Construction of Ideal One-Dimensional Spin Chains by Topochemical Dehydration/Rehydration Route.

One-dimensional (1D) Heisenberg antiferromagnets are of great interest due to their intriguing quantum phenomena. However, the experimental realization of such systems with large spin S remains challenging because even weak interchain interactions induce long-range ordering. In this study, we present an ideal 1D S = 5/2 spin chain antiferromagnet achieved through a multistep topochemical route involving dehydration and rehydration. By desorbing three water molecules from (2,2'-bpy)FeF3(H2O)·2H2O (2,2'-bpy = 2,2'-bipyridyl) at 150 °C and then intercalating two water molecules at room temperature (giving (2,2'-bpy)FeF3·2H2O 1), the initially isolated FeF3ON2 octahedra combine to form corner-sharing FeF4N2 octahedral chains, which are effectively separated by organic and added water molecules. Mössbauer spectroscopy reveals significant dynamical fluctuations down to 2.7 K, despite the presence of strong intrachain interactions. Moreover, results from electron spin resonance (ESR) and heat capacity measurements indicate the absence of long-range order down to 0.5 K. This controlled topochemical dehydration/rehydration approach is further extended to (2,2'-bpy)CrF3·2H2O with S = 3/2 1D chains, thus opening the possibility of obtaining other low-dimensional spin lattices.

Skin-Deep Aspect of Thermopower in Bi2Q3, PbQ, and BiCuQO (Q = Se, Te): Hidden One-Dimensional Character of Their Band Edges Leading to High Thermopower.

ConspectusThermoelectric (TE) materials have received much attention because of their ability to convert heat energy to electrical energy. At a given temperature T, the efficiency of a TE material for this energy conversion is measured by the figure of merit zT, which is related to the thermopower (or Seebeck coefficient) S, the thermal conductivity κ, and the electrical conductivity σ of the TE material as zT = (S2σT)/κ. Bi2Q3 and PbQ (Q = Se, Te) are efficient TE materials with high zT, although they are not ecofriendly and their stability is poor at high temperature. In principle, a TE material can have a high zT if it has a low thermal conductivity and a high electrical conductivity, but the latter condition is hardly met in a real material because the parameters S, σ and κ have a conflicting dependence on material properties. The difficulty in searching for TE materials of high zT is even more exasperated because the relationship between the thermopower S and the carrier density n (hereafter, the S-vs-n relationship) for the well-known hole-doped samples of BiCuSeO showed that the hole carriers responsible for their thermopower are associated largely with the electronic states lying within ∼0.5 eV of its valence band maximum (VBM). Thus, the states governing the TE properties lie in the "skin-deep" region from the VBM. For electron-doped TE systems, the electron carriers responsible for their thermopower should also be associated with the electronic states lying within ∼0.5 eV of the conduction band minimum (CBM). This makes it difficult to predict TE materials of high zT. One faces a similar skin-deep phenomenon in searching for superconductors of high transition temperature because the transition from a normal metallic to a superconducting state involves the normal metallic states in the vicinity of the Fermi level EF. Other skin-deep phenomena in metallic compounds include the formation of charge density wave (CDW), which involves the electronic states in the vicinity of their Fermi levels. For magnetic materials of transition-metal ions, the preferred orientation of their spin moments is a skin-deep phenomenon because it is governed by the interaction between the highest-occupied and the lowest unoccupied d-states of these ions. In the present work we probe the issues concerning how to find the possible range of thermopower expected for a given TE material and hence how to recognize what experimental values of thermopower are expected or unusual. For these purposes, we analyze the accumulated S and n data on the three well-studied TE materials, Bi2Q3, PbQ, and BiCuQO (Q = Se, Te), as representative examples, in terms of the ideal theoretical S-vs-n relationships, which we determine for their defect-free Bi2Q3, PbQ, and BiCuQO structures using density functional theory (DFT) calculations under the rigid band approximation. We find that the general trends in the experimental S-vs-n relationships are reasonably well explained by the calculated S-vs-n relationships, and the carrier densities covering these relationships are associated with the states lying within ∼0.5 eV from their band edges confirming the skin-deep nature of their thermoelectric properties. Despite the fact that these TE materials are not one-dimensional (1D) in structure, they mostly possess sharp density-of-state peaks around their band edges because their band dispersions have a hidden 1D character so their thermopower is generally high in magnitude.

