序的趋势。实验继续提供更多的例子，使测试理论观点成为可能，即物质的新状态将从失效的磁性中产生。物质新状态的发现为具有理想性能的新材料和与新材料相关的现象打开了大门，这些现象可能构成未来技术的基础或可能解决现有问题。这项研究将为理解这些材料奠定基础，并为未来的实验奠定基础，这些实验将更好地理解这些受挫磁铁的不寻常特性。参与该项目的研究生将接受凝聚态物理现代理论技术的培训。该项目将为本科生提供夏季研究机会。在犹他大学的定期本科物理研讨会上，将对一般物理水平的研究进行定性讨论。此外，将开发一个网站，以研究生水平描述概述的研究主题及其相互联系，以便将结果传达给更广泛的受众。

TECHNICAL SUMMARYThis award supports theoretical research to investigate competition between different ordering tendencies in low-dimensional strongly correlated electron systems such as frustrated quantum magnets and fabricated and self-assembled nanostructures. Both of these areas are at the forefront of modern condensed matter physics. The research has 3 objectives:1.) Develop a consistent theoretical description of spin excitations in spatially anisotropic quantum antiferromagnets. This description will include both fractionalized high-energy spinons of one-dimensional chains as well as low-energy magnons of the weakly ordered ground state. Particular attention will be paid to a kinematic binding mechanism when a composite spin-1 pair, formed by two spin-1/2 spinons, lowers the energy via delocalization along the direction transverse to the chains. Effects of symmetry-lowering Dzyaloshinskii-Moriya interaction, thermal fluctuations, and external magnetic field will be included. The PI also aims to investigate the singlet sector of multi-spinon continuum which can be probed by resonant inelastic x-ray scattering, phonon-assisted optical absorption, and Raman scattering.2.) Determine the phase diagram of two families of spatially anisotropic triangular antiferromagnets. Both systems exhibit strong competition between collinear spin fluctuations, dimer ordering tendencies and classical spiral instability, but differ in the role that phonons play. Anisotropic response of this material to the applied magnetic field will be analyzed, and experimental properties of the field-induced ordered phases will be calculated by a combination of the renormalization group, chain mean-field theories and interacting spin waves and large-N Schwinger boson techniques. In addition, a careful analysis of symmetry lowering anisotropic Dzyaloshinskii-Moriya interaction in the quasi-one-dimensional geometry will be carried out.3.) Analyze spin-orbit induced instabilities of low-dimensional interacting electrons subject to significant structure inversion asymmetry as appropriate for various electrostatically confined and/or surface nanostructures. I will investigate the limit of strongly correlated electron Wigner crystal where spin-orbit effects are bound to dominate over exponentially weak exchange interaction.Graduate students involved in the project will be trained in modern theoretical techniques such as bosonization, renormalization group, quantum field and many-body theories. The project will involve summer research opportunity for undergraduate students. Qualitative discussion of the research on the general physics level will be given during regular undergraduate physics seminars at the University of Utah. In addition, a web site with a graduate student level description of the outlined research topics and their interconnections will be developed in order to communicate results to a broader audience.NON-TECHNICAL SUMMARYThis award supports theoretical research and education at a frontier of condensed matter physics. The research is focused on understanding unusual magnetic properties revealed by experiments on recently discovered materials, for example herbertsmithite and volborthite.These materials have the necessary ingredients to become magnets, but do not exhibit magnetism. On the scale of atoms, there is a competition between the interactions that would favor aligning the fundamental building blocks of magnetism and the geometrical arrangements of the atoms. This frustrates the tendency to magnetic order. Experiments continue to deliver more examples, enabling the test of theoretical ideas that new states of matter will arise from failed magnetism. The discovery of new states of matter opens the door to new materials with desirable properties and new materials-related phenomena that may form the basis for future technologies or may solve existing problems.The research will lay the foundations for understanding these materials and for future experiments that will better understand the unusual properties of these frustrated magnets. Graduate students involved in the project will be trained in modern theoretical techniques of condensed matter physics. The project will involve summer research opportunity for undergraduate students. Qualitative discussion of the research on the general physics level will be given during regular undergraduate physics seminars at the University of Utah. In addition, a web site with a graduate student level description of the outlined research topics and their interconnections will be developed in order to communicate results to a broader audience.