Theoretical Study of the Localized Spin States at the Surface of a Ferromagnetic Diatomic Alloys

Quantum entanglement between the spin states of a metal center and radical ligands is suggested in an iron(II) [Fe(dipyvd)2]2+ compound (dipyvd = 1-isopropyl-3,5-dipyridil-6-oxoverdazyl). Wave function ab initio (Difference Dedicated Configuration Interaction, DDCI) inspections were carried out to stress the versatility of local spin states. We named this phenomenon excited state spinmerism, in reference to our previous work (see Roseiro et al., ChemPhysChem 2022, e202200478) where we introduced the concept of spinmerism as an extension of mesomerism to spin degrees of freedom. The construction of localized molecular orbitals allows for a reading of the wave functions and projections onto the local spin states. The low-energy spectrum is well-depicted by a Heisenberg picture. A 60 cm-1 ferromagnetic interaction is calculated between the radical ligands with the Stotal = 0 and 1 states largely dominated by a local low-spin SFe = 0. In contrast, the higher-lying Stotal = 2 states are superpositions of the local SFe = 1 (17%, 62%) and SFe = 2 (72%, 21%) spin states. Such mixing extends the traditional picture of a high-field d6 Tanabe-Sugano diagram. Even in the absence of spin-orbit coupling, the avoided crossing between different local spin states is triggered by the field generated by radical ligands. This puzzling scenario emerges from versatile local spin states in compounds which extend the traditional views in molecular magnetism.

The spectral change in the 3d resonant X-ray inelastic scattering (RIXS) induced by the spin-state transition between Kondo singlet (KS) and localized spin (LS) state is theoretically investigated for γ-like Ce intermetallics by means of a single impurity Anderson model. The basis configurations with an electron–hole pair are included in the calculation within the configuration interaction scheme, in addition to the intra-atomic full multiplet coupling of the Ce impurity. A distinct spectral change is found across the KS–LS transition in the RIXS excited at the charge-transfer satellite of the 3d X-ray absorption spectrum (XAS) under a polarized geometry. In contrast, the 3d XAS and RIXS spectra under a depolarized geometry are rather insensitive to the spin-state transition.

Recent experiments have suggested a possibility of room-temperature ferromagnetism in graphite-like materials. We analyzed multiple spin states in asymmetric graphene molecules to find the mechanism responsible for ferromagnetism. First principle density functional theory was applied to calculate ground state spin density, energy, and atom position depending on each spin state. Molecules with dihydrogenated zigzag edges like C64H27, C56H24, C64H25, C56H22, and C64H23 indicated that the highest spin state in every molecule is the most stable having an energy difference of kT = 3000 K with the next spin state. In contrast, nitrogen substituted molecules like C59N5H22, C52N4H20, C61N3H22, C54N2H20, and C63N1H22 demonstrated opposite results where the lowest spin state was the most stable. The magnetic stability of graphene molecules can be explained through three key factors depending on the edge specified localized spin state, the exchange interaction between parallel spins inside a molecule, and optimized atom position. We intend to apply these results to design carbon-based magnets, ultra high density information storage, and spintronic devices.

We have investigated the charge dynamics and local spin state in half-doped layered cobaltates La${}_{1.5}$Ca${}_{0.5}$CoO${}_{4}$ and La${}_{1.5}$Sr${}_{0.5}$CoO${}_{4}$. By examining temperature-dependent infrared-active phonon modes, we found clear signatures of the structural distortion related to the spin-state transition around ${T}_{S}=400--600$ K. While the kinetic energy of the electronic system, estimated by the low-energy spectral weight in the optical conductivity spectrum, as well as the optical gap energy is strongly affected by the charge-order instability, it shows a noticeable enhancement upon the spin-state transition which is attributed to the release of the spin blockade of the electron hopping between the low-spin (Co${}^{3+}$) and high-spin (Co${}^{2+}$) states. These understandings of the spin state are further evidenced by the reexamination of high-temperature Seebeck coefficient and magnetic susceptibility.

In this work, we investigate the scattering phenomena at the inhomogeneous boundary of a magnetic interface in two-dimensional (2D)-triangular ferromagnetic waveguide. We especially examine two ferromagnetic interfaces, named heavy and superheavy solitons in 2D-triangular lattices. The system is supported on a nonmagnetic substrate. Therefore, each spin site in the lattice can be considered free from magnetic interactions with its environment. The spin excitations in the modeled system are studied by the field matching theory (FMT). Their magnons transmission/reflection, localized spin states as well as the local density of spin states (LDOS) are calculated and analyzed. They are derived as elements of a Landauer type scattering matrix. The magnonic spectra are calculated specifically for two distinct interfaces, which join the two semi-infinite perfect 2D-triangular waveguides. The inter-atomic magnetic exchange is varied on the interface domain to investigate the consequences of magnetic softening and hardening for the calculated magnetic properties. The numerical results show the interference effects between the incident magnons and the localized spin states on the interface domain, with characteristic magnetic resonances that vary according to each configuration. The numerical results yield an understanding for the relation between the coherent magnon propagation and the interface configuration in the perfect 2D-triangular system.

