The history of crystal growth

Quantum magnetism in minerals

“…Another example of a classical antiferromagnet that was investigated by neutron scattering is hauerite (MnS 2 , pyrite structure), which has a habit of forming large cm-sized octahedral single crystals of high natural quality. It adopts a commensurate collinear AFM structure with a k = 1 1 2 0 wave vector below T N = 48 K [28]. Above this temperature, diffuse critical scattering of magnetic origin was revealed by INS at an incommensurate wave vector (1 0.44 0), with a temperature dependence characteristic of a lock-in transition of a three-dimensionally (3D) ordered system [29,30].…”

“…Many developments in solid-state physics and crystallography were historically inspired by observations on naturally occurring minerals. Various phenomena in condensed-matter physics were first discovered in natural samples, which had unsurpassed quality as compared to synthetic materials before the advent of modern chemical and crystal-growth technology [1,2]. Among the most eminent examples are the first observations of ferromagnetism in lodestone dating back to the Greek philosopher and engineer Thales of Miletus in the 6 th century BC [3].…”

“…Here I will focus mainly on "quantum" magnets that exhibit emergent phenomena that cannot be captured by the classical models. In a rather vague definition, this includes spin- 1 2 systems and higher-spin lattices with strongly pronounced magnetic frustration that tends to suppress conventional long-range magnetic order and promote more exotic magnetic states at low temperatures. At the start of the new millennium, we saw a surge of interest in low-temperature quantum magnetism, magnetic frustration, and exotic magnetic phases such as spin liquids [57][58][59][60][61][62][63].…”

“…This stimulated an intensive search for new materials realizing complex crystal structures with specific geometries of magnetic lattices. It was noticed that intricately connected spin- 1 2 magnetic sublattices are found in many copper-bearing minerals that are difficult or impossible to reproduce artificially in the form of large single crystals. Among such structures are those that realize various spin-dimer and spin-chain models, two-and three-dimensional geometrically frustrated lattices, as well as quasi-isolated frustrated magnetic clusters that are natural archetypes of quantum molecular magnets.…”

“…3 (a)]. The intradimer exchange interaction between the spin- 1 2 Cu 2+ ions is AFM with J 1 ≡ J ≈ 190 K, while the interdimer exchange within the chains is about twice weaker, J 2 ≡ J ≈ 90 K, as estimated from susceptibility data that could be well fitted by the alternating Heisenberg chain model [88][89][90]. While reporting correct values for the leading exchange interactions, the first work by Janod et al misplaced the spin dimers in the lattice, assuming that the strongest J 1 coupling [78].…”