Unquenched Orbital Angular Momentum Research Articles

An Isolable One-Coordinate Lead(I) Radical with Strong g-Factor Anisotropy.

Lead-based radicals in the oxidation state of +1 are elusive species and are highly challenging to isolate in the condensed phase. In this study, we present the synthesis and characterization of the first isolable free plumbylyne radical 2 bearing a one-coordinate Pb(I) atom. It reacts with an N-heterocyclic carbene (NHC) to afford a two-coordinate NHC-ligated Pb(I) radical 3. 2 and 3 represent the first isolable Pb(I)-based radicals. Theoretical calculations and electron paramagnetic resonance analysis revealed that the unpaired electron mainly resides at the Pb 6p orbital in both radicals. Owing to the unique one-coordinate nature of the Pb atom in 2, it possesses two-fold orbital pseudo-degeneracy and substantial unquenched orbital angular momentum, and exhibits hitherto strongest g-factor anisotropy (gx,y,z=1.496, 1.166, 0.683) amongst main group radicals. Preliminary investigations into the reactivity of 2 unveiled its Pb-centered radical nature, and plumbylenes were isolated as products.

An Isolable One‐Coordinate Lead(I) Radical with Strong g‐Factor Anisotropy

AbstractLead‐based radicals in the oxidation state of +1 are elusive species and are highly challenging to isolate in the condensed phase. In this study, we present the synthesis and characterization of the first isolable free plumbylyne radical 2 bearing a one‐coordinate Pb(I) atom. It reacts with an N‐heterocyclic carbene (NHC) to afford a two‐coordinate NHC‐ligated Pb(I) radical 3. 2 and 3 represent the first isolable Pb(I)‐based radicals. Theoretical calculations and electron paramagnetic resonance analysis revealed that the unpaired electron mainly resides at the Pb 6p orbital in both radicals. Owing to the unique one‐coordinate nature of the Pb atom in 2, it possesses two‐fold orbital pseudo‐degeneracy and substantial unquenched orbital angular momentum, and exhibits hitherto strongest g‐factor anisotropy (gx,y,z=1.496, 1.166, 0.683) amongst main group radicals. Preliminary investigations into the reactivity of 2 unveiled its Pb‐centered radical nature, and plumbylenes were isolated as products.

Monosubstituted Doublet Sn(I) Radical Featuring Substantial Unquenched Orbital Angular Momentum

Due to their intrinsic high reactivity, isolation of heavier analogues of carbynes remains a great challenge. Here, we report the synthesis and characterization of a neutral monosubstituted Sn(I) radical (2) supported by a sterically hindered hydrindacene ligand, which represents the first tin analogue of a free carbyne. Different from all Sn(I/III) species reported thus far, the presence of a sole Sn-C σ bond in 2 renders the remaining two Sn 5p orbitals energetically almost degenerate, of which one is singly occupied and the other is empty. Consequently, its S = 1/2 ground state possesses two-fold orbital pseudo-degeneracy and substantial unquenched orbital angular momentum, as evidenced by one component of its g matrix (1.957, 1.896, and 1.578) being considerably less than 2. Consistent with this unique electronic structure, 2 can bind to an N-heterocyclic carbene to afford a neutral two-coordinate Sn(I) radical and initiate a one-electron transfer to benzophenone to furnish a Sn(II)-ketyl radical anion adduct. As a manifestation of its Sn-centered radical nature, 2 reacts with diphenyl diselenide and p-benzoquinone to form Sn-S and Sn-O bonds, respectively.

Pentagonal-bipyramidal 4d and 5d complexes with unquenched orbital angular momentum as a unique platform for advanced single-molecule magnets: current state and perspectives.

