Spin-mixed States Research Articles

Single and double quantum transitions in spin-mixed states under photo-excitation

Electronic spins associated with the Nitrogen-Vacancy (NV) center in diamond offer an opportunity to study spin-related phenomena with extremely high sensitivity owing to their high degree of optical polarization. Here, we study both single- and double-quantum transitions (SQT and DQT) in NV centers between spin-mixed states, which arise from magnetic fields that are non-collinear to the NV axis. We demonstrate the amplification of the ESR signal from both these types of transition under laser illumination. We obtain hyperfine-resolved X-band ESR signal as a function of both excitation laser power and misalignment of static magnetic field with the NV axis. This, combined with our analysis using a seven-level model that incorporates thermal polarization and double quantum relaxation, allows us to comprehensively analyze the polarization of NV spins under off-axis fields. Such detailed understanding of spin-mixed states in NV centers under photo-excitation can help greatly in realizing NV-diamond platform’s potential in sensing correlated magnets and biological samples, as well as other emerging applications, such as masing and nuclear hyperpolarization.

Ab initio molecular dynamics study of intersystem crossing dynamics for MH2 (M = Si, Ge, Sn, Pb) on spin-pure and spin-mixed potential energy surfaces.

Recently, surface-hopping ab initio molecular dynamics (SH-AIMD) simulations have come to be used to discuss the mechanisms and dynamics of excited-state chemical reactions, including internal conversion and intersystem crossing. In dynamics simulations involving intersystem crossing, there are two potential energy surfaces (PESs) governing the motion of nuclei: PES in a spin-pure state and PES in a spin-mixed state. The former gives wrong results for molecular systems with large spin-orbit coupling (SOC), while the latter requires a potential gradient that includes a change in SOC at each point, making the computational cost very high. In this study, we systematically investigate the extent to which the magnitude of SOC affects the results of the spin-pure state-based dynamics simulations for the hydride MH2 (M = Si, Ge, Sn, Pb) by performing SH-AIMD simulations based on spin-pure and spin-mixed states. It is clearly shown that spin-mixed state PESs are indispensable for the dynamics simulation of intersystem crossing in systems containing elements Sn and Pb from the fifth period onward. Furthermore, in addition to the widely used Tully's fewest switches (TFS) algorithm, the Zhu-Nakamura (ZN) global switching algorithm, which is computationally less expensive, is applied to SH for comparison. The results from TFS- and ZN-SH-AIMD methods are in qualitative agreement, suggesting that the less expensive ZN-SH-AIMD can be successfully utilized to investigate the dynamics of photochemical reactions based on quantum chemical calculations.

Mechanistic photophysics of tellurium-substituted cytosine: Electronic structure calculations and nonadiabatic dynamics simulations.

Previously, the MS-CASPT2 method was performed to study the static and qualitative photophysics of tellurium-substituted cytosine (TeC). To get quantitative information, we used our recently developed QTMF-FSSH dynamics method to simulate the excited-state decay of TeC. The CASSCF method was adopted to reduce the calculation costs, which was confirmed to provide reliable structures and energies as those of MS-CASPT2. A detailed structural analysis showed that only 5% trajectories will hop to the lower triplet or singlet state via the twisted (S2 /S1 /T2 )T intersection, while 67% trajectories will choose the planar intersections of (S2 /S1 /T3 /T2 /T1 )P and (S2 /S1 /T2 /T1 )P but subsequently become twisted in other electronic states. By contrast, ~28% trajectories will maintain in a plane throughout dynamics. Electronic population revealed that the S2 population will ultrafast transfer to the lower triplet or singlet state. Later, the TeC system will populate in the spin-mixed electronic states composed of S1 , T1 and T2 . At the end of 300 fs, most trajectories (~74%) will decay to the ground state and only 17.4% will survive in the triplet states. Our dynamics simulation verified that tellurium substitution will enhance the intersystem crossings, but the very short triplet lifetime (ca. 125 fs) will make TeC a less effective photosensitizer.

Excited-State Dynamics during Primary C-I Homolysis in Acetyl Iodide Revealed by Ultrafast Core-Level Spectroscopy.

