Multiple Spin States Research Articles

Chemical Origins of Optically Addressable Spin States in Eu2(P2S6) and Eu2(P2Se6).

Lanthanide materials with a 4f7 electron configuration (8S7/2) offer an exciting system for realizing multiple addressable spin states for qubit design. While the 8S7/2 ground state of 4f7 free ions displays an isotropic character, breaking degeneracy of this ground state and excited states can be achieved through local symmetry of the lanthanide and the choice of ligands. This makes Eu2+ attractive as it mirrors Gd3+ in exhibiting the 8S7/2 ground state, capable of seven spin-allowed transitions. In this work, we identify Eu2(P2S6) and Eu2(P2Se6) as viable candidates for optically addressable spin states. The materials feature paramagnetic behavior at 2.0 ≤ T ≤ 400 K and μ0 H = 0.01 and 7 T. The field-dependent magnetization M(H) curve reveals a single-ion spin with effective magnetic moments comparable to the expected magnetic moment of Eu2+. Seven well-defined narrow peaks in the excitation and emission spectra of Eu2+ are resolved. Phonon contributions to the Eu2+ spin environment are evaluated through heat capacity measurements. Insights into how the spin-polarized band structure and density of states of the materials influence the physical properties are described by using density functional theory calculations. These results present a foundational study of Eu2(P2S6) and Eu2(P2Se6) as a feasible platform for harnessing the spin, charge, orbital, and lattice degrees of freedom of Eu2+ for qubit design.

Tunneling current-controlled spin states in few-layer van der Waals magnets.

Effective control of magnetic phases in two-dimensional magnets would constitute crucial progress in spintronics, holding great potential for future computing technologies. Here, we report a new approach of leveraging tunneling current as a tool for controlling spin states in CrI3. We reveal that a tunneling current can deterministically switch between spin-parallel and spin-antiparallel states in few-layer CrI3, depending on the polarity and amplitude of the current. We propose a mechanism involving nonequilibrium spin accumulation in the graphene electrodes in contact with the CrI3 layers. We further demonstrate tunneling current-tunable stochastic switching between multiple spin states of the CrI3 tunnel devices, which goes beyond conventional bi-stable stochastic magnetic tunnel junctions and has not been documented in two-dimensional magnets. Our findings not only address the existing knowledge gap concerning the influence of tunneling currents in controlling the magnetism in two-dimensional magnets, but also unlock possibilities for energy-efficient probabilistic and neuromorphic computing.

Thermodynamics of mantle minerals – III: the role of iron

SUMMARY We expand the scope of HeFESTo by encompassing the rich physics of iron in the mantle, including the existence of multiple valence and spin states. In our previous papers, we considered iron only in its most common state in the mantle: the high-spin divalent (ferrous) cation. We now add ferric iron end-members to six phases, as well as the three phases of native iron. We also add low-spin states of ferrous and ferric iron and capture the behaviour of the high-spin to low-spin transition. Consideration of the multi-state nature of iron, unique among the major elements, leads to developments of our theory, including generalization of the chemical potential to account for the possibility of multiple distinguishable states of iron co-existing on a single crystallographic site, the effect of the high-spin to low-spin transition on seismic wave velocities in multiphase systems, and computation of oxygen fugacity. Consideration of ferric iron also motivates the addition of the chromia component to several phases, so that we now consider the set of components: Ca, Na, Fe, Mg, Al, Si, O and Cr (CNFMASO+Cr). We present the results of a new global inversion of mineral properties and compare our results to experimental observations over the entire pressure–temperature range of the mantle and over a wide range of oxygen fugacity. Applications of our method illustrate how it might be used to better understand the seismic structure, dynamics and oxygen fugacity of the mantle.

New physical insights into the supporting subspace factorization of XMS-CASPT2 and generalization to multiple spin states via spin-free formulation.

