Explore the vast range of titles available.

In this review on spin exchanges, written to provide guidelines useful for finding the spin lattice relevant for any given magnetic solid, we discuss how the values of spin exchanges in transition metal magnetic compounds are quantitatively determined from electronic structure calculations, which electronic factors control whether a spin exchange is antiferromagnetic or ferromagnetic, and how these factors are related to the geometrical parameters of the spin exchange path. In an extended solid containing transition metal magnetic ions, each metal ion M is surrounded with main-group ligands L to form an MLn polyhedron (typically, n = 3–6), and the unpaired spins of M are represented by the singly-occupied d-states (i.e., the magnetic orbitals) of MLn. Each magnetic orbital has the metal d-orbital combined out-of-phase with the ligand p-orbitals; therefore, the spin exchanges between adjacent metal ions M lead not only to the M–L–M-type exchanges, but also to the M–L…L–M-type exchanges in which the two metal ions do not share a common ligand. The latter can be further modified by d0 cations A such as V5+ and W6+ to bridge the L…L contact generating M–L…A…L–M-type exchanges. We describe several qualitative rules for predicting whether the M–L…L–M and M–L…A…L–M-type exchanges are antiferromagnetic or ferromagnetic by analyzing how the ligand p-orbitals in their magnetic orbitals (the ligand p-orbital tails, for short) are arranged in the exchange paths. Finally, we illustrate how these rules work by analyzing the crystal structures and magnetic properties of four cuprates of current interest: α-CuV2O6, LiCuVO4, (CuCl)LaNb2O7, and Cu3(CO3)2(OH)2.

To search for a conceptual picture describing the magnetization plateau phenomenon, we surveyed the crystal structures and the spin lattices of those magnets exhibiting plateaus in their magnetization vs. magnetic field curves by probing the three questions: (a) why only certain magnets exhibit magnetization plateaus, (b) why there occur several different types of magnetization plateaus, and (c) what controls the widths of magnetization plateaus. We show that the answers to these questions lie in how the magnets under field absorb Zeeman energy, hence changing their magnetic structures. The magnetic structure of a magnet insulator is commonly described in terms of its spin lattice, which requires the determination of the spin exchanges’ nonnegligible strengths between the magnetic ions. Our work strongly suggests that a magnet under the magnetic field partitions its spin lattice into antiferromagnetic (AFM) or ferrimagnetic fragments by breaking its weak magnetic bonds. Our supposition of the field-induced partitioning of spin lattices into magnetic fragments is supported by the anisotropic magnetization plateaus of Ising magnets and by the highly anisotropic width of the 1/3-magnetization plateau in azurite. The answers to the three questions (a)–(c) emerge naturally by analyzing how these fragments are formed under the magnetic field.

We examined the magnetic ground states, the preferred spin orientations and the spin exchanges of four layered phases MPS3 (M = Mn, Fe, Co, Ni) by first principles density functional theory plus onsite repulsion (DFT + U) calculations. The magnetic ground states predicted for MPS3 by DFT + U calculations using their optimized crystal structures are in agreement with experiment for M = Mn, Co and Ni, but not for FePS3. DFT + U calculations including spin-orbit coupling correctly predict the observed spin orientations for FePS3, CoPS3 and NiPS3, but not for MnPS3. Further analyses suggest that the ||z spin direction observed for the Mn2+ ions of MnPS3 is caused by the magnetic dipole–dipole interaction in its magnetic ground state. Noting that the spin exchanges are determined by the ligand p-orbital tails of magnetic orbitals, we formulated qualitative rules governing spin exchanges as the guidelines for discussing and estimating the spin exchanges of magnetic solids. Use of these rules allowed us to recognize several unusual exchanges of MPS3, which are mediated by the symmetry-adapted group orbitals of P2S64− and exhibit unusual features unknown from other types of spin exchanges.