Anodic oxygen evolution reaction (OER) that involves a spin-dependent singlet-to-triplet oxygen changeover largely restrains the water electrolysis efficiency for hydrogen production. However, the modulation of spin state is still challengeable for most OER catalysts, and there remains a debate on deciphering the active spin state in OER. Here, we pioneered an asymmetric Fe-incorporated NiPS3 tactic system to retune the metal localized spin for efficient OER electrocatalysis. It is unraveled that the synergistic effect of medium-spin FeIII site and P/S coordination can effectively boost OER activity and Cl resistance selectivity in alkaline/sea water. Resultantly, the Fe/NiPS3-based asymmetric electrodes exhibit low cell voltages of 1.50volts/1.52volts in alkaline/sea water at 10milliamperes per square centimeter, together with a sustainable retention for 1000 hours. It also delivers the durable performance in anion exchange membrane water electrolyzers with a low operation voltage at 45°C. This research navigates the atomic localized spin state as the criterion in rationalizing efficient nonprecious alkaline/sea water oxidation electrocatalysts.

Due to the high energy barrier, slow reaction kinetics, and complex reaction environments of Li-CO2 batteries, the development of durable and efficient catalysts is essential. Transition metal oxides are promising for their availability, stability, and 3d electronic features, with spin states playing an important role in CO2 activation. In this study, the local spin states are regulated by incorporating Ni into Co3O4 and its impact on activity in Li-CO2 batteries is explored. The results show that Ni atoms with high spin states in Ni0.1Co2.9O4 facilitate electron transfer from the catalyst to the unoccupied orbitals of CO2, providing sufficient active sites for the nucleation and growth of small Li2CO3 crystals. These small crystals have a low decomposition barrier, leading to improved battery efficiency. Therefore, Ni0.1Co2.9O4 shows superior catalytic performance with an overpotential of 0.72V and an energy efficiency of ≈70% after 500h. This work provides insights into the relationship between spin states and CO2 reactions, highlighting a promising avenue for developing high-performance metal-CO2 batteries.

We present a theoretical study of electron transport in Ni4 molecular transistors in the presence of Zeeman spin splitting and magnetic quantum coherence (MQC). The Zeeman interaction is extended along the leads which produces gaps in the energy spectrum which allow electron transport with spin polarized along a certain direction. We show that the coherent states in resonance with the spin up or down states in the leads induces an effective coupling between localized spin states and continuum spin states in the single molecule magnet and leads, respectively. We investigate the conductance at zero temperature as a function of the applied bias and magnetic field by means of the Landauer formula, and show that the MQC is responsible for the appearence of resonances. Accordingly, we name them MQC resonances.

A synthetic protocol is developed for the preparation of a thallium complex featuring the tris(phosphino)borate ligand [PhBP3] ([PhBP3] = [PhB(CH2PPh2)3]-). The transmetallating reagent, [PhBP3]Tl, is characterized by single crystal X-ray diffraction and solution NMR spectroscopy, and is the first example of a stable homoleptic Tl(I)-phosphine complex. The synthesis and characterization of [PhBP3]Co-X (X = I, Br or Cl) is discussed. These halide complexes are structurally characterized and magnetic investigations establish that they are low spin when monomeric. The low spin iodide complex is a monomer in solution and in the solid state. The other halides exhibit a monomer/dimer equilibrium that complicates their magnetic behavior. Theoretical calculations help provide a rationale as to why these pseudotetrahedral species are low spin. A classic high spin species supported by [PhBP3] is compared to the low spin complexes. Spin state control involving pseudotetrahedral [PhBP3]Co(II) complexes is explored. Both high and low spin, as well as spin crossover, complexes are synthesized and structurally characterized. The complexes are discussed in terms of the relationship between local geometry and spin state. Changing the axial or tripodal ligand can cause a different spin state to be favored. Since the energy difference between the states is small, ligand changes at remote positions from the metal center have a significant effect on spin crossover phenomena. Theoretical calculations help illuminate why the low spin state is preferred for many of the complexes. The first examples of cobalt imide complexes ([PhBP3]Co≡NR (R = aryl or alkyl)) are prepared and they are supported by the [PhBP3] ligand. These diamagnetic species are evaluated by NMR and single crystal X-ray diffraction. Theoretical studies suggest that they have a similar molecular orbital bonding scheme as the previously prepared group 9 imides. A cobalt μ2-bridging nitride complex (([PhBP3]Co)2(μ-N)) is synthesized and structurally characterized. This mixed-valence species is evaluated by magnetometry to determine its ground state, which is low spin (S = ½). Several cobalt diazoalkane complexes are prepared. These diamagnetic species adopt two different bonding modes depending on the nature of the diazoalkane ligand.