This paper introduces a spin-free formulation of the supporting subspace factorization [C. Song and T. J. Martínez, J. Chem. Phys. 149, 044108 (2018)], enabling a reduction in the computational scaling of the extended multi-state complete active space second-order perturbation (XMS-CASPT2) method for arbitrary spins. Compared to the original formulation that is defined in the spin orbitals and is limited to singlet states, the spin-free formulation in this work treats different spin states equivalently, thus naturally generalizing the idea beyond singlet states. In addition, we will present a new way of deriving the supporting subspace factorization with the purpose of understanding its physical interpretation. In this new derivation, we separate the sources that make CASPT2 difficult into the "same-site interactions" and "inter-site interactions." We will first show how the Kronecker sum can be used to remove the same-site interactions in the absence of inter-site interactions, leading to MP2 energy in dressed orbitals. We will then show how the inter-site interactions can be exactly recovered using Löwdin partition, where the supporting subspace concept will naturally arise. The new spin-free formulation maintains the main advantage of the supporting subspace factorization, i.e., allowing XMS-CASPT2 energies to be computed using highly optimized MP2 energy codes and Fock build codes, thus reducing the scaling of XMS-CASPT2 to the same scaling as MP2. We will present and discuss results that benchmark the accuracy and performance of the new method. To demonstrate how the new method can be useful in studying real photochemical systems, the supporting subspace XMS-CASPT2 is applied to a photoreaction sensitive to magnetic field effects. The new spin-free formulation makes it possible to calculate the doublet and quartet states required in this particular photoreaction mechanism.

Light-Controlled Multiconfigurational Conductance Switching in a Single 1D Metal-Organic Wire.

Precise control of multiple spin states on the atomic scale presents a promising avenue for designing and realizing magnetic switches. Despite substantial progress in recent decades, the challenge of achieving control over multiconfigurational reversible switches in low-dimensional nanostructures persists. Our work demonstrates multiple, fully reversible plasmon-driven spin-crossover switches in a single π-d metal-organic chain suspended between two electrodes. The plasmonic nanocavity stimulated by external visible light allows for reversible spin crossover between low- and high-spin states of different cobalt centers within the chain. We show that the distinct spin configurations remain stable for minutes under cryogenic conditions and can be nonperturbatively detected by conductance measurements. This multiconfigurational plasmon-driven spin-crossover demonstration extends the available toolset for designing optoelectrical molecular devices based on SCO compounds.

A general method for locating stationary points on the mixed-spin surface of spin-forbidden reaction with multiple spin states.

Some chemical reactions proceed on multiple potential energy surfaces and are often accompanied by a change in spin multiplicity, being called spin-forbidden reactions, where the spin-orbit coupling (SOC) effects play a crucial role. In order to efficiently investigate spin-forbidden reactions with two spin states, Yang et al. [Phys. Chem. Chem. Phys. 20, 4129-4136 (2018)] proposed a two-state spin-mixing (TSSM) model, where the SOC effects between the two spin states are simulated by a geometry-independent constant. Inspired by the TSSM model, we suggest a multiple-state spin-mixing (MSSM) model in this paper for the general case with any number of spin states, and its analytic first and second derivatives have been developed for locating stationary points on the mixed-spin potential energy surface and estimating thermochemical energies. To demonstrate the performance of the MSSM model, some spin-forbidden reactions involving 5d transition elements are calculated using the density functional theory (DFT), and the results are compared with the two-component relativistic ones. It is found that MSSM DFT and two-component DFT calculations may provide very similar stationary-point information on the lowest mixed-spin/spinor energy surface, including structures, vibrational frequencies, and zero-point energies. For the reactions containing saturated 5d elements, the reaction energies by MSSM DFT and two-component DFT agree very well within 3 kcal/mol. As for the two reactions OsO+ + CH4 → OOs(CH2)+ + H2 and W + CH4 → WCH2 + H2 involving unsaturated 5d elements, MSSM DFT may also yield good reaction energies of similar accuracy but with some counterexamples. Nevertheless, the energies may be remarkably improved by a posteriori single point energy calculations using two-component DFT at the MSSM DFT optimized geometries, and the maximum error of about 1 kcal/mol is almost independent of the SOC constant used. The MSSM method as well as the developed computer program provides an effective utility for studying spin-forbidden reactions.