This article overviews the current state and prospects of the concept of advanced single-molecule magnets (SMMs) based on low-spin (S = 1/2) pentagonal-bipyramidal (PBP) 4d3 and 5d3 complexes with unquenched orbital angular momentum. This approach is based on the unique property of PBP 4d3 and 5d3 complexes to cause highly anisotropic spin coupling of perfect uniaxial symmetry, -JzSziSzj - Jxy(SxiSxj + SyiSyj), regardless of the local geometric symmetry. The M(4d/5d)-M(3d) exchange-coupled pairs in the apical positions of the PBP complexes produce Ising-type exchange interactions (|Jz| > |Jxy|), which serve as a powerful source of uniaxial magnetic anisotropy of a SMM cluster. In polynuclear heterometallic 4d/5d-3d complexes embodying PBP 4d/5d units and high-spin 3d ions, anisotropic Ising-type exchange interactions produce a double-well potential with high energy barriers Ueff, which is controlled by the anisotropic exchange parameters Jz, Jxy. Theoretical analysis shows that the barrier is proportional to the difference |Jz - Jxy| and to the number n of the apical 4d/5d-3d pairs in a SMM cluster, Ueff ∝ |Jz - Jxy|n, which provides an opportunity to scale up the barrier Ueff and blocking temperature TB up to the record values. A novel family of 4d/5d complexes with forced PBP coordination provided by structurally rigid planar pentadentate Schiff-base ligands in the equatorial plane is discussed as a better alternative to the cyanometallates. The possibility of a significant increase in the anisotropic exchange parameters Jz, Jxy in PBP complexes with monoatomic apical μ-bridging ligands is examined. The basic principles of molecular engineering the highest barrier through anisotropic exchange interactions of PBP 4d/5d complexes are formulated. The theoretical and experimental results taken together indicate that the concept of high-performance SMMs based on 4d/5d PBP complexes with unquenched orbital angular momentum is an attractive alternative to the currently dominant lanthanide-based SMM strategy.

(Et4N)[WIII(DAPBH)(CN)2], the first pentagonal-bipyramidal W(III) complex with unquenched orbital angular momentum: a novel Ising-type magnetic building block for single-molecule magnets.

The first pentagonal-bipyramidal tungsten(III) complex (Et4N)[WIII(DAPBH)(CN)2] with a N3O2-type Schiff-base ligand and two apical cyanide groups was synthesized and characterized structurally and magnetically. The complex has a low-spin (S = 1/2) ground state and features unquenched orbital angular momentum ML = ±1 causing very strong Ising-type magnetic anisotropy.

Reaching the Maximal Unquenched Orbital Angular Momentum L = 3 in Mononuclear Transition-Metal Complexes: Where, When and How?

The conditions for achieving the maximal unquenched orbital angular momentum L = 3 and the highest magnetic anisotropy in mononuclear 3d complexes with axial coordination symmetry are examined in terms of the ligand field theory. It is shown that, apart from the known linear two-coordinate 3d7 complex CoII(C(SiMe2ONaph)3)2 characterized by record magnetic anisotropy and single-molecule magnet (SMM) performance (with the largest known spin-reversal barrier Ueff = 450 cm−1), the maximal orbital angular momentum L = 3 can also be obtained in linear two-coordinate 3d2 complexes (V3+, Cr4+) and in trigonal-prismatic 3d3 (Cr3+, Mn4+) and 3d8 (Co+, Ni2+) complexes. A comparative assessment of the SMM performance of the 3d2, 3d3 and 3d8 complexes indicates that they are unlikely to compete with the record linear complex CoII(C(SiMe2ONaph)3)2, whose magnetic anisotropy is close to the physical limit for a 3d metal.

High Magnetic Anisotropy of a Square-Planar Iron-Carbene Complex.

