Emergence and out-of-equilibrium phenomena in frustrated magnets on pyrochlore lattices

涌现-一个大的相互作用粒子集合产生超越微观成分的性质和行为的能力-远离平衡现象是现代物理学的一些重大挑战。磁系统中的挫折一直是新的涌现和平衡现象的肥沃土壤。“挫折”一词表示系统无法达到所有相互作用项同时最小化的最低能量状态。典型的例子是三角形伊辛反铁磁体。在磁学中，阻挫阻止铁磁或反铁磁有序相在低温下的形成。这使得出现新的阶段，往往逃脱了传统的描述，在当地的顺序参数。挫折也是典型的非平衡系统，如自旋玻璃的核心。在阻挫磁性中出现的各种新现象，加上为磁性系统开发的许多实验探测器，继续产生新的和令人兴奋的物理学，无论是关于热力学还是远离平衡的行为。例子包括具有涌现规范对称性的广泛简并基态（例如，具有二聚体和顶点约束的系统），以及拓扑顺序（例如，旋转液体）。一种晶格结构被证明是特别有利于挫折和新的涌现现象，是从平铺一个体积与角共享四面体，被称为烧绿石晶格。自旋冰材料就是一个值得注意的例子，由于磁共振激发的理论提出和实验发现，自旋冰材料最近受到了广泛的关注。这是一个罕见的三维分形实验实例，也是我们可以访问和操纵自由磁荷的第一个背景。这些紧急激发的存在已被证明对这些系统的热力学性质有直接影响（观察到前所未有的现象，如局部磁系统中的液-气转变），以及对它们的响应，弛豫和远离平衡的行为。2012年，这一研究成果得到了欧洲科学基金会凝聚态物质部的国际认可，欧洲物理学奖授予S.布拉姆韦尔、C.Castelnovo、S.Grigera、R.Moessner、S.Sondhi和A.Tennant，以表彰他们对自旋冰中磁单极子的预测和实验观察。该提案的总体目标是研究涌现现象，特别是自旋冰中磁单极子的物理学。一个中心焦点是非平衡动力学和平衡的主题。最近对这些材料的实验突出了它们在平衡状态下的行为的有趣争议，许多结果有待理论理解。该提案的设置是由烧绿石晶格上的受挫磁性系统提供的，该系统允许与目前在广泛材料上进行的众多实验研究进行密切互动，使我们不仅能够在解释结果方面提供理论支持，而且还能够塑造未来的实验议程。该提案的具体目标包括：对处于和处于平衡状态的自旋冰材料形成一致的理解（例如，研究与交流磁化率，磁化强度和$\mu$SR测量相关的自旋和自旋动力学，并开发检测和操纵自旋激发的新方法;研究自旋冰和相关化合物中杂质和化学取代的作用;建模和理解具有较少各向异性自旋的系统中的量子效应;研究阻挫磁系统中传导电子对烧绿石晶格的影响。

Emergence -- the ability of a large ensemble of interacting particles to give rise to properties and behaviours that transcend those of the microscopic constituents -- and far from equilibrium phenomena are some of the grand challenges of modern day physics. Frustration in magnetic systems has been fertile ground for novel emergent and out of equilibrium phenomena. The term ``frustration'' indicates the inability of a system to reach its lowest energy state where all interaction terms are simultaneously minimised. The quintessential example is the triangular Ising antiferromagnet. In magnetism, frustration prevents the formation of ferro- or antiferromagnetically ordered phases at low temperature. This allows the emergence of new phases that often escape a conventional description in terms of local order parameters. Frustration is also at the core of paradigmatic non-equilibrium systems such as spin glasses. The variety of new phenomena that emerge in frustrated magnetism, combined with the many experimental probes that have been developed for magnetic systems, continue to produce new and exciting physics both concerning thermodynamic as well as far from equilibrium behaviours. Examples include extensively degenerate ground states with emergent gauge symmetries (e.g., systems with dimer and vertex constraints), and topological order (e.g., spin liquids). A lattice structure that has been demonstrated to be particularly conducive to frustration and novel emergent phenomena is the one that is obtained from tiling a volume with corner-sharing tetrahedra, dubbed the pyrochlore lattice. A notable example are spin ice materials, which received much attention of late thanks to the theoretical proposal and experimental discovery of magnetic monopole excitations. This is a rare experimental instance of fractionalisation in three dimensions and the first context where we can access and manipulate free magnetic charges. The existence of these emergent excitations has been demonstrated to have a direct effect on the thermodynamic properties of these systems (with the observation of unprecedented phenomena such as a liquid-gas transition in a localised magnetic system) as well as on their response, relaxation, and far from equilibrium behaviour. In 2012, this research effort was recognised internationally by the Condensed Matter Division of the Europen Science Foundation with the award of the Europhysics Prize ``\emph{to S.Bramwell, C.Castelnovo, S.Grigera, R.Moessner, S.Sondhi and A.Tennant for the prediction and experimental observation of magnetic monopoles in spin ice}''. The overall aim of the proposal is to investigate emergent phenomena, in particular the physics of magnetic monopoles in spin ice. A central focus is the theme of non-equilibrium dynamics and equilibration. Recent experiments on these materials highlighted interesting controversies in their behaviour out of equilibrium and many of the results await theoretical understanding. The setting of the proposal is provided by frustrated magnetic systems on pyrochlore lattices, which allow a close interaction with numerous experimental studies currently undertaken on a broad range of materials, enabling us not only to provide theoretical support in interpreting results but also to shape the future experimental agenda. Specific objectives of the proposal include: developing a consistent understanding of spin ice materials in and out of equilibrium (e.g., to study spin and monopole dynamics in relation to AC susceptibility, magnetisation, and $\mu$SR measurements, and to develop new ways to detect and manipulate the monopole excitations); studying the role of impurities and chemical substitutions in spin ice and related compounds; modelling and understanding quantum effects in systems with less anisotropic spins; investigating the effects of conduction electrons in frustrated magnetic systems on the pyrochlore lattice.