In typical carbonyl-containing molecules, bond dissociation events follow initial excitation to nπC═O* states. However, in acetyl iodide, the iodine atom gives rise to electronic states with mixed nπC═O* and nσC-I* character, leading to complex excited-state dynamics, ultimately resulting in dissociation. Using ultrafast extreme ultraviolet (XUV) transient absorption spectroscopy and quantum chemical calculations, we present an investigation of the primary photodissociation dynamics of acetyl iodide via time-resolved spectroscopy of core-to-valence transitions of the I atom after 266 nm excitation. The probed I 4d-to-valence transitions show features that evolve on sub-100-fs time scales, reporting on excited-state wavepacket evolution during dissociation. These features subsequently evolve to yield spectral signatures corresponding to free iodine atoms in their spin-orbit ground and excited states with a branching ratio of 1.1:1 following dissociation of the C-I bond. Calculations of the valence excitation spectrum via equation-of-motion coupled cluster with single and double substitutions (EOM-CCSD) show that initial excited states are of spin-mixed character. From the initially pumped spin-mixed state, we use a combination of time-dependent density functional theory (TDDFT)-driven nonadiabatic ab initio molecular dynamics and EOM-CCSD calculations of the N4,5 edge to reveal a sharp inflection point in the transient XUV signal that corresponds to rapid C-I homolysis. By examining the molecular orbitals involved in the core-level excitations at and around this inflection point, we are able to piece together a detailed picture of C-I bond photolysis in which d → σ* transitions give way to d → p excitations as the bond dissociates. We also report theoretical predictions of short-lived, weak 4d → 5d transitions in acetyl iodide, validated by weak bleaching in the experimental transient XUV spectra. This joint experimental-theoretical effort has thus unraveled the detailed electronic structure and dynamics of a strongly spin-orbit coupled system.

The Influence of the Substrate on the Functionality of Spin Crossover Molecular Materials.

Spin crossover complexes are a route toward designing molecular devices with a facile readout due to the change in conductance that accompanies the change in spin state. Because substrate effects are important for any molecular device, there are increased efforts to characterize the influence of the substrate on the spin state transition. Several classes of spin crossover molecules deposited on different types of surface, including metallic and non-metallic substrates, are comprehensively reviewed here. While some non-metallic substrates like graphite seem to be promising from experimental measurements, theoretical and experimental studies indicate that 2D semiconductor surfaces will have minimum interaction with spin crossover molecules. Most metallic substrates, such as Au and Cu, tend to suppress changes in spin state and affect the spin state switching process due to the interaction at the molecule-substrate interface that lock spin crossover molecules in a particular spin state or mixed spin state. Of course, the influence of the substrate on a spin crossover thin film depends on the molecular film thickness and perhaps the method used to deposit the molecular film.

Spin–Orbit Coupling Notably Retards Non-radiative Electron–Hole Recombination in Methylammonium Lead Triiodide Perovskites

The giant spin-orbit coupling (SOC) of a heavy lead element significantly extends charge carrier lifetimes of lead halide perovskites (LHPs). The physical mechanism remains unclear and requires a quantum dynamics perspective. Taking methylammonium lead iodide (MAPbI3) as a prototypical system and using non-adiabatic molecular dynamics combined with 1/2 electron correction, we show that SOC notably reduces the non-radiative electron-hole (e-h) recombination by decreasing the non-adiabatic coupling (NAC) primarily as a result of SOC decreasing the e-h wave function overlap by reshaping the electron and hole wave functions. Second, SOC causes spin mismatch subject to spin-mixed states, which further decreases NAC. The charge carrier lifetime is about 3-fold longer in the present of SOC relative to the absence of SOC. Our study generates the fundamental understanding of SOC minimizing non-radiative charge and energy losses in LHPs.

Dynamic-dependent selectivity in a bisphosphine iron spin crossover C-H insertion/π-coordination reaction.

