Cr-Cr Distance Research Articles

Cr-Cr distance and magnetism in the phase diagram of triangular lattice antiferromagnets: A systematic comparative study

Cr-Cr distance and magnetism in the phase diagram of triangular lattice antiferromagnets: A systematic comparative study

Chromium doped NH2(CH3)2Ga(SO4)2 × 6H2O crystal – representative of a new family of magnetoelectric materials

The paper is devoted to the detailed study of electric and magnetic properties and magnetoelectric interactions in NH2(CH3)2Ga(SO4)2 × 6H2O crystals doped with chromium—DMAGaS:Cr. The temperature dependence of the specific heat revealed clear evidence of a series of phase transitions related to the electric dipoles ordering. The different types of the DMA cation ordering in the structure of DMAGaS:Cr were evidenced in the temperature evolution of the EPR spectra. In addition, a considerable magnetoelectric coupling was demonstrated within the paramagnetic and ferroelectric phase of DMAGaS:Cr crystal. In the narrow temperature range in the vicinity of the Curie point, this crystal was found to possess the largest values of the coefficient of ME interaction as well as the largest magnetodielectric effect within the family of ferroics with organic cation. The model describing the ME effect was proposed. The magnetic field through the magnetostriction effect changes the level of the local lattice deformations caused by metal ion substitution. The applied magnetic field changes Cr-Cr distances and modifies the hydrogen bonds and process of DMA group ordering, affecting spontaneous polarization.

Spin-lattice couplings in two-dimensional CrI3 from first-principles computations

Since thermal fluctuations become more important as dimensions shrink, it is expected that low-dimensional magnets are more sensitive to lattice distortions and phonons than bulk systems are. Here we present a fully relativistic first-principles study on the spin-lattice coupling, i.e. how the magnetic interactions depend on local lattice distortions, of the prototypical two-dimensional ferromagnet CrI$_3$. We extract an effective measure of the spin-lattice coupling in CrI$_3$ which is up to ten times larger than what is found for bcc Fe. The magnetic exchange interactions, including Heisenberg and relativistic Dzyaloshinskii-Moriya interactions, are sensitive both to the in-plane motion of Cr atoms and out-of-plane motion of ligand atoms. We find that significant magnetic pair interactions change sign from ferromagnetic (FM) to anti-ferromagnetic (AFM) for atomic displacements larger than 0.16 {\AA}. We explain the observed strong spin-lattice coupling by analyzing the orbital decomposition of isotropic exchange interactions, involving different crystal-field-split Cr$-3d$ orbitals. The competition between the AFM t$_{2g}$ - t$_{2g}$ and FM t$_{2g}$ - e$_{g}$ contributions depends on the bond angle formed by Cr and I atoms as well as Cr-Cr distance. In particular, if a Cr atom is displaced, the FM-AFM sign change when the I-Cr-I bond angle approaches 90$^\circ$. The obtained spin-lattice coupling constants, along with the microscopic orbital analysis can act as a guiding principle for further studies of the thermodynamic properties and combined magnon-phonon excitations in two-dimensional magnets.

Computational Spectroscopy of the Cr-Cr Bond in Coordination Complexes.

We report the accurate computational vibrational analysis of the Cr-Cr bond in dichromium complexes using second-order multireference complete active space methods (CASPT2), allowing direct comparison with experimental spectroscopic data both to facilitate interpreting the low-energy region of the spectra and to provide insights into the nature of the bonds themselves. Recent technological development by the authors has realized such computation for the first time. Accurate simulation of the vibrational structure of these compounds has been hampered by their notorious multiconfigurational electronic structure that yields bond distances that do not correlate with bond order. Some measured Cr-Cr vibrational stretching modes, ν(Cr2), have suggested weaker bonding, even for so-called ultrashort Cr-Cr bonds, while others are in line with the bond distance. Here, we optimize geometries and compute ν(Cr2) with CASPT2 for three well-characterized complexes, Cr2(O2CCH3)4(H2O)2, Cr2(mhp)4, and Cr2(dmp)4. We obtain CASPT2 harmonic ν(Cr2) modes in good agreement with experiment at 282 cm-1 for Cr2(mhp)4 and 353 cm-1 for Cr2(dmp)4, compute 50Cr and 54Cr isotope shifts, and demonstrate that the use of the so-called IPEA shift leads to improved Cr-Cr distances. Additionally, normal mode sampling was used to estimate anharmonicity along ν(Cr2), leading to an anharmonic mode of 272 cm-1 for Cr2(mhp)4 and 333 cm-1 for Cr2(dmp)4.