K2Mn3O(OH)(VO4)(V2O7) with Sawtooth Chains of Multivalent Manganese Triangular Trimer Units: Magnetic Susceptibility Shrouding a Long-Range Antiferromagnetic Order of Ferromagnetic Triangles.

ortho-Pyrovanadate (or ortho-diorthovanadate) K2Mn23+Mn2+O(OH)(VO4)(V2O7) synthesized hydrothermally crystallizes in the orthorhombic space group Pnma with a = 17.9155(5), b = 5.8940(2), c = 10.9971(3) Å, V = 1161.23(6) Å3, and Z = 4. Its crystal structure features linear chains of edge-sharing Mn3+O6 octahedra with every second pair of Mn3+O6 octahedra condensed with a Mn2+O6 octahedron on one side of a chain in a sawtooth pattern so that each sawtooth chain consists of a triangular trimer. These sawtooth chains, running parallel to the b axis and linked by the VO4 and V2O7 groups, form a framework with channels populated by K atoms. The new compound is a structural analogue of the mineral zoisite Ca2Al3O(OH)(SiO4)(Si2O7), showing a striking example of very different chemical compositions. K2Mn3O(OH)(VO4)(V2O7) undergoes a phase transition into an ordered antiferromagnetic (AFM) state at TN = 14.4 K, which was detected by high-frequency electron spin resonance as well as by both specific heat Cp and Fisher's specific heat d(χT)/dT measurements. However, this phase transition was not detected by magnetic susceptibility measurements. The origin of this puzzling observation was resolved by evaluating the spin exchanges of K2Mn3O(OH)(VO4)(V2O7), which revealed that each triangular trimer is a ferromagnetically coupled cluster, and the observed ordering involves an AFM ordering between the ferromagnetic (FM) clusters. This ordering is shrouded in magnetic susceptibility measurements due to the susceptibility contributions from the individual FM triangular trimers even below TN. We showed that the magnetic susceptibility of K2Mn3O(OH)(VO4)(V2O7) between ∼30 K and room temperature is satisfactorily described by an AFM chain made up of ferromagnetically coupled triangular clusters, as described by a few spin-exchange parameters.

High-Spin Orbital Interactions Across van der Waals Gaps Controlling the Interlayer Ferromagnetism in van der Waals Ferromagnets.

We examined what interactions control the sign and strength of the interlayer coupling in van der Waals ferromagnets such as Fe3-xGeTe2, Cr2Ge2Te6, CrI3, and VI3 to find that high-spin orbital interactions across the van der Waals gaps are a key to understanding their ferromagnetism. Interlayer ferromagnetic coupling in Fe3-xGeTe2, Cr2Ge2Te6, and CrI3 is governed by the high-spin two-orbital two-electron destabilization, but that in VI3 by the high-spin four-orbital two-electron stabilization. These interactions explain a number of seemingly puzzling observations in van der Waals ferromagnets.

Spin-Peierls Distortion of TiPO4 Causing a Transition from a Magnetic to a Nonmagnetic Insulating State and Its Effect on the Thermoelectric Properties: Density Functional Theory Analysis.

Density functional theory calculations were carried out to probe the nature of the electronic structure change in TiPO4 before and after its spin-Peierls distortion at 74.5 K, which is characterized by the dimerization in the chains of Ti3+ (d1) ions present in TiPO4. These calculations suggest strongly that the electronic state of TiPO4 is magnetic insulating before the distortion, but becomes nonmagnetic insulating after the distortion. Consistent with this suggestion, the phonon dispersion relations calculated for TiPO4 show that the undistorted TiPO4 is stable, while the distorted TiPO4 is not, if each Ti3+ ion has a spin moment, and that the opposite is true if each Ti3+ ion has no spin moment. These observations suggest that the driving force for the spin-Peierls distortion is the formation of direct metal-metal bonds leading to the dimerized chains of Ti3+ ions. The abrupt change in the electronic structures from a magnetic insulating state to a nonmagnetic insulating state explains why the spin-Peierls distortion of TiPO4 exhibits a first-order character. Although the two electronic states of TiPO4 before and after the distortion have a band gap, the substantial spin-Peierls distortion is found to enhance the thermoelectric properties of TiPO4.