Among Earth-abundant catalyst systems, iron-carbene intermediates that perform C-C bond forming reactions such as cyclopropanation of olefins and C-H functionalization via carbene insertion are rare. Detailed descriptions of the possible electronic structures for iron-carbene bonds are imperative to obtain better mechanistic insights and enable rational catalyst design. Here, we report the first square-planar iron-carbene complex (MesPDPPh)Fe(CPh2), where [MesPDPPh]2- is the doubly deprotonated form of [2,6-bis(5-(2,4,6-trimethylphenyl)-3-phenyl-1H-pyrrol-2-yl)pyridine]. The compound was prepared via reaction of the disubstituted diazoalkane N2CPh2 with (MesPDPPh)Fe(thf) and represents a rare example of a structurally characterized, paramagnetic iron-carbene complex. Temperature-dependent magnetic susceptibility measurements and applied-field Mössbauer spectroscopic studies revealed an orbitally near-degenerate S = 1 ground state with large unquenched orbital angular momentum resulting in high magnetic anisotropy. Spin-Hamiltonian analysis indicated that this S = 1 spin system has uniaxial magnetic properties arising from a ground MS = ±1 non-Kramers doublet that is well-separated from the MS = 0 sublevel due to very large axial zero-field splitting (D = -195 cm-1, E/D = 0.02 estimated from magnetic susceptibility data). This remarkable electronic structure gives rise to a very large, positive magnetic hyperfine field of more than +60 T for the 57Fe nucleus along the easy magnetization axis observed by Mössbauer spectroscopy. Computational analysis with complete active space self-consistent field (CASSCF) calculations provides a detailed electronic structure analysis and confirms that (MesPDPPh)Fe(CPh2) exhibits a multiconfigurational ground state. The majority contribution originates from a configuration best described as a singlet carbene coordinated to an intermediate-spin FeII center with a (dxy)2{(dxz),(dz2)}3(dyz)1(dx2-y2)0 configuration featuring near-degenerate dxz and dz2 orbitals.

Slow Magnetic Relaxation in Mono- and Bimetallic Lanthanide Tetraimido-Sulfate S(NtBu)4 2- Complexes.

Lanthanide ions are particularly well‐suited for the design of single‐molecule magnets owing to their large unquenched orbital angular momentum and strong spin‐orbit coupling that gives rise to high magnetic anisotropy. Such nanoscopic bar magnets can potentially revolutionize high‐density information storage and processing technologies, if blocking temperatures can be increased substantially. Exploring non‐classical ligand scaffolds with the aim to boost the barriers to spin‐relaxation are prerequisite. Here, the synthesis, crystallographic and magnetic characterization of a series of each isomorphous mono‐ and dinuclear lanthanide (Ln=Gd, Tb, Dy, Ho, Er) complexes comprising tetraimido sulfate ligands are presented. The dinuclear Dy complex [{(thf)2Li(NtBu)2S(tBuN)2DyCl2}2 ⋅ ClLi(thf)2] (1c) shows true signatures of single‐molecule magnet behavior in the absence of a dc field. In addition, the mononuclear Dy and Tb complexes [{(thf)2Li(NtBu)2S(tBuN)2LnCl2(thf)2] (2b,c) show slow magnetic relaxation under applied dc fields.

Two-Coordinate, Nonlinear Vanadium(II) and Chromium(II) Complexes of the Silylamide Ligand–N(SiMePh2)2: Characterization and Confirmation of Orbitally Quenched Magnetic Moments in Complexes with Sub-d5 Electron Configurations

The two-coordinate metal amide complexes V{N(SiMePh2)2}2 (1) and Cr{N(SiMe2Ph)2}2 (2) were synthesized by reaction of two equivalents of LiN(SiMePh2)2 with VI2(THF)4 or CrCl2(THF)2 in n-hexane. Their crystal structures showed that they have bent coordination, N-V-N = 137.0(4)°, N-Cr-N = 139.19(5)°, at the metals. The vanadium complex (1) displayed no tendency to isomerize as previously observed for some V(II) amido complexes. Curie fits of SQUID magnetic measurements afforded magnetic moments of 3.36 (1) and 4.68 (2) μB, consistent with high-spin configurations. These values are lower than the spin-only values of 3.88 and 4.90 μB expected for d3 and d4 complexes, suggesting a significant unquenched orbital angular momentum contribution to the overall moment, which is lower as a result of the positive spin-orbit coupling constants.

A Molecular Crystal Shows Multiple Correlated Magnetic and Ferroelectric Switchings

Simultaneous control of the magnetic and electric properties of materials is crucial for their application in next-generation memory and sensor devices. Herein, we report a single-crystal Co(II) co...