Iron and nitrogen codoped carbon (Fe-N-C) materials are promising alternatives to precious metal catalysts for the carbon dioxide electrochemical reduction reaction (CO2RR); however, the influence of the oxidation state, spin state, N-type and local environment of Fe-N on its catalytic activity remains poorly understood. In this study, we employed density functional theory (DFT) calculations to evaluate the catalytic activity of the pyridine-type FeIII/IIN4 motifs at the armchair and zigzag edges, the activity of the pyrrole-type FeIII/IIN4 sites in the bulk plane of carbon-based materials for the two-electron CO2RR by analyzing the stability of initial reactants, free-energy evolutions and energy barriers for the possible elementary reactions in the different spin states. The Fe ions in the armchair-edge pyridine-type FeN4 are mainly in the +2 oxidation state, and use the high spin state in the spin uncoupling manner to achieve the most efficient CO2-COOH-CO conversion. In contrast, the zigzag-edge pyridine-type FeIIN4 employs the medium spin state in the spin uncoupling manner to achieve the highest catalytic activity in the two-electron CO2RR. However, the Fe ions in the pyrrole-type bulk-hosted FeN4 mainly remain in the +3 valence state during the conversion process of CO2 to CO and utilize the medium spin state with spin coupling to obtain the highest catalytic activity. The corresponding kinetic analyses show that the armchair-edge pyridine-type FeIIN4 catalyst exhibited the best catalytic performance among the three cases. Consequently, these findings present significant insights into the design of Fe single-atom catalysts for enhancing CO2RR catalytic activity by producing more armchair-edge pyridine-type FeN4 sites, which may be constructed by introducing micropores in the carbon materials.

Hydride complexes are important in catalysis and in iron–sulfur enzymes like nitrogenase, but the impact of hydride mobility on local iron spin states has been underexplored. We describe studies of a dimeric diiron(ii) hydride complex using X-ray and neutron crystallography, Mössbauer spectroscopy, magnetism, DFT, and ab initio calculations, which give insight into the dynamics and the electronic structure brought about by the hydrides. The two iron sites in the dimer have differing square-planar (intermediate-spin) and tetrahedral (high-spin) iron geometries, which are distinguished only by the hydride positions. These are strongly coupled to give an Stotal = 3 ground state with substantial magnetic anisotropy, and the merits of both localized and delocalized spin models are discussed. The dynamic nature of the sites is dependent on crystal packing, as shown by changes during a phase transformation that occurs near 160 K. The change in dynamics of the hydride motion leads to insight into its influence on the electronic structure. The accumulated data indicate that the two sites can trade geometries by rotating the hydrides, at a rate that is rapid above the phase transition temperature but slow below it. This small movement of the hydrides causes large changes in the ligand field because they are strong-field ligands. This suggests that hydrides could be useful in catalysis not only due to their reactivity, but also due to their ability to rapidly modulate the local electronic structure and spin states at metal sites.

1,5-Dimethyl-3-(2,2'-bipyridine-6-yl)-6-oxoverda-zyl (bipyvd) was used as a tridentate radical ligand toward iron(II) perchlorate to yield bis(1,5-dimethyl-3-(2,2'-bipyridine-6-yl)-6-oxoverdazyl)iron(II) perchlorate, [Fe(bipyvd)2] (ClO4)2. The single-crystal X-ray Fe-N distances are compatible with a low spin (SFe = 0) iron(II) center surrounded by two bipyvd radical ligands. A similar conclusion is reached from difference dedicated configuration interaction (DDCI) wave function calculations, which support the coupling of radicals through a closed-shell metal ion bridge. The singlet-triplet splitting is ferromagnetic, with a calculated exchange coupling constant JLLSFe=0 = +120 cm-1. Higher in energy, the calculated spin states split into two subsets successively characterized by pure local spin states SFe = 2 and SFe = 1. In contrast, the coordination sphere exhibits either a pure local spin state or a superposition of SL = 1 and SL = 0 local spin states, a phenomenon previously coined into spinmerism. A marked modification of the ligand-ligand ferromagnetic coupling is evaluated, with JLLSFe=2 = +89 cm-1 and JLLSFe=1 = +140 cm-1, whereas the metal-ligand interactions remain almost constant at ca. +290 cm-1. The control of the magnetic interactions between organic radicals through a spin-crossover ion revisits the traditional picture dominated by the metal ions and stresses the manifestation of spin entanglement between the coordination sphere and the metal center environment.