Enhanced Magnetic Interaction by Face-Shared Hydride Anions in 6H-BaCrO2H.

Studies on magnetic oxyhydrides have been almost limited to perovskite-based lattices with corner-sharing octahedra with a M-H-M (M: transition metal) angle of θ ∼ 180°. Using a high-pressure method, we prepared BaCrO2H with a 6H-type hexagonal perovskite structure with corner- and face-sharing octahedra, offering a unique opportunity to investigate magnetic interactions based on a θ ∼ 90° case. Neutron diffraction for BaCrO2H revealed an antiferromagnetic (AFM) order at TN ∼ 375 K, which is higher than ∼240 K in BaCrO3-xFx. The relatively high TN of BaCrO2H can be explained by the preferred occupancy of H- at the face-sharing site that provides AFM superexchange in addition to AFM direct exchange interactions. First-principles calculations on BaCrO2H in comparison with BaCrO2F and BaMnO3 further reveal that the direct Cr-Cr interaction is significantly enhanced by shortening the Cr-Cr distance due to the covalent nature of H-. This study provides a useful strategy for the extensive control of magnetic interactions by exploiting the difference in the covalency of multiple anions.

Linear Trimer Formation with Antiferromagnetic Ordering in 1T-CrSe2 Originating from Peierls-like Instabilities and Interlayer Se-Se Interactions.

Anomalous successive structural transitions in layered 1T-CrSe2 with an unusual Cr4+ valency were investigated by synchrotron X-ray diffraction. 1T-CrSe2 exhibits dramatic structural changes in in-plane Cr-Cr and interlayer Se-Se distances, which originate from two interactions: (i) in-plane Cr-Cr interactions derived from Peierls-like trimerization instabilities on the orbitally assisted one-dimensional chains and (ii) interlayer Se-Se interactions through p-p hybridization. As a result, 1T-CrSe2 has the unexpected ground state of an antiferromagnetic metal with multiple Cr linear trimers with three-center-two-electron σ bonds. Interestingly, partial substitution of Se for S atoms in 1T-CrSe2 changes the ground state from an antiferromagnetic metal to an insulator without long-range magnetic ordering, which is due to the weakening of interlayer interactions between anions. The unique low-temperature structures and electronic states of this system are determined by the competition and cooperation of in-plane Cr-Cr and interlayer Se-Se interactions.

Spherical Closo Deltahedra with Surface Metal-Metal Multiple Bonding versus Oblate Deltahedra with Internal Metal-Metal Bonding in Dichromadicarbaborane Structures: The Nature of Stone's Icosahedral Dichromadicarbaborane.

The dichromadicarbaboranes Cp2Cr2C2B n-4H n-2 ( n = 8-12) related to the icosahedral structure reported in 1983 by Stone and co-workers and formulated by them as Cp2Cr2C2B8H10 have been investigated using density functional theory. In most cases, the lowest-energy structures are flattened oblatocloso structures with degree 6 and 7 chromium vertices similar to the lowest-energy and experimental structures of the isoelectronic dirhenaboranes Cp2Re2B n-2H n-2. However, most isomeric spherical closo deltahedral structures with surface Cr≣Cr quadruple bonds as well as isocloso structures with surface metal-metal Cr≡Cr triple bonds lie at accessible energies, typically lower than those in the corresponding dirhenaborane systems. However, for the 11-vertex Cp2Cr2C2B7H9 system, the most spherical closo/ isocloso deltahedral structure with a degree 6 metal vertex and degree 4 carbon vertices as well as a surface M≡M triple bond lies energetically below the lowest-energy oblatocloso structure. Calculations of the Cr-Cr distances in an icosahedral Cp2Cr2C2B8H10 structure and in a dihydrogenated icosahedral Cp2Cr2(μ-H)2C2B8H10 structure suggest the latter structure for "Cp2Cr2C2B8H10" reported by Stone and co-workers.