Magnetic fluctuations and the spin–orbit interaction in Mott insulating CoO

Motivated by the presence of an unquenched orbital angular momentum in CoO, a team at Chalk River, including a recently hired research officer Roger Cowley, performed the first inelastic neutron scattering experiments on the classic Mott insulator [Sakurai et al 1968 Phys. Rev. 167 510]. Despite identifying two magnon modes at the zone boundary, the team was unable to parameterise the low energy magnetic excitation spectrum below TN using conventional pseudo-bosonic approaches, instead achieving only qualitative agreement. It would not be for another 40 years that Roger, now at Oxford and motivated by the discovery of the high-Tc cuprate superconductors [Bednorz and Muller 1986 Z. Phys. B 64 189], would make another attempt at the parameterisation of the magnetic excitation spectrum that had previously alluded him at the start of his career. Upon his return to CoO, Roger found a system embroiled in controversy, with some of its most fundamental parameters still remaining undetermined. Faced with such a formidable task, Roger performed a series of inelastic neutron scattering experiments in the early 2010s on both CoO and a magnetically dilute structural analogue Mg0.97Co0.03O. These experiments would prove instrumental in the determination of both single-ion [Cowley et al 2013 Phys. Rev. B 88 205117] and cooperative magnetic parameters [Sarte et al 2018 Phys. Rev. B 98 024415] for CoO. Both these sets of parameters would eventually be used in a spin–orbit exciton model [Sarte et al 2019 Phys. Rev. B 100 075143], developed by his longtime friend and collaborator Bill Buyers, to successfully parameterise the complex spectrum that both measured at Chalk River almost 50 years prior. The story of CoO is of one that has come full circle, one filled with both spectacular failures and intermittent, yet profound, little victories.

Role of coupling between surface orbitals in SOC enhanced spin splitting

In this study we investigate the role of coupling between surface orbitals in a giant spin splitting (GSS) observed in the Pb/Ge(111)-1 × 1 adsorption system along Γ−M−Γ′. We report, based on the density functional theory that, the magnitude of the GSS depends on the bonding structure of the Pb/Ge interface, varying from 242 to 667 meV for the metallic surface bands. The splitting is shown to be SOC enhanced, with ∼ 93% of the effect being of SOC origin. The split-energy difference observed in the system is a result of a different coupling strength between px/py(Pb) and pz(Pb) orbitals, which produces corresponding values of unquenched orbital angular momentum. The described spin-split pattern corresponds to those observed in Tl/Si(111)-1 × 1, Bi/Si(111)-(3×3)R30∘, and 4/3ML Pb/Ge(111)-(3×3)R30∘, which suggests that, their GSS may also be SOC enhanced.

Covalency and magnetic anisotropy in lanthanide single molecule magnets: the DyDOTA archetype.

Lanthanide ions when complexed by polyamino-polycarboxylate chelators form a class of compounds of paramount importance in several research and technological areas, particularly in the fields of magnetic resonance and molecular magnetism. Indeed, the gadolinium derivative is one of the most employed contrast agents for magnetic resonance imaging while the dysprosium one belongs to a new generation of contrast agents for T2-weighted MRI. In molecular magnetism, Single Molecule Magnets (SMMs) containing lanthanide ions have become readily popular in the chemistry and physics communities since record energy barriers to the reversal of magnetization were reported. The success of lanthanide complexes lies in their large anisotropy due to the contribution of the unquenched orbital angular momentum. However, only a few efforts have been made so far to understand how the f-orbitals can be influenced by the surrounding ligands. The outcomes have been rationalized using mere electrostatic perturbation models. In the archetype compound [Na{Dy(DOTA) (H2O)}]·4H2O (Na{DyDOTA}·4H2O) an unexpected easy axis of magnetization perpendicular to the pseudo-tetragonal axis of the molecule was found. Interestingly, a dependency of the orientation of the principal magnetization axis on the simple rotation of the coordinating apical water molecule (AWM) - highly relevant for MRI contrast - around the Dy-OAWM bond was predicted by ab initio calculations, too. However, such a behaviour has been contested in a subsequent paper justifying their conclusions on pure electrostatic assumptions. In this paper, we want to shed some light on the nature of the subtle effects induced by the water molecule on the magnetic properties of the DyDOTA archetype complex. Therefore, we have critically reviewed the structural models already published in the literature along with new ones, showing how the easy axis orientation can dangerously depend on the chosen model. The different computed behaviors of the orientation of the easy axis of magnetization have been rationalized as a function of the energy gap between the ground and the first excited doublet. Magneto-structural correlations together with a mapping of the electrostatic potential generated by the ligands around the Dy(iii) ion through a multipolar expansion have also been used to evidence and quantify the covalent contribution of the AWM orbitals.