Microscopic Mechanism of the Heat-Induced Blueshift in Phosphors and a Logarithmic Energy Dependence on the Nearest Dopant-Vacancy Distance.

Heat-induced blueshift (HIB) observed in many luminescent materials is a puzzling phenomenon that has remained unexplained for decades. By using the high-throughput first-principles calculations and energy-screening techniques, we generated a number of model structures for five phosphors, RbLi[Li3 SiO4 ]2 :Eu2+ , Na[Li3 SiO4 ]:Eu2+ , K[Li3 SiO4 ]:Eu2+ , Sr[LiAl3 N4 ]:Eu2+ , and Ca[LiAl3 N4 ]:Eu2+ . Our analyses suggest, to a first approximation, a logarithmic energy dependence on the nearest distance between the dopant and the metal-cation vacancy. By identifying the 5 d → 4 f transition energies from the electronic structures calculated for the screened model structures, we show that the vibration of the Eu2+ ion lying in an asymmetric and anharmonic potential well couples with the electronic states, leading to their HIB phenomena.

Factors Governing the Propagation Direction and Spin-Rotation Plane of Noncollinear Magnetic Structures: A Helix vs Cycloid in Doubly Ordered Perovskites NaYMnWO6 and NaYNiWO6.

The magnetic structure of NaYMnWO6 was determined by neutron powder diffraction measurements. Below 9 K, the magnetic structure is a helix to wave vector k = (0, 0.447, 1/2), in contrast with NaYNiWO6, which shows a transverse spin density wave with k = (0.47, 0, 0.49). By analyzing the differences in the spin exchanges of NaYMnWO6 and NaYNiWO6, and in the magnetic anisotropies of the Mn2+ (d5, S = 5/2) and the Ni2+ (d2, S = 1) ions, we show what factors govern the propagation direction of a noncollinear magnetic structure and whether it becomes a helix or a cycloid.

Unusual Spin Exchanges Mediated by the Molecular Anion P2S64-: Theoretical Analyses of the Magnetic Ground States, Magnetic Anisotropy and Spin Exchanges of MPS3 (M = Mn, Fe, Co, Ni).

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.

Spin Exchanges Between Transition Metal Ions Governed by the Ligand p-Orbitals in Their Magnetic Orbitals.

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: -CuV2O6, LiCuVO4, (CuCl)LaNb2O7, and Cu3(CO3)2(OH)2.

In Honor of John Bannister Goodenough, an Outstanding Visionary.

John B [...].

Spin Hamiltonians in Magnets: Theories and Computations.

The effective spin Hamiltonian method has drawn considerable attention for its power to explain and predict magnetic properties in various intriguing materials. In this review, we summarize different types of interactions between spins (hereafter, spin interactions, for short) that may be used in effective spin Hamiltonians as well as the various methods of computing the interaction parameters. A detailed discussion about the merits and possible pitfalls of each technique of computing interaction parameters is provided.

Synthesis of the Elusive S = 1/2 Star Structure: A Possible Quantum Spin Liquid Candidate.

Materials with two-dimensional, geometrically frustrated, spin-1/2 lattices provide a fertile playground for the study of intriguing magnetic phenomena such as quantum spin liquid (QSL) behavior, but their preparation has been a challenge. In particular, the long-sought, exotic spin-1/2 star structure has not been experimentally realized to date. Here we report the synthesis of [(CH3)2(NH2)]3[CuII3(µ3-OH)(µ3-SO4)(µ3-SO4)3]·0.24H2O with an S = 1/2 star lattice. On the basis of the magnetic susceptibility and heat capacity measurements, the layered Cu-based compound exhibits antiferromagnetic interactions but no magnetic ordering or spin freezing down to 2 K. The spin-frustrated material appears to be a promising QSL candidate.