Trends in the Bond Multiplicity of Cr2, Cr3, and Cr2M (M = Zn, Ni, Fe, Mn) Complexes Extracted from Multiconfigurational Wave Functions.

Extended metal atom chains constitute an interesting class of molecules from both theoretical and applied points of view. In the chromium-based series Cr2M(dpa)4X2 (with M = Zn, Ni, Fe, Mn, Cr), the direct metal-metal interactions span a wide range of possibilities and so do their associated properties. The multiplicity and symmetry components of the metal-metal bond are herein analyzed via the effective bond order (EBO) concept using complete active space self-consistent field wave functions and compared with similar bimetallic Cr2L4X2 systems. The bond multiplicity follows a trend dominated by the Cr-Cr distance which, in turn, depends on the nature of the axial ligand (X). Cr2M compounds present asymmetric structures with virtually no interaction between the Cr2 unit and M, whereas fully symmetric structures with delocalized bonding among the three metals are also possible in Cr3 complexes. In such cases, a strategy that involves localization of the molecular orbitals into each Cr-Cr pair is applied to quantify the contribution of each pair to the overall metal-metal bond multiplicity.

Strong electronic influence of equatorial ligands on frontier orbitals in paddlewheel dichromium(ii,ii) complexes.

A series of substituted benzoate-bridged dichromium(ii,ii) complexes [Cr2(RCO2)4(THF)2] ([Cr2]), where RCO2- is substituted benzoate, was synthesized and its structural and magnetic properties were investigated. The orbital energies, as well as magnetic coupling energies, were also investigated using computational approaches. The HOMO/LUMO energy levels of the complexes are strongly dependent on the acidity, i.e., pKa, of the corresponding benzoic acids (RCO2H), revealing a linear trend in the respective groups of non-ortho, mono-ortho, and bi-ortho substituted groups. The CrCr magnetic coupling constant (ES-T) is little affected by pKa; instead, the ES-T is associated with the HOMO/LUMO gap and strongly correlated with the CrCr distance.

Magnetophononics: Ultrafast spin control through the lattice

Using a combination of first-principles and magnetization-dynamics calculations, we study the effect of the intense optical excitation of phonons on the magnetic behavior in insulating magnetic materials. Taking the prototypical magnetoelectric \CrO\ as our model system, we show that excitation of a polar mode at 17 THz causes a pronounced modification of the magnetic exchange interactions through a change in the average Cr-Cr distance. In particular, the quasi-static deformation induced by nonlinear phononic coupling yields a structure with a modified magnetic state, which persists for the duration of the phonon excitation. In addition, our time-dependent magnetization dynamics computations show that systematic modulation of the magnetic exchange interaction by the phonon excitation modifies the magnetization dynamics. This temporal modulation of the magnetic exchange interaction strengths using phonons provides a new route to creating non-equilibrium magnetic states and suggests new avenues for fast manipulation of spin arrangements and dynamics.

One-Dimensional Chains of Paddlewheel-Type Dichromium(II,II) Tetraacetate Complexes: Study of Electronic Structure Influenced by σ- and π-Donation of Axial Linkers.