New Gradient Correction Scheme for Electronically Nonadiabatic Dynamics Involving Multiple Spin States

It has been recommended that the best representation to use for trajectory surface hopping (TSH) calculations is the fully adiabatic basis in which the Hamiltonian is diagonal. Simulations of intersystem crossing processes with conventional TSH methods require an explicit computation of nonadiabatic coupling vectors (NACs) in the molecular-Coulomb-Hamiltonian (MCH) basis, also called the spin-orbit-free basis, in order to compute the gradient in the fully adiabatic basis (also called the diagonal representation). This explicit requirement destroys some of the advantages of the overlap-based algorithms and curvature-driven algorithms that can be used for the most efficient TSH calculations. Therefore, although these algorithms allow one to perform NAC-free simulations for internal conversion processes, one still requires NACs for intersystem crossing. Here, we show that how the NAC requirement is circumvented by a new computation scheme called the time-derivative-matrix scheme.

Two-dimensional short-range spin-spin correlations in the layered spin- 32 maple leaf lattice antiferromagnet Na2Mn3O7 with crystal stacking disorder

We report the nature of magnetic structure, and microscopic spin-spin correlations and their dependence on the underlying crystal structure of the geometrically frustrated layered spin-$\frac{3}{2}$ maple leaf lattice (MLL) antiferromagnet ${\mathrm{Na}}_{2}{\mathrm{Mn}}_{3}{\mathrm{O}}_{7}$ by a comprehensive neutron diffraction study. Crystal structural studies by x-ray and neutron diffraction reveal that the MLL layers (constituted by ${\mathrm{Mn}}_{3}{\mathrm{O}}_{7}{}^{2\ensuremath{-}}$ units) are well separated by nonmagnetic Na layers. The studies also conclude the presence of stacking faults (in-plane sliding of magnetic MLL layers) as well as a distortion in the MLL of ${\mathrm{Mn}}^{4+}$. Temperature dependent magnetic susceptibility, heat capacity, and neutron diffraction data yield a short-range antiferromagnetic (AFM) ordering below $\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ without a long-range magnetic ordering down to 1.5 K. The analysis of the diffuse magnetic neutron scattering patterns by the reverse Monte Carlo method reveals two-dimensional (2D) spin-spin correlations within the MLL layers. Additionally, we establish a relation between the correlation length of the short-range magnetic ordering with the stacking faults through a varying synthesis condition. The present study, therefore, explores a microscopic picture of the crystal and spin structures, as well as their correlation; hence it provides experimental insight of the magnetic ordering in a MLL AFM. Further, we have outlined the formation of several 2D frustrated lattice geometries having triangular plaquettes, including the MLL, by crystal engineering of the triangular lattice, and their role in the stabilization of multiple unique chiral spin states which opens up the door for study of unique chiral spin states.

Redox-Responsive MRI Probes Based on First-Row Transition-Metal Complexes.

The presence of multiple oxidation and spin states of first-row transition-metal complexes facilitates the development of switchable MRI probes. Redox-responsive probes capitalize on a change in the magnetic properties of the different oxidation states of the paramagnetic metal ion center upon exposure to biological oxidants and reductants. Transition-metal complexes that are useful for MRI can be categorized according to whether they accelerate water proton relaxation (T1 or T2 agents), induce paramagnetic shifts of 1H or 19F resonances (paraSHIFT agents), or are chemical exchange saturation transfer (CEST) agents. The various oxidation state couples and their properties as MRI probes are summarized with a focus on Co(II)/Co(III) or Fe(II)/Fe(III) complexes as small molecules or as liposomal agents. Solution studies of these MRI probes are reviewed with an emphasis on redox changes upon treatment with oxidants or with enzymes that are physiologically important in inflammation and disease. Finally, we outline the challenges of developing these probes further for in vivo MRI applications.

