Frustration through anisotropy in quantum magnets

这项研究计划旨在提高我们对磁性材料的理论理解。这些材料，以及更广泛的凝聚态物理学，为量子和经典多体现象领域提供了一个无与伦比的窗口。通过对这些系统的研究，人们有望了解甚至潜伏在日常材料中的涌现和集体行为的丰富挂毯。 特别是，我们的目标是提高对高度各向异性和高度挫败的磁铁的理解。各向异性，指的是材料的物理学取决于原子的微观磁矩相对于晶格的取向-相对论效应，自旋轨道耦合的结果。挫折，指的是多种趋势的不相容性;当它不可能满足所有的磁矩之间的相互作用在同一时间。结合这两者，通过各向异性的挫折是当挫折的起源是由于磁相互作用中的各向异性，而不是通过晶体中原子的几何排列。通过各向异性，挫折可以以各种各样的方式产生，每一种方式都有可能导致新的和有趣的物质相。 本提案从两个不同但相关的方向对这一主题进行了探讨。首先，我们解决的微观起源的磁相互作用中的一个最大的和最多样化的类的各向异性磁体，那些磁性离子是一种稀土元素。我们将从理论上研究在与真实的材料相关的各种不同晶格和结构中可能存在的磁相互作用，目的是识别新的和未探索的挫折类型。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所呈现的状态，就像在许多实验研究中用光或中子探测它们时所发生的那样。这一努力将通过使用一种级数展开技术的定量计算视角，以及通过更多的分析，涉及表现出粒子的固有损失或增益的系统理论的数学路线来进行。这项研究对于理论和实验凝聚态物理界都很重要，因为它将为理解已知的受挫折的各向异性材料提供新的方法，并激励新材料的探索。这些新材料，以及对它们的物理学的理解，应该能为经典和量子多体物理学的基本问题提供见解，也许还能激发新的技术应用。

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.