On the complexity of spinels: Magnetic, electronic, and polar ground states

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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 AB2X4, 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.