Dispersive Readout of Molecular Spin Qudits

We study the physics of a magnetic molecule described by a "giant" spin with multiple ($d > 2$) spin states interacting with the quantized cavity field produced by a superconducting resonator. By means of the input-output formalism, we derive an expression for the output modes in the dispersive regime of operation. It includes the effect of magnetic anisotropy, which makes different spin transitions addressable. We find that the measurement of the cavity transmission allows to uniquely determine the spin state of the qudits. We discuss, from an effective Hamiltonian perspective, the conditions under which the qudit read-out is a non-demolition measurement and consider possible experimental protocols to perform it. Finally, we illustrate our results with simulations performed for realistic models of existing magnetic molecules.

FeN4-doped carbon nanotubes derived from metal organic frameworks for effective degradation of organic dyes by peroxymonosulfate: Impacts of FeN4 spin states

• FeN 4 -doped carbon nanotubes by ball milling and pyrolysis of ZIF-8 and MIL-101. • D 2 -FeN 4 the main active site in PMS activation. • 1 O 2 the major active species in the degradation of organic pollutants. • Minor contributions from • OH and SO 4 ∙ - radicals to pollutant degradation. Development of low-cost, high-performance catalysts for the effective degradation of organic dyes is of both fundamental and technological significance for environmental remediation. Herein, FeN 4 -doped carbon nanotubes exhibit a remarkable catalytic activity towards the degradation of acid orange 7 (AO7) in the presence of peroxymonosulfate (PMS). This is accounted for by the abundant well-dispersed FeN 4 sites and appropriate adsorption energy. Radical quenching experiments and electron paramagnetic resonance measurements suggest that singlet oxygen is the main reactive oxygen species. 57 Fe Mossbauer spectroscopy measurements show that the FeN 4 moieties contain multiple spin states, and in conjunction with density functional theory calculations, confirm that FeN 4 with a low/medium spin state serves as the key sites for PMS activation and hence AO7 degradation. Results from this study highlight the critical role of spin states in FeN 4 in the generation of singlet oxygen for effective degradation of organic pollutants.

Constructive Quantum Interference in Photochemical Reactions.

Interferences emerge when multiple pathways coexist together, leading toward the same result. Here, we report a theoretical study for a reaction scheme that leads to constructive quantum interference in a photoassociation (PA) reaction of a 87Rb Bose-Einstein condensate where the reactant spin state is prepared in a coherent superposition of multiple bare spin states. This is achieved by changing the reactive scattering channel in the PA reaction. As the origin of coherent control comes from the spin part of the wavefunction, we show that it is sufficient to use radio frequency (RF) coupling to achieve the superposition state. We simulate the RF coupling on a quantum processor (IBMQ Lima), and our results show that interferences can be used as a resource for the coherent control of photochemical reactions. The approach is general and can be employed to study a wide spectrum of chemical reactions in the ultracold regime.

Magnetic Behavior of an Iron Gluconate/Polyaniline Composite

Oxidative polymerization conducted the synthesis of polyaniline in the presence of iron gluconate in the water. Iron gluconate is present in the resulting polyaniline (PANI). The PANI composite exhibited multiple signals in electron spin resonance, including half-field resonance of multiple spin states, the center-field resonance of polarons as radical cations in conducting polymer, and a signal from a defect in the main chain. Infrared (IR) absorption spectroscopy measurements confirmed the chemical structure of the PANI composite. The composite exhibits the mixed magnetism of PANI as a conducting polymer and Fe ions in the composite according to superconducting interference device (SQUID) measurements. Combining organic-conjugated polymers and inorganic materials can result in a unique magnetism.