Orbital Magnetic Moments of the High-Spin Co2+ Ions at Axially-Elongated Octahedral Sites: Unquenched as Reported from Experiment or Quenched as Predicted by Theory?

Neutron diffraction studies on magnetic solids composed of axially elongated CoO4X2 (X = Cl, Br, S, Se) octahedra show that the ordered magnetic moments of their high-spin Co2+ (d7, S = 3/2) ions are greater than 3 µB, i.e., the spin moment expected for S = 3/2 ions, and increase almost linearly from 3.22 to 4.45 µB as the bond-length ratio rCo-X/rCo-O increases from 1.347 to 1.659 where rCo-X and rCo-O are the Co-X and Co-O bond lengths, respectively. These observations imply that the orbital moments of the Co2+ ions increase linearly from 0.22 to 1.45 µB with increasing the rCo-X/rCo-O ratio from 1.347 to 1.659. We probed this implication by examining the condition for unquenched orbital moment and also by evaluating the magnetic moments of the Co2+ ions based on DFT+U+SOC calculations for those systems of the CoO4X2 octahedra. Our work shows that the orbital moments of the Co2+ ions are essentially quenched and, hence, that the observations of the neutron diffraction studies are not explained by the current theory of magnetic moments. This discrepancy between experiment and theory urges one to check the foundations of the current theory of magnetic moments as well as the current method of neutron diffraction refinements for ordered magnetic structures.

Aggregation of Polybismuthide Anions in a Single Compound Using +Rh-CO Units: Heterometallic Cluster Ions [Rh@Bi10(RhCO)6]3- and [Rh@Bi9(RhCO)5]3.

In the presence of the roughly flat sequestering agent, [K(18-crown-6)]+, the reaction of Rh2(CO)4Cl2 with K5Bi4 in ethylenediamine (en) solution at room temperature yielded the heterometallic cluster anion [Rh@Bi10(RhCO)6]3- (1), in which two hitherto unknown Binm- building blocks (i.e., Bi6 crown and Bi4 pyramid) were stabilized by six +Rh-CO units. When the reaction was carried out at 60 °C using Rh(acac)(CO)2 (acac = acetylacetonate) as the source of +Rh-CO units, one obtained the anion [Rh@Bi9(RhCO)5]3- (2) in which two different Binn- units (n = 2, 3) and two weakly bonded Bi atoms were stabilized by five +Rh-CO units. The structures and bonding of the novel heterometallic cluster anions 1 and 2 were discussed.

On Ferro- and Antiferro-Spin-Density Waves Describing the Incommensurate Magnetic Structure of NaYNiWO6.

The incommensurate magnetic structure (0.47, 0, 0.49) of NaYNiWO6 exhibits unconventional spin-density waves (SDWs) along the [100] direction, in which up and down spins alternate in each half-wave. This is in contrast to conventional SDWs, in which only one type of spin is present in each half-wave. We probed the formation of these unconventional SDWs by evaluating the spin exchanges of NaYNiWO6 based on density functional theory calculations and analyzing the nature of the spin frustration in NaYNiWO6 and by noting that a SDW is a superposition of two cycloids of opposite chirality. The unconventional SDWs along the [100] direction originate from the spin-frustrated antiferromagnetic chains of Ni2+ ions along that direction, leading to conventional SDWs along the [101] direction and unconventional SDWs along the [001] direction.

The partition principles for atomic-scale structures and their physical properties: application to the nonlinear optical crystal material KBe2BO3F2.

In implementing the materials genome approach to search for new materials with interesting properties or functions, it is necessary to find the correct functional motif. To this end, it is common to partition an extended structure into various building units and then partition its properties to find the appropriate functional motif. We have developed the general principles for partitioning a structure and its properties in terms of a set of atoms and bonds by analyzing the differential cross-sections of neutron and X-ray scattering phenomena and proposed the procedures with which to partition an extended structure and its properties. We demonstrate how these procedures work by analyzing the nonlinear optical crystal KBe2BO3F2. Our partitioning analysis of KBe2BO3F2 leads to the conclusion that the second harmonic generation response of KBe2BO3F2 is dominated by the ionically bonded metal-centered groups.