Reaction pathway selectivity is generally controlled by competitive transition states. Organometallic reactions are complicated by the possibility that electronic spin state changes rather than transition states can control the relative rates of pathways, which can be modeled as minimum energy crossing points (MECPs). Here we show that in the reaction between bisphosphine Fe and ethylene involving spin state crossover (singlet and triplet spin states) that neither transition states nor MECPs model pathway selectivity consistent with experiment. Instead, single spin state and mixed spin state quasiclassical trajectories demonstrate nonstatistical intermediates and that C-H insertion versus π-coordination pathway selectivity is determined by the dynamic motion during reactive collisions. This example of dynamic-dependent product outcome provides a new selectivity model for organometallic reactions with spin crossover.

Jahn-Teller states mixed by spin-orbit coupling in an electromagnetic field

Spin-orbit coupling plays a pivotal role in condensed matter physics. For instance, spin-orbit interactions affect the magnetization and transport dynamics in solids, while spins and momenta are locked in topological matter. Alternatively, spin-orbit entanglement may play an important role in exotic phenomena, like quantum spin liquids in 4d and 5d systems. An interesting question is how electronic states mixed by spin orbit coupling interact with electromagnetic fields, which may hold potential to tune their properties and reveal interesting physics. Motivated by our recent discovery of large gyrotropic signals in some Jahn-Teller manganites, here we explore the interaction of light with spin-mixed states in a d4 transition metal. We show that spin-orbit mixing enables electronic transitions that are sensitive to circularly polarized light, giving rise to a gyrotropic response that increases with spin-orbit coupling. Interestingly, photoexcited transitions that involve spin reversal are behind such gyrotropic resonances. Additionally, we find that the interaction with the electromagnetic field depends strongly on the relative orientation of the propagation of light with respect to Jahn-Teller distortions and spin quantization. We suggest that such interactions offer the opportunity to use electromagnetic waves at optical wavelengths to entangle orbital and spin degrees of freedom. Our approach, which includes a group-theoretical treatment of spin-orbit coupling, has wide applicability and provides a versatile tool to explore the interaction of electromagnetic fields with electronic states in transition metals with arbitrary spin-orbit coupling strength and pointgroup symmetries.

Absence of spin-mixed states in ferrimagnet Yttrium iron garnet

The spectroscopic g-factor of epitaxial thin film Yttrium Iron Garnet (YIG) has been studied using a combination of ferromagnetic resonance spectroscopy and x-ray magnetic circular dichroism. The values obtained by the two techniques are found, within experimental error, to be in agreement using Kittel's original derivation for the g-factor. For an insulating material with an entirely Fe3+ configuration, a spin mixing correction to Kittel's derivation of the spectroscopic g-factor, as recently shown by Shaw et al. [Phys. Rev. Lett. 127, 207201 (2021)] for metallic systems, is not required and demonstrates that the spin mixing parameter is small in YIG due to negligible spin–orbit coupling.

Nonadiabatic excited-state dynamics of ReCl(CO)3(bpy) in two different solvents.

We present a study of excited-states relaxation of the complex ReCl(CO)3(bpy) (bpy = 2,2-bipyridine) using a nonadiabatic TD-DFT dynamics on spin-mixed potential energy surfaces in explicit acetonitrile (ACN) and dimethylsulfoxide (DMSO) solutions up to 800 fs. ReCl(CO)3(bpy) belongs to a group of important photosensitizers which show ultrafast biexponential subpicosecond fluorescence decay kinetics. The choice of solvents was motivated by the different excited-state relaxation dynamics observed in subpicosecond time-resolved IR (TRIR) experiments. Simulations of intersystem crossing (ISC) showed the development of spin-mixed states in both solvents. Transformation of time-dependent populations of spin-mixed states enabled to monitor the temporal evolution of individual singlet and triplet states, fitting of bi-exponential decay kinetics, and simulating the time-resolved fluorescence spectra that show only minor differences between the two solvents. Analysis of structural relaxation and solvent reorganization employing time-resolved proximal distribution functions pointed to the factors influencing the fluorescence decay time constants. Nonadiabatic dynamics simulations of time-evolution of electronic, molecular, and solvent structures emerge as a powerful technique to interpret time-resolved spectroscopic data and ultrafast photochemical reactivity.

Quantifying Spin-Mixed States in Ferromagnets.