Quantum Mechanistic Studies of the Oxidation of Ethylene by Rhenium Oxo Complexes

Transition-metal-mediated oxygen transfer reactions are of importance in both industry and academia; thus, a series of rhenium oxo complexes of the type ReO3L (L = O−, Cl−, F−, OH−, Br−, I−) and their effects as oxidation catalysts on ethylene have been studied. The activation and reaction energies for the addition pathways involving multiple spin states (singlet and triplet) have been computed. In all cases, structures on the singlet potential energy surfaces showed higher stability compared to their counterparts on the triplet potential energy surfaces (PESs). Frontier Molecular Orbital calculations show electrons flow from the HOMO of ethylene to the LUMO of rhenium for all complexes studied except ReO4− where the reverse case occurs. In the reaction between ReO3L (L = O−, Cl−, F−, OH−, Br−, and I−) and ethylene, the concerted [3 + 2] addition pathway on the singlet PES leading to the formation of dioxylate intermediate is favored over the [2 + 2] addition pathway leading to the formation of a metallaoxetane intermediate and subsequent rearrangement to the dioxylate. The activation and the reaction energies for the formation of the dioxylate on the singlet PES for the ligands studied followed the order O− > OH− > I− > F− > Br− > Cl− and O− > OH− > F− > I− > Br− > Cl−, respectively. Furthermore, the activation and the reaction energies for the formation of the metallaoxetane intermediate increase in the order O− > OH− > I− > Br− > Cl− > F− and O− > Br− > I− > Cl− > OH− > F−, respectively. The subsequent rearrangement of the metallaoxetane intermediate to the dioxylate is only feasible in the case of ReO4−. Of all the complexes studied, the best dioxylating catalyst is ReO3Cl (singlet surface) and the best epoxidation catalyst is ReO3F (singlet surface).

Four-step spin-crossover in an oxamide-decorated metal-organic framework

Spin-crossover (SCO) complexes with multiple spin states are promising candidates for high-order magnetic storage and multiple switches. Here, by employing the N,Nʹ-4-dipyridyloxalamide (dpo) ligand, we synthesize two Hofmann-type metal-organic frameworks (MOFs) [Fe(dpo){Ag(CN)2}2]·3DMF (1) and [Fe(dpo){Ag(CN)2}2]·0.5MeCN·2DEF (2), which exhibit guest dependent four-step SCO behaviors with the sequences of LS → ∼LS2/3HS1/3 → LS1/2HS1/2 → ∼LS3/10HS7/10 → HS and LS → ∼LS2/3HS1/3 → LS1/2HS1/2 → ∼LS1/4HS3/4 → HS, respectively. Therefore, the incorporation of hydrogen-donating/hydrogen-accepting groups into the Hofmann-type MOFs may effectively explore the multi-step SCO materials by tuning hydrogen-bonding interactions.

Coexistence and Coupling of Multiple Charge Orderings and Spin States in Hexagonal Ferrite.

The coupling between charge and spin orderings in strongly correlated systems plays a crucial role in fundamental physics and device applications. As a candidate of multiferroic materials, LuFe2O4 with a nominal Fe2.5+ valence state has the potential for strong charge-spin interactions; however, these interactions have not been fully understood until now. Here, combining complementary characterization methods with theoretical calculations, two types of charge orderings with distinct magnetic properties are revealed. The ground states of LuFe2O4 are decided by the parallel/antiparallel coupling of both charge and spin orderings in the adjacent FeO double layers. Whereas the ferroelectric charge ordering remains ferrimagnetic below 230 K, the antiferroelectric ordering undergoes antiferromagnetic-ferrimagnetic-paramagnetic transitions from 2 K to room temperature. This study demonstrates the unique aspects of strong spin-charge coupling within LuFe2O4. Our results shed light on the coexistence and competing nature of orderings in quantum materials.