Paddlewheel-type carboxylate-bridged dichromium(II,II) complexes possess intriguing properties such as high redox activity and thermally assisted paramagnetism. However, the relationship of their structures with electronic states and physical properties has not been extensively studied. In this work, we investigated a series of one-dimensional chain complexes based on the paddlewheel-type dichromium(II,II) tetraacetate complex ([Cr2II,II(OAc)4] = [Cr2II,II]) with pyridine/pyrazine-type organic linkers (μ2-Lax) having different σ- and π-donating abilities to clarify the electronic structure of [Cr2II,II] assemblies. The chain compounds are stable in air, probably owing to their robust polymerized forms. X-ray crystallographic studies and magnetic measurements revealed that the basicity (p Kb) of Lax, which quantitatively correlates with the σ-donor strength of Lax, modulates the Cr-Cr and Cr-Lax distances and the energy separation ( ES-T) between the diamagnetic (singlet) and thermally populated paramagnetic (triplet) states. The Cr-Cr and Cr-Lax distances are strongly influenced by σ- and π-donation from Lax, while the frontier δ orbital makes only a small contribution to the structural features. Density functional theory calculations were conducted to clarify this issue. The calculations produced the following unanticipated results against the long-known model: (i) the σ bonding orbital is the HOMO and dominates bonding in the [Cr2II,II] unit, (ii) the total Cr-Cr bond order is less than 1.0, and (iii) the δ orbital electron density is almost completely localized on the chromium sites. The computational results accurately predict the magnetic behavior and provide evidence for a new configuration of frontier orbitals in [Cr2II,II(RCO2)4(Lax)2].

Removal of hexavalent chromium in aqueous solutions using biochar: Chemical and spectroscopic investigations

Biochar is an emerging low-cost sorbent used for removing trace metals from water. In this study, we evaluated the removal potential of aqueous hexavalent chromium (Cr(VI)) by biochars produced from soybean (Glycinemax L.) and burcucumber (Sicyos angulatus L.) residues. The highest Cr(VI) removal from solution occurred at low pH values (pH2–5), and adsorption decreased approximately tenfold when the pH increased from 2 to 10. Synchrotron-based X-ray absorption spectroscopy (XAS) investigations showed that Cr(VI) species were reduced to trivalent chromium (Cr(III)) at the biochar surface following Cr(VI) adsorption. Linear combination fitting (LCF) of X-ray absorption near edge structure (XANES) data indicated that approximately 90% of the total Cr(VI) (962μM) was reduced to Cr(III). Extended X-ray absorption fine structure (EXAFS) fitting results yielded interatomic chromium (CrCr) distances consistent with the formation of Cr(III) precipitates as Cr(OH)3. Trivalent chromium is far less soluble than Cr(VI) and typically precipitates as amorphous Cr(III) solids. Thus, biochars produced by soybean and burcucumber residues are a promising technique for both adsorbing and reductively immobilizing Cr(VI) from aqueous solutions.

Cis-Thioindigo (TI) - a new ligand with accessible radical anion and dianion states. Strong magnetic coupling in the {[TI-(μ2-O),(μ-O)]Cp*Cr}2 dimers.

Reaction of decamethylchromocene (Cp*2Cr) with thioindigo (TI) yields a coordination complex {[TI-(μ2-O), (μ-O)]Cp*Cr}2·C6H14 (1) in which one Cp* ligand in Cp*2Cr is substituted by TI. TI adopts cis-conformation in 1 allowing the coordination of both carbonyl groups to chromium. Additionally, one oxygen atom of TI becomes a μ2-bridge for two chromium atoms to form {[TI-(μ2-O), (μ-O)]Cp*Cr}2 dimers with a CrCr distance of 3.12 Å. According to magnetic data, diamagnetic TI2- dianions and two Cr3+ atoms with a high S = 3/2 spin state are present in a dimer allowing strong antiferromagnetic coupling between two Cr3+ spins with an exchange interaction of -35.4 K and the decrease of molar magnetic susceptibility below 140 K. Paramagnetic TI˙- radical anions with the S = 1/2 spin state have also been obtained and studied in crystalline {cryptand[2,2,2](Na+)}(TI˙-) (2) salt showing that both radical anion and dianion states are accessible for TI.