We quantify the presence of spin-mixed states in ferromagnetic 3D transition metals by precise measurement of the orbital moment. While central to phenomena such as Elliot-Yafet scattering, quantification of the spin-mixing parameter has hitherto been confined to theoretical calculations. We demonstrate that this information is also available by experimental means. Comparison of ferromagnetic resonance spectroscopy with x-ray magnetic circular dichroism results show that Kittel's original derivation of the spectroscopic g factor requires modification, to include spin mixing of valence band states. Our results are supported by abinitio relativistic electronic structure theory.

The Role of Triplet States in the Photodissociation of a Platinum Azide Complex by a Density Matrix Renormalization Group Method.

Platinum azide complexes are appealing anticancer photochemotherapy drug candidates because they release cytotoxic azide radicals upon light irradiation. Here we present a density matrix renormalization group self-consistent field (DMRG-SCF) study of the azide photodissociation mechanism of trans,trans,trans-[Pt(N3)2(OH)2(NH3)2], including spin–orbit coupling. We find a complex interplay of singlet and triplet electronic excited states that falls into three different dissociation channels at well-separated energies. These channels can be accessed either via direct excitation into barrierless dissociative states or via intermediate doorway states from which the system undergoes non-radiative internal conversion and intersystem crossing. The high density of states, particularly of spin-mixed states, is key to aid non-radiative population transfer and enhance photodissociation along the lowest electronic excited states.

Extracting Design Principles for Efficient Thermally Activated Delayed Fluorescence (TADF) from a Simple Four-State Model

We introduce a simple quantum-mechanical model for thermally activated delayed fluorescence (TADF). The Hamiltonian is represented in the basis of four spin-mixed diabatic states representing pure ...

Kinematic spin decoherence of a wave packet in a gravitational field

The spin state of a wave packet of a spin-1/2 particle in a gravitational field is a mixed state, obtained by integrating out the momentum degree of freedom. The entropy of this spin mixed state depends on the deviation of spacetime from the flatness. In terms of a succession of local inertial frames, it is shown that spin decoherence occurs even if the particle is uniformly moving or static in a gravitational field.

Theoretical study of laser-induced ultrafast spin dynamics in small iron-benzene clusters and of related laser and magnetic-field effects

Using high-level quantum chemistry calculations, we predict various ultrafast laser-induced spin dynamics scenarios in clusters ${\mathrm{Fe}}_{m}{\mathrm{Bz}}_{n}$ ($m,n=1,2$) based on the nonadiabatic $\mathrm{\ensuremath{\Lambda}}$ process---an indirect transition channel from the initial state to the final state through the participation of several spin-mixed intermediate states. The geometry-dependent electronic structures of the four clusters are found to exhibit distinct characteristics, and prove to strongly affect the laser parameters and dynamical behavior of the spin-flip scenarios. For the two Fe-dimer clusters, a charge-transfer state involving spin-transfer scenario is achieved in ${\mathrm{Fe}}_{2}\mathrm{Bz}$, which turns to be much faster than the ordinary one obtained in ${\mathrm{Fe}}_{2}{\mathrm{Bz}}_{2}$, and thus is considered to be promising for future spintronics applications. Furthermore, to provide valuable information for the measurement and implementation of the ultrafast magnetism response, the effects of the full width at half maximum (FWHM) of the laser pulse and the magnitude of the external magnetic field on the proposed spin scenarios are investigated. The analysis of the stability and sensitivity of each scenario shows that the spin-transfer scenarios have smaller tolerance values than spin-flip scenarios with respect to the laser FWHM, and a desired spin scenario is only possible when the magnetic field strength lies in a moderate region. The latter effect enables us to obtain the lateral resolution of the device sample for its possible memory usage and to reach the complementary metal oxide semiconductor scale, beyond the optical resolution limit. All the results in this paper contribute a further step toward the experimental realization of our spin dynamics and their future nanospintronics applications.

Spin-Orbit Coupling Constants in Atoms and Ions of Transition Elements: Comparison of Effective Core Potentials, Model Core Potentials, and All-Electron Methods.