Physical Properties of Molecules and Condensed Materials Governed by Onsite Repulsion, Spin-Orbit Coupling and Polarizability of Their Constituent Atoms.

The onsite repulsion, spin-orbit coupling and polarizability of elements and their ions play important roles in controlling the physical properties of molecules and condensed materials. In celebration of the 150th birthday of the periodic table this year, we briefly review how these parameters affect the physical properties and are interrelated.

Triple-Kagomé-Layer Slabs of Mixed-Valence Rare-Earth Ions Exhibiting Quantum Spin Liquid Behaviors: Synthesis and Characterization of Eu9MgS2B20O41.

We prepared a new rare-earth compound, Eu9MgS2B20O41 (EMSBO), and characterized its structural and physical properties. EMSBO consists of triple-Kagomé-layer slabs separated by nonmagnetic ions and groups. Within each slab, intervalence charge transfer has been found to occur between the Eu2+ and Eu3+ Kagomé layers, a new channel for quantum fluctuation of magnetic moments. The measured magnetic susceptibilities and the specific heat capacity exhibit very similar features characteristic of quantum spin liquid behaviors observed in other materials.

Effect of Nonmagnetic Ion Deficiency on Magnetic Structure: Density Functional Study of Sr2MnO2Cu2-xTe2, Sr2MO2Cu2Te2 (M = Co, Mn), and the Oxide-Hydrides Sr2VO3H, Sr3V2O5H2, and SrVO2H.

Two seemingly puzzling observations on two magnetic systems were analyzed. For the oxide-hydrides Sr2VO3H, Sr3V2O5H2, and SrVO2H, made up of VO4H2 octahedra, the spin orientations of the V3+ (d2, S = 1) ions were reported to be different, namely, perpendicular to the H-V-H bond in Sr2VO3H but parallel to the H-V-H bond in Sr3V2O5H2 and SrVO2H, despite that the d-state split patterns of the VO4H2 octahedra are similar in the three oxide-hydrides. Another puzzling observation is the contrasting magnetic structures of Sr2CoO2Cu2Te2 and Sr2MnO2Cu1.58Te2, consisting of the layers made up of corner-sharing MO4Te2 (M = Co, Mn) octahedra. The Co2+ spins in each CoO2Te2 layer are antiferromagnetically coupled with spins perpendicular to the Te-Co-Te bond, whereas the Mn3+/Mn2+ ions of each MnO2Te2 layer are ferromagnetically coupled with spins parallel to the Te-Mn-Te bonds. We investigated the cause for these observations by performing first-principles density functional theory (DFT) calculations for stoichiometric phases Sr2VO3H, Sr3V2O5H2, SrVO2H, Sr2CoO2Cu2Te2, and Sr2MnO2Cu2Te2, as well as nonstoichiometric phase Sr2MnO2Cu1.5Te2. Our study reveals that the V3+ ions in all three oxide-hydrides should have the spin orientation parallel to the H-V-H bond. The unusual magnetic structure of the MnO2Te2 layers of Sr2MnO2Cu1.52Te2 arises from the preference of a Mn3+ spin to be parallel to the Te-Mn-Te bond, the ferromagnetic spin exchange between adjacent Mn3+ and Mn2+ ions, and the nearly equal numbers of Mn3+ and Mn2+ ions in each MnO2Te2 layer. We show that the spin orientation of the magnetic ions in an antiferromagnetically coupled perovskite layer, expected in the absence of nonmagnetic ion vacancies, cannot be altered by the magnetic ions of higher oxidation that result from trace vacancies at the nonmagnetic ion sites.

Dependence of the Second-Harmonic Generation Response on the Cell Volume to Band-Gap Ratio.

The second-harmonic generation (SHG) coefficients of 12 nonlinear optical chalcopyrites, ABC2 (A = Zn, Cd; B = Si, Ge, Sn; C = P, As) were calculated by first-principles methods to find that given the primitive cell volume V and the band gap Eg of ABC2, the SHG coefficients dav of ABC2 increase almost linearly with increasing value of V/Eg. This suggests that a noncentrosymmetric crystal has a large SHG response when it consists of large atoms, leading to a small band gap.