Spin Frustration and Magnetic Ordering from One-Dimensional Stacking of Cr3 Triangles in TiCrIr2B2

Spin-frustrated chains of Cr3 triangles are found in the new metal boride TiCrIr2B2 by synergistic experimental and theoretical investigations. Although magnetic ordering is found at 275 K, competing ferro- and anti-ferromagnetic interactions coupled with spin frustration induce a rather small total magnetic moment (0.05 μB at 5 T), and density functional theory (DFT) calculations propose a canted, nonlinear magnetic ground-state ordering in the new phase. TiCrIr2B2 crystallizes in the hexagonal Ti1+xOs2-xRuB2 structure type (space group P6̅2m, No. 189, Pearson symbol hP18). The structure contains trigonal planar B4 boron fragments with B-B distances of 1.76(3) Å alternating along the c-direction with Cr3 triangles with intra- and intertriangle Cr-Cr distances of 2.642(9) and 3.185(1) Å, respectively. Magnetization measurements of TiCrIr2B2 reveal ferrimagnetic behavior and a large, negative Weiss constant of -750 K. DFT calculations demonstrate a strong site preference of Cr for the triangle sites, as well as magnetic frustration due to indirect anti-ferromagnetic interactions within the Cr3 triangles.

Cr-Cr Quintuple Bonds: Ligand Topology and Interplay Between Metal-Metal and Metal-Ligand Bonding.

Chromium-chromium quintuple bonds seem to be approaching the lower limit for their bond distances, and this computational density functional theory study tries to explore the geometrical and electronic factors that determine that distance and to find ways to fine-tune it via the ligand choice. While for monodentate ligands the Cr-Cr distance is predicted to shorten as the Cr-Cr-L bond angle increases, with bridging bidentate ligands the trend is the opposite, since those ligands with a larger number of spacers between the donor atoms favor larger bond angles and longer bond distances. Compared to Cr-Cr quadruple bonds, the quintuple bonding in Cr2L2 compounds (with L a bridging bidentate N-donor ligand) involves a sophisticated mechanism that comprises a positive pyramidality effect for the σ and one π bond, but a negative effect for one of the δ bonds. Moreover, the shorter Cr-Cr distances produce a mismatch of the bridging ligand lone pairs and the metal acceptor orbitals, which results in a negative correlation of the Cr-Cr and Cr-N bond distances in both experimental and calculated structures.

Nickelacyclopentadienylchromium tricarbonyl unit as a bulky pseudohalogen in cyclopentadienylchromium complexes leading to low-energy high-spin structures.

Recent studies, particularly from the laboratory of Buchalski and co-workers, have resulted in the syntheses of nickelacyclopentadienyl and nickelafluorenyl metallacycles that can function as pentahapto ligands in transition-metal complexes, similar to the ubiquitous cyclopentadienyl ligand. The structures and energetics of the neutral binuclear chromium carbonyls (CpNiC4H4)2Cr2(CO)n (n = 6, 5, 4, 3; Cp = η(5)-C5H5) containing the unsubstituted nickelacyclopentadienyl ligand have been investigated by density functional theory. The lowest energy (CpNiC4H4)2Cr2(CO)n (n = 6, 4) structures are similar to the corresponding experimentally characterized Cp2Cr2(CO)n structures with predicted Cr-Cr distances of ∼3.22 and ∼2.27 Å corresponding to the formal single and triple bonds, respectively. This gives the chromium atoms, as well as the nickel atoms, the favored 18-electron configuration. These species appear to be promising synthetic targets. However, the lowest energy (CpNiC4H4)2Cr2(CO)n (n = 5, 3) structures, as well as two (CpNiC4H4)2Cr2(CO)4 structures ∼10 to 12 kcal/mol in energy above the global minimum, can be dissected into a discrete pseudohalogen (CpNiC4H4)Cr(CO)3 unit and a (CpNiC4H4)Cr(CO)n-3 unit linked by a Cr-Cr bond flanked by one to three generally weakly semibridging CO groups. In most cases, the chromium atoms in the (CpNiC4H4)Cr(CO)n-3 units of these structures have 14-16-electron configurations rather than the favored 18-electron configuration. This leads to triplet and even quintet spin states in the lowest energy structures.