Suppressed and enhanced spin polarization in the 1ML-Pb/Ge(1 1 1)-1 [formula omitted] 1 system

It is shown, based on the density functional theory (DFT), that the spin splitting of surface electronic states induced by a Pb monolayer on the Ge(111)-1 × 1 surface depends on the bonding structure of the Pb/Ge interface and may be either significant, ∼0.8 eV, (H3/T4) or completely suppressed (T1). It is also shown that for the former the bonding configuration facilitates an emergence of unquenched orbital angular momentum L along Γ-K-M direction, which then lifts the spin degeneracy of the electronic states through the spin-orbit coupling (SOC) of electrons in Pb. Along with the DFT data, we present a complementary analysis conducted withing the orbital Rashba framework, which provides an additional insight into the SOC-induced splitting.

Orbital angular momentum analysis for giant spin splitting in solids and nanostructures

Giant spin splitting (GSS) of electronic bands, which is several orders of magnitude greater than the standard Rashba effect has been observed in various systems including noble-metal surfaces and thin films of transition-metal dichalcogenides. Previous studies reported that orbital angular momentum (OAM) is not quenched in some GSS materials and that the atomic spin-orbit interaction (SOI) generates spin splitting in some solid states via the interorbital hopping. Although the unquenched OAM may be closely related to the interorbital hopping, their relationship is hardly studied in the aspect of using the unquenched OAM as a control parameter of GSS. Here, we analyze OAM in GSS materials by using the interorbital-hopping mechanism and first-principles calculations. We report that the interatomic hopping between different-parity orbitals, which is generated by specific broken mirror symmetry, produces k-dependent OAM, resulting in valley-dependent GSS in WSe2 monolayer, Rashba-type GSS in Au (111) surface, and Dresselhaus-type GSS in bulk HgTe. We also demonstrate systematic control of OAM by pressure, external fields, and substrates, thereby controlling the spin splitting, and discuss the temperature dependence of OAM. Our results provide a simplified picture for systematic design and control of GSS materials.

Some new trends in the design of single molecule magnets

Abstract In this review we briefly discuss some new trends in the design of single molecule magnets based on transition (3d, 4d, 5d) and rare-earth (4f) metal ions. Within this broad theme the emphasis of the present review is placed on the molecules which exhibit strong magnetic anisotropy originating from the unquenched orbital angular momenta in the ground orbitally degenerate (or quasi-degenerate) states. Along with the general concepts we consider selected examples of the systems comprising orbitally-degenerate metal ions and demonstrate how one can benefit from strong single-ion anisotropy arising from the first-order orbital angular momentum. The role of crystal fields, spin-orbit coupling and structural factors is discussed. Some observation stemming from the analysis of the isotropic exchange interactions, magnetic anisotropy and strongly anisotropic orbitally-dependent superexchange are summarized as guiding rules for the controlled design of single molecule magnets exhibiting high barriers for magnetization reversal and, consequently, high blocking temperatures.

