Spin Density Operator Research Articles

The impacts of spin–orbit coupling and strain on transverse dynamical spin susceptibility in undoped phosphorene: Kane–Mele model study

We present the behaviors of dynamical transverse spin susceptibilities of undoped phosphorene monolayer using the Green’s function approach in the context of Kane–Mele model Hamiltonian. Such dynamical spin susceptibility is proportional to inelastic cross section of neutron beam from the layer. Specially, the effects of magnetic field and spin–orbit coupling strength on the spin excitation modes of phosphorene monolayer are investigated via calculating correlation function of spin density operators. Our results show the increase of magnetic field leads to move the magnetic excitation energy to higher values. Also, the intensity of peaks in inelastic cross section reduces with increase of magnetic field. We also show that applying both uniaxial and biaxial strains causes to decrease the intensity of peaks in dynamical spin susceptibility. Finally the effects of both compressive and tensile strains on frequency dependence of dynamical spin structure factor of phosphorene layer are studied. Moreover, the frequency positions of spin excitation mode of phosphorene layer have been investigated due to the effects of spin orbit coupling strength in details.

The local electronic interaction and strain effects on transverse dynamical spin susceptibility of [formula omitted]-graphyne

We present the behaviors of dynamical transverse spin susceptibilities of undoped β-graphyne monolayer using the Green’s function approach in the context of Hubbard model Hamiltonian. Such dynamical spin susceptibility is proportional to inelastic cross section of neutron beam from the layer. Specially, the effects of magnetic field, on-site coulomb repulsion strength and strain parameter on the spin excitation modes of β-graphyne monolayer are investigated via calculating correlation function of transverse components of spin density operators. Our results show the increase of absolute value of compressive strain parameter leads to move the magnetic excitation modes to higher energies. Also the intensity of peaks in inelastic cross section reduces with absolute value of compressive strain parameter. We also show that applying biaxial tensile strain causes to decrease the intensity of peaks in dynamical transverse spin susceptibility. Finally the effects of magnetic field and on-site coulomb repulsion interaction strength on frequency dependence of dynamical spin structure factor of β-graphyne layer are studied. Moreover the frequency positions of spin excitation mode of β-graphyne monolayer have been investigated due to the effects of biaxial strains, applied magnetic field and Hubbard parameter strength in details.

Спинтроника немагнитных хиральных сред на примере эффекта Зеебека

Spin transport in chiral materials is considered as the main direction for the spintronics development. Experimental work on the study of the spin Seebeck effect shows that in chiral materials it is possible to achieve effective generation of spin-polarized current at distances up to several millimeters. In the presented work, we develop a theoretical approach to describe the spin Seebeck effect based on the spin Hamiltonian for conduction electrons in a chiral medium. Taking into account this Hamiltonian, the equation of electron spin dynamics averaged over the polycrystalline sample is obtained. In the approximation of ideal Fermi-gas and local-quasi-equilibrium distribution, the spin density operator of conduction electrons is constructed. It is shown that averaging over randomly oriented crystallites does not destroy spin ordering at strong spin-orbit interaction, and the temperature gradient generates spin polarization directed predominantly along the temperature gradient. Spin polarization by the described in the paper mechanism does not require external magnetic fields and remanent magnetization and therefore does not interfere with the operation of micro- and nano-sized structures of spintronics. Since the spin Seebeck effect is reciprocal with the spin Peltier effect, the theoretical approach presented in this work can form the basis of new methods for controlling heat flow in spintronics systems.

DNPSOUP: A simulation software package for dynamic nuclear polarization

Dynamic Nuclear Polarization Simulation Optimized with a Unified Propagator (DNPSOUP) is an open-source numerical software program that models spin dynamics for dynamic nuclear polarization (DNP). The software package utilizes a direct numerical approach using the inhomogeneous master equation to treat the time evolution of the spin density operator under coherent Hamiltonians and stochastic relaxation effects. Here we present the details of the theory behind the software, starting from the master equation, and arriving at characteristic operators for any section of density operator time-evolution. We then provide an overview of the DNPSOUP software architecture. The efficacy of the program is demonstrated by simulating DNP field profiles on small spin systems exploiting both continuous wave and time-domain DNP mechanisms. Examples include Zeeman field profiles for the solid effect, Overhauser effect, and cross effect, and microwave field profiles for NOVEL, off-resonance NOVEL, the integrated solid effect, the stretched solid effect, and TOP-DNP. The software should facilitate a better understanding of the DNP process, aid in the design of optimized DNP polarizing agents, and allow us to examine new pulsed DNP methods at conditions that are not currently experimentally accessible, especially at high magnetic fields with high-power microwave pulses.

Centralizer theory for long-lived spin states.