The spin-orbit coupling constants (SOCC) in atoms and ions of the first- through third-row transition elements were calculated for the low-lying atomic states whose main electron configuration is [ nd] q ( q = 1-4 and 6-9, n = the principal quantum number), using four different approaches: (1) a nonrelativistic Hamiltonian used to construct multiconfiguration self-consistent field (MCSCF) wave functions utilizing effective core potentials and their associated basis sets within the framework of second-order configuration interaction (SOCI) to calculate spin-orbit couplings (SOC) using one-electron Breit-Pauli Hamiltonian (BPH), (2) a nonrelativistic Hamiltonian used to construct MCSCF wave functions utilizing model core potentials and their associated basis sets within the framework of SOCI to calculate SOC using the full BPH, (3) nonrelativistic and spin-independent relativistic Hamiltonians used to construct MCSCF wave functions utilizing all-electron (AE) basis sets within the framework of SOCI to calculate SOC using the full BPH, and (4) a relativistic Hamiltonian given by the exact two-component (X2C) transformation for construction of Kramers-restricted relativistic configuration interaction wave functions. In this investigation, these four approaches are referred to as ECP, MCP, AE, and X2C methods, respectively. The ECP, MCP, and AE methods are so-called two-step approaches (TSA), while the X2C method is a one-step approach (OSA). In the AE method, three different calculations-relativistic elimination of small components (RESC), third-order Douglas-Kroll-Hess (DKH3), and infinite-order two-component (IOTC) relativistic correction-were performed for the estimation of the scalar relativistic components in addition to those of the nonscalar relativistic (NSR) contributions. The calculated SOCC are compared to the available experimental data via the Landé interval rule. Although there are several exceptions, including states whose main configuration is [ nd]5, the average differences between the ECP and AE (IOTC) SOCC and between the ECP and the X2C SOCC are mostly less than 20%. The differences between the ECP and the experimental SOCC are even smaller. No serious discrepancy was found between the TSA and OSA predictions of SOCC for the first- and second-row transition elements in comparison to experiment. For atoms and ions of the third-row transition elements, the SOCC calculated through the Landé interval rule are not reliable. The low-energy spin-mixed (SM) states originating from a [5d] q configuration ( q = 2-4) have a larger energy lowering due to the SOC effects, in comparison with those for atoms and ions of the first- and second-row transition elements. For the spin-mixed (SM) states originating from a [5d] q configuration ( q = 6-8), the energy lowering of all 4F7/2, 5D1, and 5D3 states due to the SOC effects is smaller than those of the other SM states. This difficulty, which also arises for the MCP, AE, and X2C (OSA) approaches, suggests that the LS-coupling scheme is inappropriate.

Ultrafast Orbital-Oriented Control of Magnetization in Half-Metallic La0.7 Sr0.3 MnO3 Films.

Manipulating spins by ultrafast pulse laser provides a new avenue to switch the magnetization for spintronic applications. While the spin-orbit coupling is known to play a pivotal role in the ultrafast laser-induced demagnetization, the effect of the anisotropic spin-orbit coupling on the transient magnetization remains an open issue. This study uncovers the role of anisotropic spin-orbit coupling in the spin dynamics in a half-metallic La0.7 Sr0.3 MnO3 film by ultrafast pump-probe technique. The magnetic order is found to be transiently enhanced or attenuated within the initial sub-picosecond when the probe light is tuned to be s- or p-polarized, respectively. The subsequent slow demagnetization amplitude follows the fourfold symmetry of the orbitals as a function of the polarization angles of the probe light. A model based on the Elliott-Yafet spin-flip scatterings is proposed to reveal that the transient magnetization enhancement is related to the spin-mixed states arising from the anisotropic spin-orbit coupling. The findings provide new insights into the spin dynamics in magnetic systems with anisotropic spin-orbit coupling as well as perspectives for the ultrafast control of information process in spintronic devices.

