This review aims to summarize more than 100 years of research on spinel compounds, mainly focusing on the progress in understanding their magnetic, electronic, and polar properties during the last two decades. Over the years, more than 200 different spinels, with the general formula ${\mathit{AB}}_2$ ${\mathit{X}}_4$, were identified or synthesized in polycrystalline or single-crystalline form. Many spinel compounds are magnetic insulators or semiconductors; however, a number of spinel-type metals exists including superconductors and some rare examples of d-derived heavy-fermion compounds. In the early days, they gained importance as ferrimagnetic or even ferromagnetic insulators with relatively high saturation magnetization and high ordering temperatures, with magnetite being the first magnetic mineral known to mankind. From a technological point of view, spinel-type ferrites with the combination of high electrical resistance, large magnetization, and high magnetic ordering temperature made them promising candidates for many applications. However, spinels are also known as beautiful gemstones, with the famous “Black Prince’s Ruby” in the front centre of the Imperial State Crown. In addition, spinels are important for the earth tectonics, and the detection of magnetite in a Martian meteorite even led to the speculation of life on Mars. However, most importantly in the perspective of this review, spinels played an outstanding role in the development of concepts of magnetism, in testing and verifying the fundamentals of magnetic exchange, in understanding orbital-ordering and charge-ordering phenomena including metal-to-insulator transitions, in developing the concepts of magnetic frustration, in establishing the importance of spin–lattice coupling, and in many other aspects. The still mysterious Verwey transition in magnetite was one of the very first illuminating examples of this complexity, which results from the fact that some ions can exist in different valence states in spinels, even at a given sublattice. In addition, the A-site as well as the B-site cations in the spinel structure form lattices prone to strong frustration effects resulting in exotic ground-state properties. The A-site ions are arranged in a diamond lattice. This bipartite lattice shows highly unusual ground states due to bond-order frustration, with a strength depending on the ratio of inter- to intra-sublattice exchange interactions of the two interpenetrating face-centred cubic lattices. The occurrence of a spiral spin-liquid state in some spinels is an enlightening example. Very recently, even a meron (half-skyrmion) spin structure was identified in MnSc ₂S₄ at moderate external magnetic fields. In case the A-site cation is Jahn–Teller active, additional entanglements of spin and orbital degrees of freedom appear, which can give rise to a spin–orbital liquid or an orbital glass state. In systems with such a strong entanglement, the occurrence of a new class of excitations – spin–orbitons – has been reported. The B-site cations form a pyrochlore lattice, one of the strongest contenders of frustration in three dimensions. A highly degenerate ground state with residual zero-point entropy and short-range spin ordering according to the ice rules is one of the fascinating consequences, which is known already for more than 50 years. At low temperatures, in B-site spinels the occurrence of spin molecules has been reported, strongly coupled spin entities, e.g., hexamers, with accompanying exotic excitations. A spin-driven Jahn–Teller effect is a further possibility to release magnetic frustration. This phenomenon has been tested in detail in a variety of spinel compounds. In addition, in spinels with both cation lattices carrying magnetic moments, competing magnetic exchange interactions become important, yielding ground states like the time-honoured triangular Yafet–Kittel structure. Very recently, it was found that under external magnetic fields this triangular structure evolves into very complex spin orders, which can be mapped on spin super-liquid and spin super-solid phases. In addition, due to magnetic frustration, competing interactions, and coupling to the lattice, very robust magnetization plateaus appear in a variety of spinel compounds as function of an external magnetic field. Furthermore, spinels gained considerable importance in elucidating the complex physics driven by the interplay of spin, charge, orbital, and lattice degrees of freedom in materials with partly filled d shells. This entanglement of the internal degrees of freedom supports an exceptionally rich variety of phase transitions and complex ground states, in many cases with emerging functionalities. It also makes these materials extremely susceptible to temperature, pressure, or external magnetic and electric fields, an important prerequisite to realize technological applications. Finally, yet importantly, there exists a long-standing dispute about the possibility of a polar ground state in spinels, despite their reported overall cubic symmetry. Indeed, recently a number of multiferroic spinels were identified, including multiferroic spin super-liquid and spin super-solid phases. The spinels also belong to the rare examples of multiferroics, where vector chirality alone drives long-range ferroelectric order. In addition, a variety of spinel compounds were investigated up to very high pressures up to 40 GPa and in high magnetic fields up to 100 T, revealing complex (p,T) and (H,T)-phase diagrams.