Nuclear long-lived spin states represent spin density operator configurations that are exceptionally well protected against spin relaxation phenomena. Their long-lived character is exploited in a variety of Nuclear Magnetic Resonance (NMR) techniques. Despite the growing importance of long-lived spin states in modern NMR, strategies for their identification have changed little over the last decade. The standard approach heavily relies on a chain of group theoretical arguments. In this paper, we present a more streamlined method for the calculation of such configurations. Instead of focusing on the symmetry properties of the relaxation superoperator, we focus on its corresponding relaxation algebra. This enables us to analyze long-lived spin states with Lie algebraic methods rather than group theoretical arguments. We show that the centralizer of the relaxation algebra forms a basis for the set of long-lived spin states. The characterization of the centralizer, on the other hand, does not rely on any special symmetry arguments, and its calculation is straightforward. We outline a basic algorithm and illustrate advantages by considering long-lived spin states for some spin-1/2 pairs and rapidly rotating methyl groups.

F-cluster: Reaction-induced spin correlation in multi-radical systems.

We provide a theoretical analysis of spin-selective recombination processes in clusters of n ≥ 3 radicals. Specifically, we discuss how spin correlation can ensue from random encounters of n radicals, i.e., "F-clusters" as a generalization of radical F-pairs, acting as precursors of spin-driven magnetic field effects. Survival probabilities and the spin correlation of the surviving radical population, as well as transients, are evaluated by expanding the spin density operator in an operator basis that is closed under application of the Haberkorn recombination operator and singlet-triplet dephasing. For the primary spin cluster, the steady-state density operator is found to be independent of the details of the recombination network, provided that it is irreducible; pairs of surviving radicals are triplet-polarized independent of whether they are actually reacting with each other. The steady state is independent of the singlet-triplet dephasing, but the kinetics and the population of sister clusters of smaller size can depend on the degree of dephasing. We also analyze reaction-induced singlet-triplet interconversion in radical pairs due to radical scavenging by initially uncorrelated radicals ("chemical Zeno effect"). We generalize previous treatments for radical triads by discussing the effect of spin-selective recombination in the original pair and extending the analysis to four radicals, i.e., radical pairs interacting with two radical scavengers.

RKKY interaction in spin polarized doped zigzag carbon nanotube in Holstein model

We have theoretically studied the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in zigzag gapped graphene nanotube in the presence of Holstein phonons . We investigate the effect of quantities such as the gap parameter, intensity of the electron-phonon interaction, nanotube diameter, next nearest neighbor hopping parameter, chemical potential, etc. on the spatial behavior of the RKKY interaction. Since the RKKY interaction can be obtained from the static spin susceptibility function, we first need to calculate this function. The spin susceptibility is calculated using Green's function approach via computing the correlation function of spin density operators for the Holstein model Hamiltonian. We also exploit the random phase approximation (RPA) to correct the spin susceptibility function using the self energy due to the electron-phonon interaction. The results indicate an oscillating behavior for the spatial dependence of the RKKY interaction. It is also clear that the mentioned quantities listed above affect the spatial behavior of RKKY interaction. • Using Holstein model Hamiltonian, the excitation spectrum of electrons on nanotube has been found. • To obtain RKKY interaction, the spin susceptibility has been calculated using Green's function approach in Holstein model. • We have the effects of diameter, electron-phonon coupling and electron doping on the RKKY interaction in zigzag nanotube. • Results show an oscillating behavior for spatial dependence of coupling exchange constant between two local impurities.

A Novel Approximate Numerical Method for Solving the Evolution of the Spin Density Operators

A Novel Approximate Numerical Method for Solving the Evolution of the Spin Density Operators

Anisotropic RKKY interaction in doped magnetic ordered bilayer graphene

Abstract We study exchange interaction between two magnetic impurities, i.e. (the Ruderman-Kittel-Kasuya-Yosida [RKKY]), in doped biased bilayer graphene by directly computing Green's function within full band method. Tight binding model Hamiltonian in the presence of magnetic long range ordering has been applied to describe electron dynamics. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a field induced ferromagnetic ordering along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. Such field induced ferromagnetic ordering is due to external magnetic field. The exchange interaction along arbitrary direction between two magnetic moments, has been obtained using the static spin susceptibilities of gapped graphene structure. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the chemical potential impacts the spatial behavior of RKKY interaction. Moreover bias voltage effects on RKKY interaction have been investigated for both stacking types of bilayer graphene.