Physics and chemistry of graphene. Emergentness, magnetism, mechanophysics and mechanochemistry

Graphene is considered a specific object whose electronic structural features are presented in the light of the general concept of emergent phenomena that arise as a result of a quantum phase transition caused by the breaking of continuous symmetry. This review starts by examining the spin symmetry breaking of the graphene electron subsystem caused by the correlation of its odd pz-electrons that depends on the distance between these electrons and becomes noticeable when the shortest distance, determined by the C = C bond length, exceeds the critical magnitude Rcr = 1.395 Å. The symmetry breaking is reliably predicted by the unrestricted Hartree–Fock (UHF) formalism, which provides a sufficient level of quantitative self-consistent description for the problem. Empirical support has been given to and reliable certification obtained for UHF emergents such as (i) open-shell electron spin-orbitals; (ii) splitting and/or spin polarization of electron spectra; (iii) a spin-mixed ground state and, as a consequence, violation of the exact spin multiplicity of electronic states, and (iv) the existence of local spins at zero total spin density. Using this approach greatly expands our understanding of the ground state of graphene and other sp2 nanocarbons and not only gives a clear insight into the spin features of graphene chemistry, accentuating its emergent character, but also expectedly predicts the occurrence of new graphene physics-related emergents. In the latter case, symmetry breaking is relevant for both the spin system and time reversal and imposes on graphene special physical properties such as ferromagnetism, superconductivity, and topological nontriviality. This review shows, for the first time, that not only the ferromagnetism but also the mechanical properties of graphene are essentially emergent, extending this feature to the entire physics of graphene.

Geometrical and electronic structure of the molybdenum and tungsten halides MX3 and MX4 (M = Mo, W; X = F, Cl): Jahn-Teller effect and spin-orbit coupling

The ground and lower-lying excited electronic states of MX3 and MX4 (M = Mo, W; X = F, Cl) molecules were systematically studied by the complete active space self-consistent field (CASSCF) and multiconfigurational quasi-degenerate second-order perturbation (XMCQDPT2) methods. Scalar-relativistic effects and spin-orbit coupling were taken into account employing the third-order Douglas-Kroll-Hess (DKH) Hamiltonian and full Breit-Pauli operator. The ground orbital state of MoF3 and MoCl3 complexes is quadruplet 4A2′ state in the equilibrium configuration with D3h symmetry. If the spin-orbit interaction is taken into account the calculations result in two 4E1/2 and 4E3/2 spin-orbit states with 11–14 cm−1 energy differences instead of one 4A2′ state. Spin-orbit interaction quenches the Jahn-Teller effect in 2E″ ground orbital state of WF3 complex in D3h configuration, and C2v configuration with (4E1/2 + 4E3/2) spin-mixed state corresponds to the minimum on the PES. The WCl3 complex reveals strong interaction of the spin-orbit states of different multiplicity. For WCl3 complex the configuration with D3h symmetry corresponds to the minimum on the PES for four lowest spin-mixed electronic states. The MoF4, MoCl4 and WCl4 complexes possess the tetrahedral equilibrium configuration with 3A2 orbital electronic state. If the spin-orbit interaction is taken into account the ground state changes to the threefold degenerated 3T2 spin-orbit state with weak Jahn-Teller effect. In the case of WF4 complex the strong Jahn-Teller effect has been discovered in the first excited 1E singlet electronic state of the tetrahedral structure, and D2d configuration with 1A1 electronic state possesses the lowest energy. The comparison with available experimental data has been performed. The tendencies in molecular parameters of complexes studied were analyzed.

Spin–Orbit Treatment of UV–vis Absorption Spectra and Photophysics of Rhenium(I) Carbonyl–Bipyridine Complexes: MS-CASPT2 and TD-DFT Analysis

The lowest-lying spectral transitions in [ReX(CO)(3)(bpy)] (X = Cl, Br, I; bpy = 2,2'-bipyridine) complexes were calculated by means of spin-orbit time-dependent density functional theory (SO-TD-DFT) and spin-orbit multistate complete active space second-order perturbation theory (SO-MS-CASPT2). Computational results are compared with absorption spectra measured in different solvents and used to qualitatively explain the temperature dependence of the phosphorescence decay parameters that were measured for the whole series of complexes. Spin-orbit excited-state calculations interpret their electronic absorption spectra as arising from a bunch of spin mixed states with a singlet component of only 50-90% (depending on the halide), and attribute the phosphorescence decay to thermal population of spin-mixed states with a substantial singlet character.