The Ligand‐Based Quintuple Bond‐Shortening Concept and Some of Its Limitations

Herein, the ligand-based concept of shortening quintuple bonds and some of its limitations are reported. In dichromium-diguanidinato complexes, the length of the quintuple bond can be influenced by the substituent at the central carbon atom of the used ligand. The guanidinato ligand with a 2,6-dimethylpiperidine backbone was found to be the optimal ligand. The reduction of its chromium(II) chloride-ate complex gave a quintuply bonded bimetallic complex with a Cr-Cr distance of 1.7056 (12) Å. Its metal-metal distance, the shortest observed in any stable compound yet, is of essentially the same length as that of the longest alkane C-C bond (1.704 (4) Å). Both molecules, the alkane and the Cr complex, are of remarkable stability. Furthermore, an unsupported Cr(I) dimer with an effective bond order (EBO) of 1.25 between the two metal atoms, indicated by CASSCF/CASPT2 calculations, was isolated as a by-product. The formation of this by-product indicates that with a certain bulk of the guanidinato ligand, other coordination isomers become relevant. Over-reduction takes place, and a chromium-arene sandwich complex structurally related to the classic dibenzene chromium complex was observed, even when bulkier substituents are introduced at the central carbon atom of the used guanidinato ligand.

A monotonic increase of formal metal–metal bond orders from one to five upon loss of carbonyl groups from binuclear benzene chromium carbonyls

Benzene forms a binuclear chromium carbonyl derivative (η6-C6H6)2Cr2(μ-CO)3, shown by X-ray crystallography to have a very short CrCr distance, suggesting the formal triple bond required to give each chromium atom the favored 18-electron configuration. We now describe theoretical studies on the entire series of binuclear benzene chromium carbonyls (C6H6)2Cr2(CO)n (n=5,4,3,2,1). The predicted Cr–Cr distances in the lowest energy singlet structures determined by the BP86 method decrease monotonically as carbonyl groups are lost starting from 2.95Å in (C6H6)2Cr2(CO)5 to 1.95Å in (C6H6)2Cr2(CO) corresponding to a steady increase in the formal bond order from one to five. This increase in formal Cr–Cr bond order is also supported by a monotonic increase in the Wiberg bond indices ranging from 0.29 for the single bond in (C6H6)2Cr2(CO)5 to ∼2 for the formal quintuple bond in (C6H6)2Cr2(CO).

Spin dynamics in the unconventional multiferroic AgCrS2

The magnetic excitation spectrum of AgCrS${}_{2}$, a layered multiferroic compound with a collinear four-sublattice antiferromagnetic order, has been investigated by means of time-of-flight inelastic neutron scattering between 5 and 300 K. Coupling mean-field and spin-wave calculations, the experimental spectrum is well reproduced introducing, in the model Hamiltonian, a ferromagnetic exchange interaction between nearest neighbors and a non-negligible antiferromagnetic in-plane next-nearest-neighbor interaction. This study shows that the sign of the magnetic interaction between chromium ions depends on the Cr-Cr distance with a threshold value above which it becomes ferromagnetic and emphasizes the role of the magnetoelastic coupling in the understanding of the physical properties of AgCrS${}_{2}$.

New Ferromagnetic Chromium Chalcogenides, <i>A</i>Cr<sub>5</sub>Te<sub>8</sub> (<i>A</i> = K, Cs and Rb)

New pseudo-hollandite chromium tellurides, ACr5Te8 (A = K, Cs and Rb), have been synthesized. KCr5Te8 is isostructural (type-A; space group C2/m) to ACr5S8, while RbCr5Te8 and CsCr5Te8 crystallize in a different structure (type-B; space group C2/m). All compounds show ferromagnetic transition, in contrast to antiferromagnetic transition in pseudo-hollandite chromium sulfides and selenides. The ferromagnetism of ACr5Te8 would be related to long Cr-Cr distances, band structure or itinerancy.