本综述旨在总结 100 多年来对尖晶石化合物的研究，主要集中在过去 20 年间对其磁性、电子和极性特性的理解进展。多年来，超过 200 种不同的尖晶石，具有通用配方${\mathit{AB}}_2$ ${\mathit{X}}_4$, 以多晶或单晶形式被鉴定或合成。许多尖晶石化合物是磁性绝缘体或半导体；然而，存在许多尖晶石型金属，包括超导体和一些罕见的d衍生的重费米子化合物。在早期，它们作为具有相对高饱和磁化强度和高有序温度的亚铁磁甚至铁磁绝缘体而变得重要，磁铁矿是人类已知的第一种磁性矿物。从技术角度来看，尖晶石型铁氧体结合了高电阻、大磁化强度和高磁有序温度，使其成为许多应用的有希望的候选者。然而，尖晶石也被称为美丽的宝石，著名的“黑王子红宝石”位于帝国皇冠的前部中央。此外，尖晶石对地球构造具有重要意义，在火星陨石中发现磁铁矿甚至引发了对火星生命的猜测。然而，最重要的是，从这次审查的角度来看，尖晶石在磁性概念的发展、测试和验证磁交换的基本原理、理解轨道排序和电荷排序现象（包括金属到绝缘体的跃迁）、发展磁挫败的概念、建立自旋-晶格耦合的重要性，以及在许多其他方面。磁铁矿中仍然神秘的 Verwey 跃迁是这种复杂性的第一个有启发性的例子，这是由于一些离子可以在尖晶石中以不同价态存在，即使在给定的亚晶格中。除此之外 在理解轨道排序和电荷排序现象，包括金属到绝缘体的跃迁，发展磁挫败的概念，建立自旋-晶格耦合的重要性，以及许多其他方面。磁铁矿中仍然神秘的 Verwey 跃迁是这种复杂性的第一个有启发性的例子，这是由于一些离子可以在尖晶石中以不同价态存在，即使在给定的亚晶格中。除此之外 在理解轨道排序和电荷排序现象，包括金属到绝缘体的跃迁，发展磁挫败的概念，建立自旋-晶格耦合的重要性，以及许多其他方面。磁铁矿中仍然神秘的 Verwey 跃迁是这种复杂性的第一个有启发性的例子，这是由于一些离子可以在尖晶石中以不同价态存在，即使在给定的亚晶格中。除此之外 这是因为一些离子可以在尖晶石中以不同的价态存在，即使在给定的亚晶格中也是如此。除此之外 这是因为一些离子可以在尖晶石中以不同的价态存在，即使在给定的亚晶格中也是如此。除此之外尖晶石结构中的A位和B位阳离子形成晶格，容易产生强烈的挫败效应，导致奇特的基态特性。的甲-site离子被布置在金刚石晶格。由于键序受挫，这种二分晶格显示出非常不寻常的基态，其强度取决于两个互穿的面心立方晶格的亚晶格间和亚晶格内交换相互作用的比率。在一些尖晶石中出现螺旋自旋液体状态是一个有启发性的例子。最近，在中等外部磁场下，甚至在 MnSc ₂ S ₄中发现了 meron（半斯格明子）自旋结构。如果A位阳离子是 Jahn-Teller 活性的，出现额外的自旋和轨道自由度纠缠，这会产生自旋轨道液体或轨道玻璃态。在具有如此强纠缠的系统中，已经报道了一类新的激发——自旋轨道子——的发生。所述乙-site阳离子形成烧绿石晶格，沮丧的在三维空间中的最强竞争者之一。根据冰规则，具有残余零点熵和短程自旋排序的高度简并基态是令人着迷的结果之一，这已经为人们所知 50 多年了。在低温下，在B位点尖晶石 已经报道了自旋分子的出现，强耦合的自旋实体，例如六聚体，伴随着奇异的激发。自旋驱动的 Jahn-Teller 效应是释放磁性挫折的另一种可能性。这种现象已在各种尖晶石化合物中进行了详细测试。此外，在两个带有磁矩的阳离子晶格的尖晶石中，相互竞争的磁交换相互作用变得重要，产生基态，如历史悠久的三角形 Yafet-Kittel 结构。最近，人们发现在外部磁场下，这种三角形结构演变成非常复杂的自旋顺序，可以映射到自旋超液相和自旋超固相。此外，由于磁挫败、竞争相互作用以及与晶格的耦合，非常强大的磁化平台出现在各种尖晶石化合物中，作为外部磁场的函数。此外，尖晶石在阐明由自旋、电荷、轨道和晶格自由度相互作用驱动的复杂物理方面具有相当重要的意义。d贝壳。这种内部自由度的纠缠支持异常丰富的相变和复杂的基态，在许多情况下具有新兴功能。它还使这些材料极易受到温度、压力或外部磁场和电场的影响，这是实现技术应用的重要前提。最后，但重要的是，尽管据报道尖晶石具有整体立方对称性，但关于尖晶石中极性基态的可能性存在长期争议。事实上，最近发现了许多多铁性尖晶石，包括多铁性自旋超液相和自旋超固相。尖晶石也属于多铁性的罕见例子，其中矢量手性单独驱动远程铁电有序。此外，p , T ) 和 ( H , T ) 相图。