Indirect RKKY interaction in doped armchair nanotube due to electron phonon interaction effects

We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in doped armchair nanotube in the presence of gap parameter. The effects of both next nearest neighbor hopping parameter and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments have been analyzed. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain the transverse static spin susceptibility of armchair graphene nanoribbon in the presence of electron-phonon coupling and gap parameter. The spin susceptibility components are calculated using Green’s function approach for Holstein model Hamiltonian. The effects of electron doping on dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of next nearest neighbor hopping parameter on the spatial behavior of RKKY interactions are different in the presence of electron phonon coupling.

Cross-polarisation ENDOR for spin-1 deuterium nuclei

Efficient transfer of spin polarisation from electron to nuclear spins is emerging as a common target of several advanced spectroscopic experiments, ranging from sensitivity enhancement in nuclear magnetic resonance (NMR) and methods for the detection of single molecules based on optically detected magnetic resonance (ODMR) to hyperfine spectroscopy. Here, we examine the feasibility of electron-nuclear cross-polarisation at a modified Hartmann-Hahn condition (called eNCP) for applications in ENDOR experiments with spin-1 deuterium nuclei, which are important targets in studies of hydrogen bonds in biological systems and materials. We have investigated a two-spin model system of deuterated malonic acid radicals in a single crystal. Energy matching conditions as well as ENDOR signal intensities were determined for a spin Hamiltonian under the effect of microwave and radiofrequency irradiation. The results were compared with numerical simulations and 94-GHz ENDOR experiments. The compelling agreement between theoretical predictions and experimental results demonstrates that spin density operator formalism in conjunction with suitable approximations in regard to spin relaxation provides a satisfactory description of the polarisation transfer effect. The results establish a basis for future numerical optimizations of polarisation transfer experiments using multiple-pulse sequences or shaped pulses and for moving from model systems to real applications in disordered systems.

RKKY interaction in doped nanotubes: A full band study

We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in doped both armchair and zigzag nanotubes. The effects of both gap parameter and electron doping on RKKY interaction have been addressed. RKKY interaction for traverse components of localized spins as a function of distance between localized moments has been analyzed. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain transverse static spin susceptibility of graphene like nanotubes in the presence of gap parameter and electron doping. The spin susceptibility components are calculated using the spin dependent Green's function approach for tight binding model Hamiltonian. The effects of tube diameter on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of electron doping on the spatial behavior of transverse RKKY interactions are different for zigzag and armchair types of nanotube.

MolSpin-Flexible and extensible general spin dynamics software.

Magnetic field effects have been measured in various processes involving radical pairs, and such magnetic field effects have provided the basis for a popular hypothesis of magnetoreception in migratory song birds. The spin dynamics of radical pairs exposed to radiofrequency radiation have also been associated with changes in the production of reactive oxygen species within a biological cell, an effect that is potentially harmful. In order to investigate such phenomena theoretically, one needs to employ complex computations which rely on solving stochastic differential equations, which may appear significantly different for slightly different problems relying on spin dynamics. To avoid creating a manifold of specialized tools for various spin chemistry problems, MolSpin has been crafted as general software to handle spin systems of varied complexity. In particular, it permits solving the Liouville-von Neumann equation to obtain the time-evolution of the spin density operator, calculate quantum yields, allows us to utilize semiclassical methods, enables calculation of energy levels in an arbitrary spin system, and predicts resonance frequencies. MolSpin is designed with a high emphasis on extensibility that makes it easy to implement new or extend existing functionality.

The effects of electron–phonon interaction on anisotropic RKKY interaction in graphene nanoribbon

We study the Ruderman–Kittle–Kasuya–Yosida (RKKY) interaction in doped armchair graphene nanoribbon. The effects of both external magnetic field and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a magnetic field along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain both transverse and longitudinal static spin susceptibilities of armchair graphene nanoribbon in the presence of electron-phonon coupling and magnetic field. The spin susceptibility components are calculated using the spin dependent Green’s function approach for Holstein model Hamiltonian. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of magnetic field on the spatial behavior of in-plane and longitudinal RKKY interactions are different in the presence of magnetic field.

Spin-selective electron transfer reactions of radical pairs: Beyond the Haberkorn master equation

Radical pair recombination reactions are normally described using a quantum mechanical master equation for the electronic and nuclear spin density operator. The electron spin state selective (singlet and triplet) recombination processes are described with a Haberkorn reaction term in this master equation. Here we consider a general spin state selective electron transfer reaction of a radical pair and use Nakajima-Zwanzig theory to derive the master equation for the spin density operator, thereby elucidating the relationship between non-adiabatic reaction rate theory and the Haberkorn reaction term. A second order perturbation theory treatment of the diabatic coupling naturally results in the Haberkorn master equation with an additional reactive scalar electron spin coupling term. This term has been neglected in previous spin chemistry calculations, but we show that it will often be quite significant. We also show that beyond the second order in perturbation theory, i.e., beyond the Fermi golden rule limit, an additional reactive singlet-triplet dephasing term appears in the master equation. A closed form expression for the reactive scalar electron spin coupling in terms of the Marcus theory parameters that determine the singlet and triplet recombination rates is presented. By performing simulations of radical pair reactions with the exact hierarchical equations of motion method, we demonstrate that our master equations provide a very accurate description of radical pairs undergoing spin-selective non-adiabatic electron transfer reactions. The existence of a reactive electron spin coupling may well have implications for biologically relevant radical pair reactions such as those which have been suggested to play a role in avian magnetoreception.

