Diverse Magnetic Chains in Inorganic Compounds

In both inorganic and metal–organic compounds, transition metals surrounded by ligands form regular or distorted polyhedra, which can be either isolated or interconnected. Distortion of the polyhedron can be caused by the degeneracy in the population of atomic or molecular orbitals, which can be removed by the cooperative Jahn–Teller effect. This effect is often accompanied by the formation of low-dimensional magnetic structures, of which we will consider only chain, or quasi-one-dimensional, magnetic compounds variety. Magnetic chains are formed when transition metal polyhedra bond through a vertex, edge, or face. Moreover, the magnetic entities can be coupled through various nonmagnetic units like NO₃, SiO₄, PnO₃ or PnO₄, ChO₃ or ChO₄, where Pn is the pnictide and Ch is the chalcogen. In most cases, the local environment of the transition metal is represented by oxygen and/or halogens. The prevailing number of chain systems is based on 3d transition metals, albeit 4d and 5d systems attract more and more attention. Mixed 3d–4f single chain magnets became popular objects in metal–organic chemistry.

Exchange interactions in quasi-one-dimensional systems can differ in sign, but no long-range magnetic order, either ferromagnetic or antiferromagnetic, can be achieved at finite temperatures due to fundamental limitations formulated in the early stages of the development of quantum mechanics. These limitations are summarized in a Mermin–Wagner theorem, which states that no continuous symmetries can be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions d ≤ 2. This means that long-range fluctuations can be created at little energy cost, and they are favored since they increase the entropy. The theorem does not apply to discrete symmetries that can be seen in the two-dimensional Ising model, in which the long-range order occurs at temperatures comparable to the exchange interaction energy. The long-range magnetic order being not the intrinsic property of the chains can appear only due to the interchain interactions if not precluded by the spin gap. The very concept of spin gap plays a key role in the field of low-dimensional magnetism. All research objects in this area can be subdivided into gapped and gapless ones. The amazing variety of manifestations of quasi-one-dimensional magnetism is due to the fact that the chains themselves can differ in a number of parameters. They can be homogeneous or alternating in terms of intrachain exchange interaction. The next-nearest-neighbor exchanges in the chains may compete with the nearest-neighbor exchanges. The chains can be organized by transition metal ions with integer or half-integer spins, and they can be constituted by different spins of the same element or by spins of different magnetic species. The chains can be cut to form the magnetic clusters, e.g., dimers or trimers, and they may pair up to form the spin ladders or group up to form the spin tubes.

Understanding the behavior of low-dimensional magnetic systems is of fundamental importance in terms of the formation of quantum ground states of matter. Many new chain magnetic materials have appeared recently due to improvements in synthetic procedures. Each such compound highlights new facets of low-dimensional magnetism, going in some cases beyond the limits of magnetism toward superconductivity, ferroelectricity, and multiferroic phenomena.