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.

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.

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.

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.

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.

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.

Electronic and Structural Factors Controlling the Spin Orientations of Magnetic Ions.

Magnetic ions M in discrete molecules and extended solids form MLn complexes with their first-coordinate ligand atoms L. The spin moment of M in a complex MLn prefers a certain direction in coordinate space because of spin-orbit coupling (SOC). In this minireview, we examine the structural and electronic factors governing the preferred spin orientations. Elaborate experimental measurements and/or sophisticated computational efforts are required to find the preferred spin orientations of magnetic ions, largely because the energy scale of SOC is very small. The latter is also the very reason why one can readily predict the preferred spin orientation of M by analyzing the SOC-induced highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) interactions of the MLn complexes in terms of qualitative perturbation theory. The strength of this HOMO-LUMO interaction depends on the spin orientation, which is governed by the selection rules based on the minimum |ΔLz| value (i.e., the minimum difference in the magnetic quantum numbers) between the HOMO and LUMO. With the local z axis of MLn chosen as its n-fold rotational axis, the preferred spin orientation is parallel to the z axis (∥z) when |ΔLz| = 0 but perpendicular to the z axis (⊥z) when |ΔLz| = 1.

Synthesis and Characterization of Sodium-Iron Antimonate Na2FeSbO5: One-Dimensional Antiferromagnetic Chain Compound with a Spin-Glass Ground State.

A new oxide, sodium-iron antimonate, Na2FeSbO5, was synthesized and structurally characterized, and its static and dynamic magnetic properties were comprehensively studied both experimentally by dc and ac magnetic susceptibility, magnetization, specific heat, electron spin resonance (ESR) and Mössbauer measurements, and theoretically by density functional calculations. The resulting single-crystal structure (a = 15.6991(9) Å; b = 5.3323 (4) Å; c = 10.8875(6) Å; S.G. Pbna) consists of edge-shared SbO6 octahedral chains, which alternate with vertex-linked, magnetically active FeO4 tetrahedral chains. The 57Fe Mössbauer spectra confirmed the presence of high-spin Fe3+ (3d5) ions in a distorted tetrahedral oxygen coordination. The magnetic susceptibility and specific heat data show the absence of a long-range magnetic ordering in Na2FeSbO5 down to 2 K, but ac magnetic susceptibility unambigously demonstrates spin-glass-type behavior with a unique two-step freezing at Tf1 ≈ 80 K and Tf2 ≈ 35 K. Magnetic hyperfine splitting of 57Fe Mössbauer spectra was observed below T* ≈ 104 K (Tf1 < T*). The spectra just below T* (Tf1 < T < T*) exhibit a relaxation behavior caused by critical spin fluctuations, indicating the existence of short-range correlations. The stochastic model of ionic spin relaxation was used to account for the shape of the Mössbauer spectra below the freezing temperature. A complex slow dynamics is further supported by ESR data revealing two different absorption modes presumably related to ordered and disordered segments of spin chains. The data imply a spin-cluster ground state for Na2FeSbO5.

Group of Quantum Bits Acting as a Bit Using a Single-Domain Ferromagnet of Uniaxial Magnetic Ions.

Read/write operations with individual quantum bits (i.e., qbits) are a challenging problem to solve in quantum computing. To alleviate this difficulty, we considered the possibility of using a group of qbits that act collectively as a bit (hereafter, a group bit or a gbit, in short). A promising candidate for a gbit is a single-domain ferromagnet (SDF) independent of its size, which can be prepared as a magnet of well-separated uniaxial magnetic ions (UMIs) at sites of no electric dipole moment with their uniaxial axes aligned along one common direction. When magnetized, the UMIs of such a magnet have a ferromagnetic (FM) arrangement and the resulting SDF becomes a gbit with its two opposite moment orientations representing the |0⟩ and |1⟩ states of a bit. We probed the requirements for such magnets and identified several 2H-perovskites as materials satisfying these requirements.

Structural and Magnetic Properties of the Trirutile-type 1D-Heisenberg Anti-Ferromagnet CuTa2O6.

We prepared trirutile-type polycrystalline samples of CuTa2O6 by low-temperature decomposition of a Cu-Ta-oxalate precursor. Diffraction studies at room temperature identified a slight monoclinic distortion of the hitherto surmised tetragonal trirutile crystal structure. Detailed high-temperature X-ray and neutron powder diffraction investigations as well as Raman scattering spectroscopy revealed a structural phase transition at 503(3) K from the monoclinic structure to the tetragonal trirutile structure. GGA+U density functional calculations of the spin-exchange parameters as well as magnetic susceptibility and isothermal magnetization measurements reveal that CuTa2O6 is a new 1D Heisenberg magnet with predominant anti-ferromagnetic nearest-neighbor intrachain spin-exchange interaction of ∼50 K. Interchain exchange is a factor of ∼5 smaller. Heat capacity and low-temperature high-intensity neutron powder diffraction studies could not detect long-range order down to 0.45 K.

Single-Domain Ferromagnet of Noncentrosymmetric Uniaxial Magnetic Ions and Magnetoelectric Interaction.