Large Magnetic Anisotropy in Linear CoII Complexes – Ab Initio Investigation of the Roles of Ligand Field, Structural Distortion, and Conformational Dynamics

Linear or near‐linear bicoordinate mononuclear CoII complexes are studied as potential single‐molecule magnets owing to the strong spin–orbit coupling constant of CoII and its low coordination number, which results in the retention of the unquenched metal‐orbital angular momentum. The spin–orbit‐coupled unquenched orbital angular momentum of the metal center produces strong magnetic anisotropy through ligand‐field interactions. The role of the ligand environment, structural distortions, and conformational changes on the magnetic anisotropy of CoII complexes are investigated through ab initio electronic‐structure calculations. The zero‐field splitting parameters, g tensors, and transition‐magnetic‐moment matrix elements among the Kramers pairs are evaluated to obtain the effective anisotropy barriers (Ueff) and the mechanism for the relaxation of magnetization in a series of CoII complexes, for which the estimated values of Ueff range between 394 and 974 cm–1 and include the largest effective anisotropy barriers reported for transition‐metal complexes. The calculations reveal that the ligand‐field strength, structural distortion, and conformational changes not only affect the magnetic anisotropy barrier but also significantly alter the mechanism of relaxation of the magnetic moments.

Anisotropic Change in the Magnetic Susceptibility of a Dynamic Single Crystal of a Cobalt(II) Complex.

Atypically anisotropic and large changes in magnetic susceptibility, along with a change in crystalline shape, were observed in a CoII complex at near room temperature. This was achieved by combining oxalate molecules, acting as rotor, and a CoII ion with unquenched orbital angular momentum. A thermally controlled 90° rotation of the oxalate counter anion triggered a symmetry-breaking ferroelastic phase transition, accompanied by contraction-expansion behavior (ca. 4.5 %) along the long axis of a rod-like single crystal. The molecular rotation induced a minute variation in the coordination geometry around the CoII ion, resulting in an abrupt decrease and a remarkable increase in magnetic susceptibility along the direction perpendicular and parallel to the long axis of the crystal, respectively. Theoretical calculations suggested that such an unusual anisotropic change in magnetic susceptibility was due to a substantial reorientation of magnetic anisotropy induced by slight disruption in the ideal D3 coordination environment of the complex cation.

3d -electron Heisenberg pyrochlore Mn2Sb2O7

In frustrated magnetic systems, geometric constraints or the competition amongst interactions introduce extremely high degeneracy and prevent the system from readily selecting a low-temperature ground state. The most frustrated known spin arrangement is on the pyrochlore lattice, but nearly all magnetic pyrochlores have unquenched orbital angular momentum, constraining the spin directions through spin-orbit coupling. Pyrochlore Mn$_2$Sb$_2$O$_7$ is an extremely rare Heisenberg pyrochlore system, with directionally-unconstrained spins and low chemical disorder. We show that it undergoes a spin-glass transition at 5.5K, which is suppressed by disorder arising from Mn vacancies, indicating this ground state to be a direct consequence of the spins' interactions. The striking similarities to $3d$ transition metal pyrochlores with unquenched angular momentum suggests that the low spin-orbit coupling in the $3d$ block makes Heisenberg pyrochlores far more accessible than previously imagined.

Synthesis, Structure, and Bonding for Bis(permethylpentalene)diiron.

The synthesis of the first homoleptic double metallocene complex of iron, Fe2Pn*2 (Pn* = permethylpentalene, C8Me6) is described. The structural and electronic properties of Fe2Pn*2 have been characterized by NMR and EPR spectroscopy, single crystal X-ray diffraction, magnetic measurements, cyclic voltammetry, and DFT calculations. Fe2Pn*2 adopts a Ci symmetry in the solid state with a Fe-Fe distance of 2.3175(9) Å, slightly lower than the sum of radii in metallic iron. Magnetic measurements in solution, and of the solid phase between 60 and 300 K, indicate that Fe2Pn*2 is a triplet (S = 1) paramagnet, with effective magnetic moments (μeff) of 3.4 and 3.48 μB, respectively. DFT calculations indicate the origin of this high magnetic moment is likely to be unquenched orbital angular momentum contributions from two SOMOs which have metal d character. Cyclic voltammetry studies demonstrate that Fe2Pn*2 can access four charge states (-1, 0, +1, +2).