AA ′ 3 B 4 O 12 quadruple perovskites, with magnetic A ′ and non-magnetic B cations, are characterized by a wide range of complex magnetic structures. These are due to a variety of competing spin-exchange interactions up to the fourth nearest neighbours. Here, we synthesize and characterize the magnetic behaviour of the CaCo 3 Ti 4 O 12 quadruple perovskite. We find that in the absence of an external magnetic field, the system undergoes antiferromagnetic ordering at 9.3 K. This magnetic structure consists of three interpenetrating mutually orthogonal magnetic sublattices. Under an applied magnetic field, this antiferromagnetic structure evolves into a canted ferromagnetic structure. In explaining these magnetic structures, as well as the seemingly unrelated magnetic structures found in other quadruple perovskites, we suggest a crucial role played by the underlying kagome lattices in these systems. All observed magnetic structures of these materials represent indeed one of the three possible ways to reduce spin frustration in the A ′ site kagome layers. More specifically, our survey of the magnetic structures observed for quadruple perovskites AA ′ 3 B 4 O 12 reveals the following three ways to reduce spin frustration, namely to make each layer ferromagnetic, to adopt a compromise 120° spin arrangement in each layer, or to have a magnetic structure with a vanishing sum of all second nearest-neighbour spin exchanges. Quadruple perovskites are characterized by competing long-range spin interactions that result in complex magnetic structures. Here, the authors synthesize and characterize the magnetic behaviour of CaCo 3 Ti 4 O 12 , suggesting that the observed magnetic structures arise from different ways to avoid frustration in underlying kagome lattices.

The static and dynamic magnetic properties and the specific heat of K2Ni2TeO6 and Li2Ni2TeO6 were examined and it was found that they undergo a long-range ordering at TN = 22.8 and 24.4 K, respectively, but exhibit a strong short-range order. At high temperature, the magnetic susceptibilities of K2Ni2TeO6 and Li2Ni2TeO6 are described by a Curie–Weiss law, with Curie-Weiss temperatures Θ of approximately −13 and −20 K, respectively, leading to the effective magnetic moment of about 4.46 ± 0.01 μB per formula unit, as expected for Ni2+ (S = 1) ions. In the paramagnetic region, the ESR spectra of K2Ni2TeO6 and Li2Ni2TeO6 show a single Lorentzian-shaped line characterized by the isotropic effective g-factor, g = 2.19 ± 0.01. The energy-mapping analysis shows that the honeycomb layers of A2Ni2TeO6 (A = K, Li) and Li3Ni2SbO6 adopt a zigzag order, in which zigzag ferromagnetic chains are antiferromagnetically coupled, because the third nearest-neighbor spin exchanges are strongly antiferromagnetic while the first nearest-neighbor spin exchanges are strongly ferromagnetic, and that adjacent zigzag-ordered honeycomb layers prefer to be ferromagnetically coupled. The short-range order of the zigzag-ordered honeycomb lattices of K2Ni2TeO6 and Li2Ni2TeO6 is equivalent to that of an antiferromagnetic uniform chain, and is related to the short-range order of the ferromagnetic chains along the direction perpendicular to the chains.

We determined the spin exchanges between the Cu2+ ions in the kagomé layers of volborthite, Cu3V2O7(OH)2·2H2O, by performing the energy-mapping analysis based on DFT+U calculations, to find that the kagomé layers of Cu2+ ions are hardly spin-frustrated, and the magnetic properties of volborthite below ~75 K should be described by very weakly interacting antiferromagnetic uniform chains made up of effective S = 1/2 pseudospin units. This conclusion was verified by synthesizing single crystals of not only Cu3V2O7(OH)2·2H2O but also its deuterated analogue Cu3V2O7(OD)2·2D2O and then by investigating their magnetic susceptibilities and specific heats. Each kagomé layer consists of intertwined two-leg spin ladders with rungs of linear spin trimers. With the latter acting as S = 1/2 pseudospin units, each two-leg spin ladder behaves as a chain of S = 1/2 pseudospins. Adjacent two-leg spin ladders in each kagomé layer interact very weakly, so it is required that all nearest-neighbor spin exchange paths of every two-leg spin ladder remain antiferromagnetically coupled in all spin ladder arrangements of a kagomé layer. This constraint imposes three sets of entropy spectra with which each kagomé layer can exchange energy with the surrounding on lowering the temperature below ~1.5 K and on raising the external magnetic field B. We discovered that the specific heat anomalies of volborthite observed below ~1.5 K at B = 0 are suppressed by raising the magnetic field B to ~4.2 T, that a new specific heat anomaly occurs when B is increased above ~5.5 T, and that the imposed three sets of entropy spectra are responsible for the field-dependence of the specific heat anomalies.