Measurement of 15N longitudinal relaxation rates in 15NH4+ spin systems to characterise rotational correlation times and chemical exchange

Many chemical and biological processes rely on the movement of monovalent cations and an understanding of such processes can therefore only be achieved by characterising the dynamics of the involved ions. It has recently been shown that 15N-ammonium can be used as a proxy for potassium to probe potassium binding in bio-molecules such as DNA quadruplexes and enzymes. Moreover, equations have been derived to describe the time-evolution of 15N-based spin density operator elements of 15NH4+ spin systems. Herein NMR pulse sequences are derived to select specific spin density matrix elements of the 15NH4+ spin system and to measure their longitudinal relaxation in order to characterise the rotational correlation time of the 15NH4+ ion as well as report on chemical exchange events of the 15NH4+ ion. Applications to 15NH4+ in acidic aqueous solutions are used to cross-validate the developed pulse sequence while measurements of spin-relaxation rates of 15NH4+ bound to a 41kDa domain of the bacterial Hsp70 homologue DnaK are presented to show the general applicability of the derived pulse sequence. The rotational correlation time obtained for 15N-ammonium bound to DnaK is similar to the correlation time that describes the rotation about the threefold axis of a methyl group. The methodology presented here provides, together with the previous theoretical framework, an important step towards characterising the motional properties of cations in macromolecular systems.

Dynamical and Static Spin Susceptibilities of Doped Gapped Graphene Nanoribbon Due to Local Electronic Interaction

We present the behaviors of both dynamical and static spin susceptibilities of doped gapped armchair graphene nanoribbon using the Green’s function approach in the context of Hubbard model Hamiltonian. Specially, the effects of spin polarization and gap parameter on the spin excitation modes of armchair graphene nanoribbon are investigated via calculating correlation function of spin density operators. Our results show the increase of electron concentration leads to disappear low frequency spin excitation mode for gapless case. We also show that low frequency excitation mode for both gapped and gapless nanoribbon disappears under spin full polarization condition. Finally, the electron density dependence of static charge structure factor of armchair graphene nanoribbon is studied. The effects of both gap parameter and magnetic ordering on the static structure factor are discussed in details.

Gauge invariant gluon spin operator for spinless nonlinear wave solutions

We consider nonlinear wave type solutions with intrinsic mass scale parameter and zero spin in a pure SU(2) quantum chromodynamics (QCD). A new stationary solution which can be treated as a system of static Wu–Yang monopole dressed in off-diagonal gluon field is proposed. A remarkable feature of such a solution is that it possesses a finite energy density everywhere. All considered nonlinear wave type solutions have common features: presence of the mass scale parameter, nonvanishing projection of the color fields along the propagation direction and zero spin. The last property requires revision of the gauge invariant definition of the spin density operator which is supposed to produce spin one states for the massless vector gluon field. We construct a gauge invariant definition of the classical gluon spin density operator which is unique and Lorentz frame independent.

Indirect exchange interaction between magnetic impurities in a gapped graphene structure

We study exchange interaction between two magnetic impurities in doped gapped graphene (the Ruderman-Kittel-Kasuya-Yosida [RKKY]) interaction by directly computing Green’s function beyond Dirac approximation. Tight binding model Hamiltonian in the presence of magnetic long range ordering has been applied to describe electron dynamics. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a magnetic ordering along the z-axis mediates two different interactions for spin directions which corresponds to a XXZ model interaction between two magnetic moments. The exchange interaction along arbitrary direction between two magnetic moments, has been obtained using the static spin susceptibilities of gapped graphene structure. The effects of spin polarization on the the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the chemical potential impacts the spatial behavior of RKKY interaction. Moreover gap parameter effects on RKKY interaction have been investigated in details.

RKKY interaction in spin polarized armchair graphene nanoribbon

We present the Ruderman–Kittle–Kasuya–Yosida (RKKY) interaction in the presence of magnetic long range ordered armchair graphene nanoribbon. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a magnetic ordering along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain the static spin susceptibilities of armchair graphene nanoribbon. The spin susceptibility components are calculated using Green's function approach for tight binding model Hamiltonian. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show that the chemical potential impacts the spatial behavior of RKKY interaction.