A nonhelical spin texture was observed in the centrosymmetric superconductor beta-PdBi2 using an imaging-type spin- and angle-resolved spectroscopy. The observed surface and bulk states near the Fermi energy are found to be spin polarized with nonhelical textures. First-principles calculations and effective models show that the inter-and intralayer hoppings account for the complex spin texture and thus play a significant role in the spatial distribution of the layer-locked spin states. Our work not only provides insights into the local spin states in inversion-symmetric systems but also paves the way to the identification of the nature of superconducting pairing in the presence of a complex spin texture in beta-PdBi2 and the related centrosymmetric superconductors.

In recent years, nano-sized systems involving local charge or spin states have received wide interests because of their potential application in emerging fields such as quantum information and quantum computation. For instance, organometallic molecular complexes may serve as building blocks of quantum storage devices, because the spin-unpaired d or f electrons at transition metal centers may be employed to construct spin qubits. Moreover, if the system contains strong electron-electron interaction, the involving local quantum states are subject to prominent electron correlation effects (such as the Kondo effect). Theoretically, spatially confined nano-systems are often described by quantum impurity models. Thus the accurate prediction of the intrinsic properties of quantum impurity systems and the deep understanding on the response and evolution of local quantum states under external fields or in dissipative environment are fundamentally important for the design and fabrication of quantum devices. The accurate characterization of quantum coherence, correlation, and entanglement in quantum impurity systems remains a great challenge. Enormous efforts have been made to achieve this goal. A variety of theoretical methods have been developed, including the numerical renormalization group method, the quantum Monte Carlo method, and many others. However, all the existing methods are subject to certain limitations regarding accuracy or efficiency. Therefore, we choose to view this problem from a new perspective—the perspective of open quantum systems. Over the past decade, we have developed a formally exact quantum dissipation theory, the hierarchical equations of motion (HEOM) theory, for fermionic open systems. The HEOM theory captures the combined effects of system-environment dissipation, many-body interaction, and non-Markovian memory in a nonperturbative manner. It is capable of addressing static and dynamic responses of system observables in both equilibrium and nonequilibrium situations. We have implemented the HEOM method in our self-designed computer program HEOM-QUICK. We have also devised a series of advanced algorithms which substantially enhance the numerical efficiency of HEOM. The HEOM-QUICK program thus provides an accurate, efficient, and versatile theoretical tool for the investigation of strongly correlated quantum impurity systems. We have applied the HEOM method to study a variety of problems associated with quantum impurity systems. These include the intrinsic properties of quantum impurity models and lattice models, the transient current response of quantum dots to ac voltages, the thermopower and local heating effect in nonequilibrium quantum dots, and the tuning of local spin states in adsorbed molecular magnets. In particular, the HEOM method has been combined with density functional theory (DFT) method, and thus allows for first-principles-based simulation on the precise tuning of local spin states in adsorbed magnetic molecules. Numerical simulations have discovered or reproduced many important quantum phenomena that are essential for relevant experiments, including the Kondo effect, Mott metal-insulator transition, quantum memristive effect, etc. This paper gives a brief overview of our development of the HEOM method for fermionic open systems, as well as its applications to various strongly correlated quantum impurity systems.

In this work, we introduce a computer model and theoretical approach based on the matching technique to investigate the spin precession and the magnetic properties of an ordered magnetic interface joining two ferromagnetic multilayers of type AB, made of 10 spin slabs, obtained by alternative two spin layers A and B. We simulate, particularly, the coherent magnon transmission through spins’ interface, in multilayered thin films, obtained by shearing a part of the film from the other at an angle of 30∘. The individual and total transmittance of bulk magnons of the thin film, scattering coherently at the shearing interface zone and the localized magnonic spin states, are calculated and analyzed. The transmission and reflection spin modes are derived as elements of a Landauer–Büttiker type scattering matrix. The results highlight the localized spin states on the interface shear domain and their interactions with incident magnons. The evolutions of the magnonic spectra can be presented for arbitrary directions of the incident magnons on the boundary zone, for all accessible frequencies in the propagating bands as well as for the magnetic exchange coupling between each spin A(B) and its adjacent sites and their spin intensity. The results demonstrate the dependence of the magnonic spectra for the perfect multilayered films and at the inhomogeneous domain of the interface shear. The analysis of the spectra illustrates the fluctuations, related to Fano resonances, due to the coupling between travelling magnons and the localized modes in the shear interface domain. The calculated spectra could yield useful information concerning the magnetic parameters of such interface slabs in multilayered films.