

Very recently, even a meron (half-skyrmion) spin structure was identified in MnSc 2S 4 at moderate external magnetic fields. The occurrence of a spiral spin-liquid state in some spinels is an enlightening example. 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 A-site ions are arranged in a diamond lattice. 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 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. 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. 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, spinels are also known as beautiful gemstones, with the famous “Black Prince’s Ruby” in the front centre of the Imperial State Crown. 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. 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. 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. Over the years, more than 200 different spinels, with the general formula AB 2 X 4, were identified or synthesized in polycrystalline or single-crystalline form. 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.