Magneto-Optical Stark Effect in Fe-Doped CdS Nanocrystals

Fe2+ doping in II-VI semiconductors, due to the absence of energetically accessible multiple spin state configurations, has not given rise to interesting spintronic applications. In this work, we demonstrate for the first time that the interaction of homogeneously doped Fe2+ ions with the host CdS nanocrystal with no clustering is different for the two spin states and produces two magnetically inequivalent excitonic states upon optical perturbation. We combine ultrafast transient absorption spectroscopy and density functional theoretical analysis within the ground and excited states to demonstrate the presence of the magneto-optical Stark effect (MOSE). The energy gap between the spin states arising due to MOSE does not decay within the time frame of observation, unlike optical and electrical Stark shifts. This demonstration provides a stepping-stone for spin-dependent applications.

Extending nudged elastic band method to reaction pathways involving multiple spin states.

There are diverse reactions including spin-state crossing, especially the reactions catalyzed by transition metal compounds. To figure out the mechanisms of such reactions, the discussion of minimum energy intersystem crossing (MEISC) points cannot be avoided. These points may be the bottleneck of the reaction or inversely accelerate the reactions by providing a better pathway. It is of great importance to reveal their role in the reactions by computationally locating the position of the MEISC points together with the reaction pathway. However, providing a proper initial guess for the structure of the MEISC point is not as easy as that of the transition state. In this work, we extended the nudged elastic band (NEB) method for multiple spin systems, which is named the multiple spin-state NEB method, and it is successfully applied to find the MEISC points while optimizing the reaction pathway. For more precisely locating the MEISC point, a revised approach was adopted. Meanwhile, our examples also suggest that special attention should be paid to the criterion to define an image optimized as the MEISC point.

Modular Tensor Diagram Approach for the Construction of Spin Eigenfunctions: The Case Study of Exciton Pair States.

Mapping out the high-dimensional state space would be valuable for better understanding the multistate quantum systems. Here, we demonstrate that high-dimensional spin state space can be mapped onto a tensor diagram in full dimension or self-similarly onto the reduced base state space. Based on the tensor diagram, a modular approach is proposed to construct spin eigenfunctions taking the basis of the lower-dimensional space as modules. The implementation of the approach on exciton pair states results in 16 spin eigenstates including 2 singlet states, 3 triplet states, and 1 quintet state with proper symmetry, in contrast to the ones generated using the conventional branching diagram method. The corresponding state energies obtained show the order of spin eigenstates reverses with respect to spin multiplicity. Interestingly, the state space can be decomposed into three subspaces corresponding to the singlet-singlet pair, singlet-triplet pair, and triplet-triplet pair, resulting in a modular structure that is invariant as intermolecular interactions diminish. The proposed approach offers a new perspective on the state space structure of multiple spin states, featuring a hierarchical symmetry, which could be extended to general high-dimensional quantum multistate systems.

Magnetism of (LaCoO3)n+(LaTiO3)n superlattices ( n=1,2 )

LaCoO$_3$ provides a poignant example of a transition metal oxide where the cobalt cations display multiple spin states and spin transitions and which continues to garner substantial attention. In this work, we describe first principles studies, based on DFT+$U$ theory, of superlattices containing LaCoO$_3$, specifically (LaCoO$_3$)$_n$+(LaTiO$_3$)$_n$ for $n=1,2$. The superlattices show strong electron transfer from Ti to Co resulting in Co$^{2+}$, significant structural distortions and a robust orbital polarization of Co$^{2+}$. We predict high-spin Co$^{2+}$ and a checkerboard or G-type antiferromagnetic (AFM) ground state. We provide a detailed analysis of the magnetic interactions and phases in the superlattices. We predict that ferromagnetic order on the Co${2+}$ can be stabilized by hole doping (e.g., replacing La by Sr) which is rather unusual for Co$^{2+}$ cations.