The feasibility of a single-domain ferromagnet based on uniaxial magnetic ions was examined. For a noncentrosymmetric uniaxial magnetic ion of magnetic moment µ at a site of local electric dipole moment p, it is unknown to date whether µ prefers to be parallel or antiparallel to µ. The nature of this magnetoelectric interaction was probed in terms of analogical reasoning based on the Rashba effect and density functional theory (DFT) calculations. We show that µ and p prefer an antiparallel arrangement, predict that Fe-doped CaZnOS is a single-domain ferromagnet like a bar magnet, and find the probable cause for the ferromagnetism and weak magnetization hysteresis in Fe-doped hexagonal ZnO and ZnS at very low dopant concentrations.

Prediction of Spin Orientations in Terms of HOMO-LUMO Interactions Using Spin-Orbit Coupling as Perturbation.

For most chemists and physicists, electron spin is merely a means needed to satisfy the Pauli principle in electronic structure description. However, the absolute orientations of spins in coordinate space can be crucial in understanding the magnetic properties of materials with unpaired electrons. At low temperature, the spins of a magnetic solid may undergo long-range magnetic ordering, which allows one to determine the directions and magnitudes of spin moments by neutron diffraction refinements. The preferred spin orientation of a magnetic ion can be predicted on the basis of density functional theory (DFT) calculations including electron correlation and spin-orbit coupling (SOC). However, most chemists and physicists are unaware of how the observed and/or calculated spin orientations are related to the local electronic structures of the magnetic ions. This is true even for most crystallographers who determine the directions and magnitudes of spin moments because, for them, they are merely the parameters needed for the diffraction refinements. The objective of this article is to provide a conceptual framework of thinking about and predicting the preferred spin orientation of a magnetic ion by examining the relationship between the spin orientation and the local electronic structure of the ion. In general, a magnetic ion M (i.e., an ion possessing unpaired spins) in a solid or a molecule is surrounded with main-group ligand atoms L to form an MLn polyhedron, where n is typically 4-6, and the d states of MLn are split because the antibonding interactions of the metal d orbitals with the p orbitals of the surrounding ligands L depend on the symmetries of the orbitals involved.1 The magnetic ion M of MLn has a certain preferred spin direction because its split d states interact among themselves under SOC.2,3 The preferred spin direction can be readily predicted on the basis of perturbation theory in which the SOC is taken as perturbation and the split d states as unperturbed states by inspecting the magnetic quantum numbers of its d orbitals present in the HOMO and LUMO of the MLn polyhedron. This is quite analogous to how chemists predict whether a chemical reaction is symmetry-allowed or symmetry-forbidden in terms of the HOMO-LUMO interactions by simply inspecting the symmetries of the frontier orbitals.4,5 Experimentally, the determination of the preferred spin orientations of magnetic ions requires a sophisticated level of experiments, for example, neutron diffraction measurements for magnetic solids with an ordered spin state at a very low temperature. Theoretically, it requires an elaborate level of electronic structure calculations, namely, DFT calculations including electron correlation and SOC. We show that the outcomes of such intricate experimental measurements and theoretical calculations can be predicted by a simple perturbation theory analysis.

On Why the Two Polymorphs of NaFePO4 Exhibit Widely Different Magnetic Structures: Density Functional Analysis.

Triphylite-NaFePO4 is a cathode material for Na(+)-ion batteries, whereas its alternative polymorph maricite-NaFePO4 is not. These two different polymorphs exhibit widely different magnetic structures; the ordered magnetic structure of triphylite-NaFePO4 below ∼50 K is described by the propagation vector q1 = (0, 0, 0) with collinear spins, and that of maricite-NaFePO4 below ∼13 K is described by q2 = (1/2, 0, 1/2) with noncollinear spins. We probed the causes for these differences by calculating the spin exchange interactions of the two polymorphs and determining the preferred orientations of their high-spin Fe(2+) (d(6), S = 2) ions on the basis of density functional calculations. Our study shows that maricite-NaFePO4 is not spin-frustrated, which is also the case for triphylite-NaFePO4, that the ordered magnetic structure of triphylite-NaFePO4 is determined mainly by spin exchange, whereas that of maricite-NaFePO4 is determined by both spin exchange and magnetic anisotropy, and that the preferred spin orientations in the two polymorphs can be explained by perturbation theory using spin-orbit coupling as the perturbation.

Pair distribution function and density functional theory analyses of hydrogen trapping by γ-MnO2.

In the presence of "Ag2O" as a promoter, γ-MnO2 traps dihydrogen in its (2 × 1) and (1 × 1) tunnels. The course of this reaction was examined by analyzing the X-ray diffraction patterns of the HxMnO2/"Ag2O" system (0 ≤ x < 1) on the basis of pair distribution function and density functional theory (DFT) analyses. Hydrogen trapping occurs preferentially in the (2 × 1) tunnels of γ-MnO2, which is then followed by that in the (1 × 1) tunnels. Our DFT analysis shows that this process is thermodynamically favorable.