The effect of antisite disorder in the layered sodium iron antimonate Na 4 FeSbO 6 was examined both experimentally and theoretically. The magnetic susceptibility and specific heat measurements show that Na 4 FeSbO 6 does not undergo a long-range antiferromagnetic order, unlike its structural analog Li 4 FeSbO 6 . The electron spin resonance yields the complicated picture of coexistence of two magnetic subsystems corresponding to two different Fe cation positions in the lattice (regular and antisite) and driving the magnetic properties of the Na 4 FeSbO 6 . This conclusion found perfect confirmation from both the Mössbauer and X-ray absorption data which show the presence of two kinds of Fe 3+ ions being in high-spin Fe 3+ ( S  = 5/2) and low-spin Fe 3+ ( S  = 1/2) states. These findings arise from the antisite disorder between the Fe 3+ and Sb 5+ ions in the (NaFeSbO 6 ) 3− layers of Na 4 FeSbO 6 . Our density functional calculations show that the Fe 3+ ions located at the Sb 5+ sites exist as low-spin Fe 3+ ions, and that the spins of each Fe 3+ ( S  = 5/2)–Fe 3+ ( S  = 1/2)–Fe 3+ ( S  = 5/2) trimer generated by the antisite disorder has a ferrimagnetic arrangement Fe 3+ ↑–Fe 3+ ↓–Fe 3+ ↑, which enhances the magnetization of Na 4 FeSbO 6 and leads to an apparently positive Curie–Weiss temperature.

Mixed-valent Ba Mn Mn (SeO ) crystallizes in a monoclinic structure and has honeycomb layers of Mn ions alternating with triangular layers of Mn ions. We established the key parameters governing its magnetic structure by magnetization and specific heat measurements. The title compound exhibits a close succession of a short-range correlation order at = 10.1 ± 0.1 K and a long-range Néel order at = 5.7 ± 0.1 K, and exhibits a metamagnetic phase transition at with hysteresis most pronounced at low temperatures. The causes for these observations were found using the spin exchange parameters evaluated by density functional theory calculations. The title compound represents a unique case in which uniform chains of integer spin Mn ( = 2) ions interact with those of half-integer spin Mn ( = 5/2) ions.

Mixed-valent Ba[sub.2]Mn[sup.2+]Mn[sub.2] [sup.3+](SeO[sub.3])[sub.6] crystallizes in a monoclinic P2[sub.1]/c structure and has honeycomb layers of Mn[sup.3+] ions alternating with triangular layers of Mn[sup.2+] ions. We established the key parameters governing its magnetic structure by magnetization M and specific heat C[sub.p] measurements. The title compound exhibits a close succession of a short-range correlation order at Tcorr = 10.1 ± 0.1 K and a long-range Néel order at TN = 5.7 ± 0.1 K, and exhibits a metamagnetic phase transition at T < TN with hysteresis most pronounced at low temperatures. The causes for these observations were found using the spin exchange parameters evaluated by density functional theory calculations. The title compound represents a unique case in which uniform chains of integer spin Mn[sup.3+] (S = 2) ions interact with those of half-integer spin Mn[sup.2+] (S = 5/2) ions.

Mixed-valent Ba2Mn2+Mn23+(SeO3)6 crystallizes in a monoclinic P21/c structure and has honeycomb layers of Mn3+ ions alternating with triangular layers of Mn2+ ions. We established the key parameters governing its magnetic structure by magnetization M and specific heat Cp measurements. The title compound exhibits a close succession of a short-range correlation order at Tcorr = 10.1 ± 0.1 K and a long-range Néel order at TN = 5.7 ± 0.1 K, and exhibits a metamagnetic phase transition at T < TN with hysteresis most pronounced at low temperatures. The causes for these observations were found using the spin exchange parameters evaluated by density functional theory calculations. The title compound represents a unique case in which uniform chains of integer spin Mn3+ (S = 2) ions interact with those of half-integer spin Mn2+ (S = 5/2) ions.