Frustration through anisotropy in quantum magnets

这一研究建议旨在提高我们对磁性材料的理论理解。这种材料，以及更广泛的凝聚态物理，为进入量子和经典多体现象领域提供了一个无与伦比的窗口。通过对这类系统的研究，人们可以希望理解隐藏在日常材料中的突发和集体行为的丰富织锦。特别是，我们的目标是提高我们对高度各向异性和高度受挫的磁体的理解。各向异性，指的是材料的物理性质取决于原子的微观磁矩相对于晶格的取向方式--这是相对论效应，即自旋-轨道耦合的结果。挫折，是指多种倾向的不相容；当不可能同时满足磁矩之间的所有相互作用时。结合这两者，各向异性受挫是指受挫的起源是由于磁相互作用的各向异性，而不是例如晶体中原子的几何排列。通过各向异性，挫折可以以丰富多样的方式产生，每一种方式都有可能导致新的和有趣的物质相。这项提议从两个不同但相关的方向来攻击这个话题。首先，我们讨论最大和最多样的各向异性磁体之一的磁相互作用的微观起源，这些磁体中的磁性离子是稀土元素。我们将从理论上研究与真实材料相关的各种不同的晶格和结构中可能存在的各种磁相互作用，目的是识别新的和未被探索的种类的挫折。其次，我们将开发新的方法来理解各向异性磁体的激发，即当它们吸收能量时，它们所呈现的状态，就像在许多实验研究中，当它们被光或中子探测时发生的那样。这项工作将通过使用一种级数展开技术的定量、计算角度来进行，以及通过一种更具分析性的、数学路线来进行，该路线涉及到显示粒子内在损失或获得的系统理论。这项研究将对理论和实验凝聚态物理学界具有重要意义，因为它将为理解已知受挫的各向异性材料提供新的途径，并激励新材料的探索。这些新材料，以及对它们物理的理解，应该会为经典和量子多体物理的基本问题提供见解，或许还会启发新的技术应用。

This research proposal aims to improve our theoretical understanding of magnetic materials. Such materials, and condensed matter physics more broadly, offer an unparalleled window into the realm of quantum and classical many-body phenomena. Through the study of such systems one can hope to understand the rich tapestry of emergent and collective behaviour that can lurk inside even everyday materials. In particular, we aim to improve our understanding of magnets that are both highly anisotropic and highly frustrated. Anisotropy, refers to the physics of the material being dependent on how the microscopic magnetic moments of the atoms are oriented relative to the crystal lattice -- a consequence of a relativistic effect, spin-orbit coupling. Frustration, refers to the incompatibility of multiple tendencies; when it is not possible to satisfy all of the interactions between the magnetic moments at the same time. Combining these two, frustration through anisotropy is when the origin of the frustration is due to the anisotropy in the magnetic interactions, and not, say, through the geometric arrangement of the atoms in the crystal. Through anisotropy, frustration can be generated in a rich variety of ways, each of which has the potential to lead to new and interesting phases of matter. This proposal attacks this topic from two different, but related, directions. First, we address the microscopic origins of magnetic interactions in one of the largest and most varied classes of anisotropic magnets, those where the magnetic ion is a rare-earth element. We will theoretically investigate what kinds of magnetic interactions are possible in a variety of different crystal lattices and structures that are relevant for real materials, with the goal of identifying new and unexplored kinds of frustration. Second, we will develop new methods for understanding the excitations of anisotropic magnets, i.e. the kinds of states they take on when they absorb energy, as happens when they are probed by light or neutrons in many experimental studies. This effort will be pursued though both a quantitative, computational perspective using a kind of series expansion technique, as well as via a more analytical, mathematical route involving the theory of systems that exhibit intrinsic loss or gain of particles. This research will be important for the theoretical and experimental condensed matter physics community, as it will provide new ways to understand known frustrated anisotropic materials, as well as motivate new materials to explore. These new materials, and an understanding of their physics, should provide insights into fundamental questions of classical and quantum many-body physics, and perhaps inspire new technological applications.